Do you want to get some REAL numbers on embedded machine learning on Arduino, STM32, ESP32, Seeedstudio boards (and more coming)?

This page will answer all your questions!

Background

If you're new to this blog, you need to know that (almost one year ago) I settled on a mission to bring machine learning to embedded microcontrollers of all sizes (even the Attiny85!).

To me, it is just insane to deploy heavyweight Neural Networks to such small devices, if you don't need their expressiveness (mainly image and audio analysis). The vast majority of embedded ML tasks is, in fact, related to sensors' readings, which can easily be solved with "traditional" ML algorithms.

Today's industry seems to be more leaned toward Neural Networks, though, so I thought it would be beneficial for you readers to get an actual grasp on the potential of traditional Machine learning algorithms in the embedded context.

On this blog you can find posts about:

• Decision Tree, Random Forest and XGBoost
• Gaussian Naive Bayes
• SEFR - a binary classifier
• PCA for dimensionality reduction
• Relevant Vector Machines
• SVM for gesture detection
• One Class SVM for anomaly detection

All these algorithms go a long way in both accuracy and resource comsumption, so (in my opinion) they should be your first choice when developing a new project.

To support my claimings I made a huge effort to collect real world data, and now I want to share this data with you.

Before you ask:

"Are Neural Networks models benchmarked here?". No.

"Will Neural Networks model be benchmarked in the future?". Yes, as soon as I'm comfortable with them: I want to create a fair comparison between NN and traditional algorithms.

So now let's move to the contents.

The boards

I run the benchmarks on the boards I have at hand: they were all purchased by me, except for the Arduino Nano BLE Sense (given to me by the Arduino team).

• Espressif ESP32
• Espressif ESP8266 NodeMCU v1.0
• STM32 Nucleo L432KC (Cortex M4)
• Seeedstudio XIAO (SAMD21 Cortex M0)
• Arduino Nano 33 BLE Sense (Cortex M4F)

The datasets

I picked a small selection of toy and real world datasets to benchmark the classifiers against (the real world ones were picked from a TinyML Talks presentation when easily available, plus some more from the UCI database almost at random).

Here's the list of the benchmarked datasets, with the shape of the dataset (in the format number of samples x number of features x number of classes).

• Iris (150 x 4 x 3): from the sklearn package
• Wine (178 x 13 x 3): from the sklearn package
• Digits (1797 x 64 x 10): from the sklearn package
• Human Activity (10299 x 561 x 6)
• Sport Activity (4800 x 180 x 10)
• Gas Sensor Array Drift (1000 x 128 x 6)
• EMG (1648 x 63 x 5 )
• Gesture Phase Segmentaion (1000 x 19 x 5)
• Statlog (Vehicle Silhouettes) (846 x 18 x 4)
• Mammographic Mass (830 x 4 x 2)
• Sensorless Drive Diagnosis (1000 x 48 x 11)

The datasets are chosen to be representative of different domains and the list will grow in the next weeks.

Some datasets are used as-is, others were pre-processed with very light feature extraction. In detail:

• Human Activity features were extracted with a rolling window, and for each window min/max/avg/std/skew/kurtosis were calculated
• Sport Activity got the same pre-processing, and the number of actvities was reduced from 19 to 10
• EMG features were extracted with a rolling window, and for each window the Root Mean Square value was calculated

The reported benchmarks only consider the inference process: any feature extraction is not included! Nevertheless, only features with linear time complexity were used, so any MCU will have no problem in computing them.

The classifiers

The following classifiers are benchmarked:

• Decision Tree
• Random Forest
• XGBoost
• Logistic Regression
• Gaussian Naive Bayes

Why these classifiers?

Because they're all supported by the micromlgen package, so they can easily be ported to plain C.

* XGBoost porting failed on some datasets, so you will see holes in the data. I will correct this in the next weeks

micromlgen actually supports Support Vector Machines, too: it is not included because on real world datasets the number of support vector is so high (hundreds or even thousands) that no single board could handle that.

If you want to stay up to date with the new numbers, subscribe to the newsletter: I promise you won't receive more than 1 mail per month.

The Results

This section reports (a selection of) the charts generated from the benchmark results to give you a quick glance of the capabilities of the aforementioned boards and algorithms in terms of performance and accuracy.

If you like an interactive view of the data, there's a Colab Notebook that reproduces the charts reported here, where you can interact with the data as you like.

At the very end of the article, you can also find a link to the raw CSV file I generated (as you can see, it required A LOT of work to create).

Accuracy

The overall accuracy of each classifier on each dataset (this plot is not bounded to any particular board, it is computed "offline").

Comment: many classifiers (Random Forest, XGBoost, Logistic Regression) can easily achieve up to 95+ % accuracy on some datasets with minimal pre-processing, while still scoring 85+ % on more difficult datasets.

Flash percent

These charts plot, for each dataset, how much flash (in percent on the total available) it takes for the classifier to compile (visit the Colab Notebook to see all the charts).

Comment: DecisionTree, GaussianNB and Logistic Regression require the least amount of flash. XGBoost is very "flash-intensive"; RandomForest sits in the middle.

How tiny can TinyML be?

As low as 6% of flash size for a fully functional DecisionTree with 85+% accuracy.

Inference time

These charts plot, for each dataset, how long it takes for the classifier to run (only the classification, no feature extraction!).

Comment: DecisionTree is the clear winner here, with minimal inference time (from 0.4 to 30 microseconds), followed by Random Forest. Logistic Regression, XGBoost and GaussianNB are the slowest.

How fast can TinyML be?

As fast as sub-millisecond inference time for a fully functional DecisionTree with 85+% accuracy.

Inference time vs Accuracy

This plot correlates the inference time vs the classification accuracy. The more upper-left a point is, the better (fast inference time, high accuracy).

Click here to open the image at full size

Comment: as already stated, you will see a lot of blue markers (Decision Tree) in the top left, since it is very fast and quite accurate. Moving to the right you can see purple (Logistic Regression) and orange (Random Forest). GaussianNB (red) exhibits quite low accuracy instead.

Inference time vs Flash percent

This plot correlates the inference time vs the the (relative) flash requirement. The more lower-left a point is, the better (fast inference time, low flash requirements).

Click here to open the image at full size

Comment: Again, we see blue (Decision Tree) is both fast and small, followed by Logistic Regression and Random Forest. Now it is clear that XGBoost (green), while not being the slowest, is the more demanding in terms of flash.

Conclusions

I hope this post helped you broaden your view on TinyML, on how tiny it can be, how fast it can be (sub-millisecond inference!), how wide it is.

Please don't hesitate to comment with your opinion on the subject, suggestions of new boards or datasets I should benchmark, or any other idea you have in mind that can contribute to the purpose of this page.

And don't forget to stay tuned for the updates: I already have 2 more boards I will benchmark in the next days!

As promised, here's the link to the raw benchmarks in CSV format.

You can run your own analysis and visualization on it: if you use it in your own work, please add a link to this post.

In future posts I will share how I collected all those numbers, so subscribe to the newsletter to stay up to date!

L'articolo The Grand Benchmark Table of Embedded Machine Learning proviene da Eloquent Arduino Blog.

Look no further: this post explains STEP-BY-STEP all you need to know to build one yourself!

As I told you in the Easier, faster pure video Esp32-cam motion detection post, motion detection on the esp32-cam seems to be the hottest topic on my blog, so I thought it deserved some more tutorials.

Without question, to #1 request you made me in the comments was

How can I save the image that triggered the motion detection to the disk?

Well, in this post I will show you how to save the image to the SPIFFS filesystem your esp32-cam comes equipped with!

Motion detection, refactored

Please read the post on easier, faster esp32-cam motion detection first if you want to understand the following code.

It took me quite some time to write this post because I was struggling to design a clear, easy to use API for the motion detection feature and the image storage.

And I have to admit that, even after so long, I'm still not satisfied with the results.

Nonetheless, it works, and it works well in my opinion, so I will publish this and maybe get feedback from you to help me improve (so please leave a comment if you have any suggestion).

I won't bother you with the design considerations I took since this is an hands-on tutorial, so let's take a look at the code to implement motion detection on the esp32-cam or any other esp32 with a camera attached (I'm using the M5Stick camera).

First of all, you need the EloquentVision library: you can install it either from Github or using the Arduino IDE's Library Manager.

Next, the code.

// Change according to your model
// The models available are
//   - CAMERA_MODEL_WROVER_KIT
//   - CAMERA_MODEL_ESP_EYE
//   - CAMERA_MODEL_M5STACK_PSRAM
//   - CAMERA_MODEL_M5STACK_WIDE
//   - CAMERA_MODEL_AI_THINKER
#define CAMERA_MODEL_M5STACK_WIDE

#include <FS.h>
#include <SPIFFS.h>
#include "EloquentVision.h"

// set the resolution of the source image and the resolution of the downscaled image for the motion detection
#define FRAME_SIZE FRAMESIZE_QVGA
#define SOURCE_WIDTH 320
#define SOURCE_HEIGHT 240
#define CHANNELS 1
#define DEST_WIDTH 32
#define DEST_HEIGHT 24
#define BLOCK_VARIATION_THRESHOLD 0.3
#define MOTION_THRESHOLD 0.2

// we're using the Eloquent::Vision namespace a lot!
using namespace Eloquent::Vision;
using namespace Eloquent::Vision::IO;
using namespace Eloquent::Vision::ImageProcessing;
using namespace Eloquent::Vision::ImageProcessing::Downscale;
using namespace Eloquent::Vision::ImageProcessing::DownscaleStrategies;

// an easy interface to capture images from the camera
ESP32Camera camera;
// the buffer to store the downscaled version of the image
uint8_t resized[DEST_HEIGHT][DEST_WIDTH];
// the downscaler algorithm
// for more details see https://eloquentarduino.github.io/2020/05/easier-faster-pure-video-esp32-cam-motion-detection
Cross<SOURCE_WIDTH, SOURCE_HEIGHT, DEST_WIDTH, DEST_HEIGHT> crossStrategy;
// the downscaler container
Downscaler<SOURCE_WIDTH, SOURCE_HEIGHT, CHANNELS, DEST_WIDTH, DEST_HEIGHT> downscaler(&crossStrategy);
// the motion detection algorithm
MotionDetection<DEST_WIDTH, DEST_HEIGHT> motion;

void setup() {
    Serial.begin(115200);
    SPIFFS.begin(true);
    camera.begin(FRAME_SIZE, PIXFORMAT_GRAYSCALE);
    motion.setBlockVariationThreshold(BLOCK_VARIATION_THRESHOLD);
}

void loop() {
    camera_fb_t *frame = camera.capture();

    // resize image and detect motion
    downscaler.downscale(frame->buf, resized);
    motion.update(resized);
    motion.detect();

    if (motion.ratio() > MOTION_THRESHOLD) {
        Serial.println("Motion detected");

        // here we want to save the image to disk
    }
}

Save image to disk

Fine, we can detect motion!

Now we want to save the triggering image to disk in a format that we can decode without any custom software. It would be cool if we could see the image using the native Esp32 Filesystem Browser sketch.

Thankfully to the guys at espressif, the esp32 is able to encode a raw image to JPEG format: it is convenient to use (any PC on earth can read a jpeg) and it is also fast.

and thanks to the reader ankaiser for pointing it out

It's really easy to do thanks to the EloquentVision library.

if (motion.ratio() > MOTION_THRESHOLD) {
        Serial.println("Motion detected");

        // quality ranges from 10 to 64 -> the higher, the more detailed
        uint8_t quality = 30;
        JpegWriter<SOURCE_WIDTH, SOURCE_HEIGHT> jpegWriter;
        File imageFile = SPIFFS.open("/capture.jpg", "wb");

        // it takes < 1 second for a 320x240 image and 4 Kb of space
        jpegWriter.writeGrayscale(imageFile, frame->buf, quality);
        imageFile.close();
}

Well done! Now your image is on the disk and can be downloaded with the FSBrowser sketch.

Now you have all the tools you need to create your own DIY surveillance camera with motion detection feature!

You can use it to catch thieves (I discourage you to rely on such a rudimentary setup however!), to capture images of wild animals in your garden (birds, sqirrels or the like), or any other application you see fit.

Further improvements

Of course you may well understand that a proper motion detection setup should be more complex than the one presented here. Nevertheless, a couple of quick fixes can greatly improve the usability of this project with little effort. Here I suggest you a couple.

#1: Debouncing successive frames: the code presented in this post is a stripped down version of a more complete esp32-cam motion detection example sketch.

That sketch implements a debouncing function to prevent writing "ghost images" (see the original post on motion detection for a clear evidence of this effect).

#2: Proper file naming: the example sketch uses a fixed filename for the image. This means any new image will overwrite the older, which may be undesiderable based on your requirements. A proper way to handle this would be to attach an RTC and name the image after the time it occurred (something like "motion_2020-12-03_08:09:10.bmp")

#3: RGB images: this is something I'm working on. I mean, the Bitmap writer is there (so you could actually use it to store images on your esp32), but the multi-channel motion detection is driving me crazy, I need some more time to design it the way I want, so stay tuned!

I hope you enjoyed this tutorial on esp32-cam motion detection with photo capture: it was born as a response to your asking, so don't be afraid and ask me anything: I will do my best to help you!

L'articolo Esp32-cam motion detection WITH PHOTO CAPTURE! (grayscale version) proviene da Eloquent Arduino Blog.

Decision Tree

Decision Tree is without doubt one of the most well-known classification algorithms out there. It is so simple to understand that it was probably the first classifier you encountered in any Machine Learning course.

I won't go into the details of how a Decision Tree classifier trains and selects the splits for the input features: here I will explain how a RAM-efficient porting of such a classifier is implemented.

To an introduction visit Wikipedia; for a more in-depth guide visit KDNuggets.

Since we're willing to sacrifice program space (a.k.a flash) in favor of memory (a.k.a RAM), because RAM is the most scarce resource in the vast majority of microcontrollers, the smart way to port a Decision Tree classifier from Python to C is "hard-coding" the splits in code, without keeping any reference to them into variables.

Here's what it looks like for a Decision tree that classifies the Iris dataset.

As you can see, we're using 0 bytes of RAM to get the classification result, since no variable is being allocated. On the other side, the program space will grow almost linearly with the number of splits.

Since program space is often much greater than RAM on microcontrollers, this implementation exploits its abundance to be able to deploy larger models. How much large? It will depend on the flash size available: many new generations board (Arduino Nano 33 BLE Sense, ESP32, ST Nucleus...) have 1 Mb of flash, which will hold tens of thousands of splits.

Random Forest

Random Forest is just many Decision Trees joined together in a voting scheme. The core idea is that of "the wisdom of the corwd", such that if many trees vote for a given class (having being trained on different subsets of the training set), that class is probably the true class.

Towards Data Science has a more detailed guide on Random Forest and how it balances the trees with thebagging tecnique.

As easy as Decision Trees, Random Forest gets the exact same implementation with 0 bytes of RAM required (it actually needs as many bytes as the number of classes to store the votes, but that's really negligible): it just hard-codes all its composing trees.

XGBoost (Extreme Gradient Boosting)

Extreme Gradient Boosting is "Gradient Boosting on steroids" and has gained much attention from the Machine learning community due to its top results in many data competitions.

1. "gradient boosting" refers to the process of chaining a number of trees so that each tree tries to learn from the errors of the previous
2. "extreme" refers to many software and hardware optimizations that greatly reduce the time it takes to train the model

You can read the original paper about XGBoost here. For a discursive description head to KDNuggets, if you want some more math refer to this blog post on Medium.

Porting to plain C

If you followed my earlier posts on Gaussian Naive Bayes, SEFR, Relevant Vector Machine and Support Vector Machines, you already know how to port these new classifiers.

If you're new, you will need a couple things:

1. install the micromlgen package with

pip install micromlgen

2. (optionally, if you want to use Extreme Gradient Boosting) install the xgboost package with

pip install xgboost

3. use the micromlgen.port function to generate your plain C code

from micromlgen import port
from sklearn.tree import DecisionTreeClassifier
from sklearn.datasets import load_iris

clf = DecisionTreeClassifier()
X, y = load_iris(return_X_y=True)
clf.fit(X, y)
print(port(clf))

You can then copy-past the C code and import it in your sketch.

Using in the Arduino sketch

Once you have the classifier code, create a new project named TreeClassifierExample and copy the classifier code into a file named DecisionTree.h (or RandomForest.h or XGBoost.h depending on the model you chose).

The copy the following to the main ino file.

#include "DecisionTree.h"

Eloquent::ML::Port::DecisionTree clf;

void setup() {
    Serial.begin(115200);
    Serial.println("Begin");
}

void loop() {
    float irisSample[4] = {6.2, 2.8, 4.8, 1.8};

    Serial.print("Predicted label (you should see '2': ");
    Serial.println(clf.predict(irisSample));
    delay(1000);
}

Bechmarks

How do the 3 classifiers compare against each other?

We will evaluate a few keypoints:

• training time
• accuracy
• needed RAM
• needed Flash

for each classifier on a variety of datasets. I will report the results for RAM and Flash on the Arduino Nano old generation, so you should consider more the relative figures than the absolute ones.

* all datasets are taken from the UCI Machine Learning datasets archive

I'm collecting more data for a complete benchmark, but in the meantime you can see that both Random Forest and XGBoost are on par: if not that XGBoost takes 5 to 25 times longer to train.

I've never used XGBoost, so I may be missing some tuning parameters, but for now Random Forest remains my favourite classifier.

Code listings

// example IRIS dataset classification with Decision Tree
int predict(float *x) {
  if (x[3] <= 0.800000011920929) {
      return 0;
  }
  else {
      if (x[3] <= 1.75) {
          if (x[2] <= 4.950000047683716) {
              if (x[0] <= 5.049999952316284) {
                  return 1;
              }
              else {
                  return 1;
              }
          }
          else {
              return 2;
          }
      }
      else {
          if (x[2] <= 4.950000047683716) {
              return 2;
          }
          else {
              return 2;
          }
      }
  }
}

// example IRIS dataset classification with Random Forest of 3 trees

int predict(float *x) {
  uint16_t votes[3] = { 0 };

  // tree #1
  if (x[0] <= 5.450000047683716) {
      if (x[1] <= 2.950000047683716) {
          votes[1] += 1;
      }
      else {
          votes[0] += 1;
      }
  }
  else {
      if (x[0] <= 6.049999952316284) {
          if (x[3] <= 1.699999988079071) {
              if (x[2] <= 3.549999952316284) {
                  votes[0] += 1;
              }
              else {
                  votes[1] += 1;
              }
          }
          else {
              votes[2] += 1;
          }
      }
      else {
          if (x[3] <= 1.699999988079071) {
              if (x[3] <= 1.449999988079071) {
                  if (x[0] <= 6.1499998569488525) {
                      votes[1] += 1;
                  }
                  else {
                      votes[1] += 1;
                  }
              }
              else {
                  votes[1] += 1;
              }
          }
          else {
              votes[2] += 1;
          }
      }
  }

  // tree #2
  if (x[0] <= 5.549999952316284) {
      if (x[2] <= 2.449999988079071) {
          votes[0] += 1;
      }
      else {
          if (x[2] <= 3.950000047683716) {
              votes[1] += 1;
          }
          else {
              votes[1] += 1;
          }
      }
  }
  else {
      if (x[3] <= 1.699999988079071) {
          if (x[1] <= 2.649999976158142) {
              if (x[3] <= 1.25) {
                  votes[1] += 1;
              }
              else {
                  votes[1] += 1;
              }
          }
          else {
              if (x[2] <= 4.1499998569488525) {
                  votes[1] += 1;
              }
              else {
                  if (x[0] <= 6.75) {
                      votes[1] += 1;
                  }
                  else {
                      votes[1] += 1;
                  }
              }
          }
      }
      else {
          if (x[0] <= 6.0) {
              votes[2] += 1;
          }
          else {
              votes[2] += 1;
          }
      }
  }

  // tree #3
  if (x[3] <= 1.75) {
      if (x[2] <= 2.449999988079071) {
          votes[0] += 1;
      }
      else {
          if (x[2] <= 4.8500001430511475) {
              if (x[0] <= 5.299999952316284) {
                  votes[1] += 1;
              }
              else {
                  votes[1] += 1;
              }
          }
          else {
              votes[1] += 1;
          }
      }
  }
  else {
      if (x[0] <= 5.950000047683716) {
          votes[2] += 1;
      }
      else {
          votes[2] += 1;
      }
  }

  // return argmax of votes
  uint8_t classIdx = 0;
  float maxVotes = votes[0];

  for (uint8_t i = 1; i < 3; i++) {
      if (votes[i] > maxVotes) {
          classIdx = i;
          maxVotes = votes[i];
      }
  }

  return classIdx;
}

L'articolo Decision Tree, Random Forest and XGBoost on Arduino proviene da Eloquent Arduino Blog.

In this post I propose a partial, naive linear-time implementation of the Fourier Transform you can use to extract features from your data for Machine Learning models.

DISCLAIMER

The contents of this post represent my own knowledge and are not supported by any academic work (as far as I know). It may really be the case that the findings of my work don't apply to your own projects; yet, I think this idea can turn useful in solving certain kind of problems.

Training-aware FFT

Fourier transform is used to describe a signal over its entire frequency range. This is useful in a number of applications, but here we're focused on the FT for the sole purpose of extracting features to be used with Machine learning models.

For this reason, we don't actually need a full description of the input signal: we're only interested in extracting some kind of signature that a ML model can use to distinguish among the different classes. Noticing that in a signal spectrum most frequencies have a low magnitude (as you can see in the picture above), the idea to only keep the most important frequencies came to my mind as a mean to speed up the computation on resource constrained microcontrollers.

I was thinking to a kind of PCA (Principal Component Analysis), but using FFT spectrum as features.

Since we will have a training set with the raw signals, we would like to select the most prominent frequencies among all the samples and apply the computation only on those: even using the naive implementation of FFT, this will yield a linear-time implementation.

Accuracy comparison

How does this Principal FFT compare to, let's say, PCA as a dimensionality reduction algorithm w.r.t model accuracy? Let's see the numbers!

Download the Principal FFT benchmark spreadsheet

I couldn't find many examples of the kind of datasets I wished to test, but in the image you can see different types of data:

• human activity classification from smartphone data
• gesture classification by IMU data
• MNIST handwritten digits image data
• free speech audio data

We can note a couple findings:

1. Principal FFT is almost on par with PCA after a certain number of components
2. PrincipalFFT definitely leaves PCA behind on audio data

From even this simple analysis you should be convinced that Principal FFT can be (under certain cases) a fast, performant features extractor for your projects that involve time-dependant data.

How to use Principal FFT in Python

I created a Python package to use Principal FFT, called principal-fft.

pip install principal-fft

The class follows the Transformer API from scikit-learn, so it has fit and transform methods.

from principalfft import PrincipalFFT
from sklearn.model_selection import train_test_split
from sklearn.datasets import load_digits
from sklearn.ensemble import RandomForestClassifier

mnist = load_digits()
X, y = mnist.data, mnist.target
Xfft = PrincipalFFT(n_components=10).fit_transform(X)

X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.3)
Xfft_train, Xfft_test, y_train, y_test = train_test_split(Xfft, y, test_size=0.3)

clf = RandomForestClassifier(50, min_samples_leaf=5).fit(X_train, y_train)
print("Raw score", clf.score(X_test, y_test))

clf = RandomForestClassifier(50, min_samples_leaf=5).fit(Xfft_train, y_train)
print("FFT score", clf.score(Xfft_test, y_test))

My results are 0.09 for raw data and 0.78 for FFT transformed: quite a big difference!

As with any dimensionality reduction, n_components is an hyperparameter you have to tune for your specific project: from my experiments, you shouldn't go lower than 8 to achieve a reasonable accuracy.

How to use Principal FFT in C

So, now that we tested our Principal FFT transformer in Python and achieved good results, how do we use it on our microcontroller? Of course with the micromlgen porter: it is now (version 1.1.9) able to port PrincipalFFT objects to plain C.

pip install micromlgen==1.1.9

What does the C code look like?

void principalFFT(float *features, float *fft) {
    // apply principal FFT (naive implementation for the top 10 frequencies only)
    const int topFrequencies[] = { 0, 8, 17, 16, 1, 9, 2, 7, 15, 6 };

    for (int i = 0; i < 10; i++) {
        const int k = topFrequencies[i];
        const float harmonic = 0.09817477042468103 * k;
        float re = 0;
        float im = 0;

        // optimized case
        if (k == 0) {
            for (int n = 0; n < 64; n++) {
                re += features[n];
            }
        }

        else {
            for (int n = 0; n < 64; n++) {
                const float harmonic_n = harmonic * n;
                const float cos_n = cos(harmonic_n);
                const float sin_n = sin(harmonic_n);
                re += features[n] * cos_n;
                im -= features[n] * sin_n;
            }
        }

        fft[i] = sqrt(re * re + im * im);
    }
}

This is the most direct porting available.

In the Benchmarks section, we'll see how this implementation can be speed-up with alternative implementations.

Benchmarking

The following table reports the benchmark on the MNIST dataset (64 features) with 10 principal FFT components vs various tecniques to decrease the computation time at the expense of memory usage.

*all the benchmarks were run on the Arduino 33 Nano BLE Sense

Some thoughts:

2. principalFFT w/ cos+sin LUT means I pre-compute the values of sin and cos at compile time, so there's no computation on the board; of course these lookup tables will eat some memory
3. principalFFT w/ cos LUT + sin sign LUT means I pre-compute the cos values only and compute sin using sqrt(1 - cos(x)^2); it adds some microseconds to the computation, but requires less memory
4. arduinoFFT library is faster than principalFFT in the execution time and requires less memory, even if principalFFT is only computing 10 frequencies: I need to investigate how it can achieve such performances

You can activate the LUT functionality with:

from micromlgen import port
from principalfft import PrincipalFFT

fft = PrincipalFFT(n_components=10).fit(X)

# cos lookup, sin computed
port(fft, lookup_cos=True)

# cos + sin lookup
port(fft, lookup_cos=True, lookup_sin=True)

Here's how the C code looks like with LUT.

void principalFFT(float *features, float *fft) {
    // apply principal FFT (naive implementation for the top N frequencies only)
    const int topFrequencies[] = { 0, 8, 17, 16, 1, 9, 2, 7, 15, 6 };
    const float cosLUT[10][64] = {
        {  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0,  1.0},
        {  1.0,  0.7071,  6.1232e-17,  -0.7071,  -1.0,  -0.7071,  -1.8369e-16,  0.7071,  1.0,  0.7071,  3.0616e-16,  -0.7071,  -1.0,  -0.7071,  -4.2862e-16,  0.7071,  1.0,  0.7071,  5.5109e-16,  -0.7071,  -1.0,  -0.7071,  -2.4499e-15,  0.7071,  1.0,  0.7071,  -9.8033e-16,  -0.7071,  -1.0,  -0.7071,  -2.6948e-15,  0.7071,  1.0,  0.7071,  -7.3540e-16,  -0.7071,  -1.0,  -0.7071,  -2.9397e-15,  0.7071,  1.0,  0.7071,  -4.9047e-16,  -0.7071,  -1.0,  -0.7071,  -3.1847e-15,  0.7071,  1.0,  0.7071,  -2.4554e-16,  -0.7071,  -1.0,  -0.7071,  -3.4296e-15,  0.7071,  1.0,  0.7071,  -6.1898e-19,  -0.7071,  -1.0,  -0.7071,  -3.6745e-15,  0.7071},   ... };
    const bool sinLUT[10][64] = {
        {  false,  false,  false,  false,  false,  false,  false,  false,  false,  false,  false,  false,  false,  false,  false,  false,  false,  false,  false,  false,  false,  false,  false,  false,  false,  false,  false,  false,  false,  false,  false,  false,  false,  false,  false,  false,  false,  false,  false,  false,  false,  false,  false,  false,  false,  false,  false,  false,  false,  false,  false,  false,  false,  false,  false,  false,  false,  false,  false,  false,  false,  false,  false,  false},
        {  false,  true,  true,  true,  true,  false,  false,  false,  false,  true,  true,  true,  true,  false,  false,  false,  false,  true,  true,  true,  true,  false,  false,  false,  false,  true,  true,  true,  true,  false,  false,  false,  false,  true,  true,  true,  true,  false,  false,  false,  false,  true,  true,  true,  true,  false,  false,  false,  false,  true,  true,  true,  false,  false,  false,  false,  false,  true,  true,  true,  true,  false,  false,  false},  ...};

    for (int i = 0; i < 10; i++) {
        const int k = topFrequencies[i];
        const float harmonic = 0.09817477042468103 * k;
        float re = 0;
        float im = 0;
        // optimized case
        if (k == 0) {
            for (int n = 0; n < 64; n++) {
                re += features[n];
            }
        }

        else {
            for (int n = 0; n < 64; n++) {
                const float cos_n = cosLUT[i][n];
                const float sin_n = sinLUT[i][n] ? sqrt(1 - cos_n * cos_n) : -sqrt(1 - cos_n * cos_n);
                re += features[n] * cos_n;
                im -= features[n] * sin_n;
            }
        }

        fft[i] = sqrt(re * re + im * im);
    }
}

This post required much work to be produced, so I hope I didn't forgot anything and you found these information useful.
As always, there's a Github repo with all the code of this post.

L'articolo “Principal” FFT components as efficient features extrator proviene da Eloquent Arduino Blog.

from https://www.udemy.com/course/learn-audio-processing-complete-engineers-course/

Updated on 16 October 2020: step by step explanation of the process with ready-made sketch code

What you'll learn

This tutorial will teach you how to capture audio from the Arduino Nano 33 BLE Sense microphone and classify it: at the end of this post, you will have a trained model able to detect in real-time the word you tell, among the ones that you trained it to recognize. The classification will occur directly on your Arduino board.

This is not a general-purpose speech recognizer able to convert speech-to-text: it works only on the words you train it on.

What you'll need

• Hardware

  1. Arduino Nano 33 BLE Sense

• Software

  1. Python
  2. Python's module scikit-learn
  3. Python's module micromlgen

To install the software, open your terminal and install the libraries.

pip install -U scikit-learn
pip install -U micromlgen

Step 1. Capture audio samples

First of all, we need to capture a bunch of examples of the words we want to recognize.

In the original post, we used an analog microphone to record the audio. It is for sure the easiest way to interact with audio on a microcontroller since you only need to analogRead() the selected pin to get a value from the sensor.

This semplicity, however, comes at the cost of a nearly inexistent signal pre-processing from the sensor itself: most of the time, you will get junk - I don't want to be rude, but that's it.

Theory: Pulse-density modulation (a.k.a. PDM)

The microphone mounted on the Arduino Nano 33 BLE Sense (the MP34DT05) is fortunately much better than this: it gives you access to a modulated signal much more suitable for our processing needs.

The modulation used is pulse-density: I won't try to explain you how this works since I'm not an expert in DSP and neither it is the main scope of this article (refer to Wikipedia for some more information).

What matters to us is that we can grab an array of bytes from the microphone and extract its Root Mean Square (a.k.a. RMS) to be used as a feature for our Machine Learning model.

I had some difficulty finding examples on how to access the microphone on the Arduino Nano 33 BLE Sense board: fortunately, there's a Github repo from DelaGia that shows how to access all the sensors of the board.

I extracted the microphone part and incapsulated it in an easy to use class, so you don't really need to dig into the implementation details if you're not interested.

Practice: the code to capture the samples

When loaded on your Arduino Nano 33 BLE Sense, the following sketch will await for you to speak in front of the microphone: once it detects a sound, it will record 64 audio values and print them to the serial monitor.

From my experience, 64 samples are sufficient to cover short words such as yes, no, play, stop: if you plan to classify longer words, you may need to increase this number.

Download the Arduino Nano 33 BLE Sense - Capture audio samples sketch, open it the Arduino IDE and flash it to your board.

Here's the main code.

#include "Mic.h"

// tune as per your needs
#define SAMPLES 64
#define GAIN (1.0f/50)
#define SOUND_THRESHOLD 2000

float features[SAMPLES];
Mic mic;

void setup() {
    Serial.begin(115200);
    PDM.onReceive(onAudio);
    mic.begin();
    delay(3000);
}

void loop() {
    // await for a word to be pronounced
    if (recordAudioSample()) {
        // print features to serial monitor
        for (int i = 0; i < SAMPLES; i++) {
            Serial.print(features[i], 6);
            Serial.print(i == SAMPLES - 1 ? '\n' : ',');
        }

        delay(1000);
    }

    delay(20);
}

/**
 * PDM callback to update mic object
 */
void onAudio() {
    mic.update();
}

/**
 * Read given number of samples from mic
 */
bool recordAudioSample() {
    if (mic.hasData() && mic.data() > SOUND_THRESHOLD) {

        for (int i = 0; i < SAMPLES; i++) {
            while (!mic.hasData())
                delay(1);

            features[i] = mic.pop() * GAIN;
        }

        return true;
    }

    return false;
}

Now that we have the acquisition logic in place, it's time for you to record some samples of the words you want to classify.

Action: capture the words examples

Now you have to capture as many samples of the words you want to classify as possible.

Open the serial monitor and pronounce a word near the microphone: a line of numbers will be printed on the monitor.

This is the description of your word.

You need many lines like this for an accurate prediction, so keep repeating the same word 15-30 times.

After you repeated the same words many times, copy the content of the serial monitor and save it in a CSV file named after the word, for example yes.csv.

Then clear the serial monitor and repeat the process for each word.

Keep all these files in a folder because we need them to train our classifier.

Step 2. Train the machine learning model

Now that we have the samples, it's time to train the classifier.

Create a Python project in your favourite IDE or use your favourite text editor, if you don't have one.

As described in my post about how to train a classifier, we create a Python script that reads all the files inside a folder and concatenates them in a single array you feed to the classifier model.

Be sure your folder structure is like the following:

ArduinoWordClassification
  |-- train_classifier.py
  |-- data/
  |---- yes.csv
  |---- no.csv
  |---- play.csv
  |---- any other .csv file you recorded

# file: train_classifier.py

import numpy as np
from os.path import basename
from glob import glob
from sklearn.svm import SVC
from micromlgen import port
from sklearn.model_selection import train_test_split

def load_features(folder):
    dataset = None
    classmap = {}
    for class_idx, filename in enumerate(glob('%s/*.csv' % folder)):
        class_name = basename(filename)[:-4]
        classmap[class_idx] = class_name
        samples = np.loadtxt(filename, dtype=float, delimiter=',')
        labels = np.ones((len(samples), 1)) * class_idx
        samples = np.hstack((samples, labels))
        dataset = samples if dataset is None else np.vstack((dataset, samples))
    return dataset, classmap

np.random.seed(0)
dataset, classmap = load_features('data')
X, y = dataset[:, :-1], dataset[:, -1]
# this line is for testing your accuracy only: once you're satisfied with the results, set test_size to 1
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2)

clf = SVC(kernel='poly', degree=2, gamma=0.1, C=100)
clf.fit(X_train, y_train)

print('Accuracy', clf.score(X_test, y_test))
print('Exported classifier to plain C')
print(port(clf, classmap=classmap))

Among the classifiers I tried, SVM produced the best accuracy at 96% with 32 support vectors: it's not a super-tiny model, but it's quite small nevertheless.

If you're not satisifed with SVM, you can use Decision Tree, Random Forest, Gaussian Naive Bayes, Relevant Vector Machines. See my other posts for a detailed description of each.

In your console, after the accuracy score, you will have the plain C implementation of the classifier you trained. The following reports my SVM model.

// File: Classifier.h

#pragma once
namespace Eloquent {
    namespace ML {
        namespace Port {
            class SVM {
            public:
                /**
                * Predict class for features vector
                */
                int predict(float *x) {
                    float kernels[35] = { 0 };
                    float decisions[6] = { 0 };
                    int votes[4] = { 0 };
                    kernels[0] = compute_kernel(x,   33.0  , 41.0  , 47.0  , 54.0  , 59.0  , 61.0  , 56.0  , 51.0  , 50.0  , 51.0  , 44.0  , 32.0  , 23.0  , 15.0  , 12.0  , 8.0  , 5.0  , 0.0  , 0.0  , 0.0  , 0.0  , 0.0  , 0.0  , 0.0  , 5.0  , 3.0  , 5.0  , 0.0  , 0.0  , 0.0  , 0.0  , 0.0  , 0.0  , 0.0  , 0.0  , 0.0  , 0.0  , 0.0  , 0.0  , 0.0  , 0.0  , 0.0  , 0.0  , 0.0  , 0.0  , 0.0  , 0.0  , 0.0  , 0.0  , 0.0  , 0.0  , 0.0  , 0.0  , 0.0  , 0.0  , 0.0  , 0.0  , 0.0  , 0.0  , 0.0  , 0.0  , 0.0  , 0.0  , 0.0 );
                    kernels[1] = compute_kernel(x,   40.0  , 50.0  , 51.0  , 60.0  , 56.0  , 57.0  , 58.0  , 53.0  , 50.0  , 45.0  , 42.0  , 34.0  , 23.0  , 16.0  , 10.0  , 7.0  , 3.0  , 3.0  , 0.0  , 0.0  , 0.0  , 0.0  , 0.0  , 0.0  , 0.0  , 14.0  , 3.0  , 8.0  , 0.0  , 0.0  , 3.0  , 0.0  , 0.0  , 0.0  , 0.0  , 0.0  , 0.0  , 0.0  , 3.0  , 0.0  , 0.0  , 5.0  , 3.0  , 0.0  , 0.0  , 0.0  , 0.0  , 0.0  , 0.0  , 3.0  , 0.0  , 5.0  , 3.0  , 0.0  , 0.0  , 0.0  , 0.0  , 0.0  , 0.0  , 3.0  , 0.0  , 0.0  , 0.0  , 3.0 );
                    kernels[2] = compute_kernel(x,   56.0  , 68.0  , 78.0  , 91.0  , 84.0  , 84.0  , 84.0  , 74.0  , 69.0  , 64.0  , 57.0  , 44.0  , 33.0  , 18.0  , 12.0  , 8.0  , 5.0  , 9.0  , 15.0  , 12.0  , 12.0  , 9.0  , 12.0  , 7.0  , 3.0  , 10.0  , 12.0  , 6.0  , 3.0  , 0.0  , 0.0  , 0.0  , 0.0  , 6.0  , 3.0  , 6.0  , 10.0  , 10.0  , 8.0  , 3.0  , 9.0  , 9.0  , 9.0  , 8.0  , 9.0  , 9.0  , 11.0  , 3.0  , 8.0  , 9.0  , 8.0  , 8.0  , 8.0  , 6.0  , 7.0  , 3.0  , 3.0  , 8.0  , 5.0  , 3.0  , 0.0  , 3.0  , 0.0  , 0.0 );

                    // ...many other kernels computations...

                    decisions[0] = 0.722587775297
                                   + kernels[1] * 3.35855e-07
                                   + kernels[2] * 1.64612e-07
                                   + kernels[4] * 6.00056e-07
                                   + kernels[5] * 3.5195e-08
                                   + kernels[7] * -4.2079e-08
                                   + kernels[8] * -4.2843e-08
                                   + kernels[9] * -9.994e-09
                                   + kernels[10] * -5.11065e-07
                                   + kernels[11] * -5.979e-09
                                   + kernels[12] * -4.4672e-08
                                   + kernels[13] * -1.5606e-08
                                   + kernels[14] * -1.2941e-08
                                   + kernels[15] * -2.18903e-07
                                   + kernels[17] * -2.31635e-07
                            ;
                    decisions[1] = -1.658344586719
                                   + kernels[0] * 2.45018e-07
                                   + kernels[1] * 4.30223e-07
                                   + kernels[3] * 1.00277e-07
                                   + kernels[4] * 2.16524e-07
                                   + kernels[18] * -4.81187e-07
                                   + kernels[20] * -5.10856e-07
                            ;
                    decisions[2] = -1.968607562265
                                   + kernels[0] * 3.001833e-06
                                   + kernels[3] * 4.5201e-08
                                   + kernels[4] * 1.54493e-06
                                   + kernels[5] * 2.81834e-07
                                   + kernels[25] * -5.93581e-07
                                   + kernels[26] * -2.89779e-07
                                   + kernels[27] * -1.73958e-06
                                   + kernels[28] * -1.09552e-07
                                   + kernels[30] * -3.09126e-07
                                   + kernels[31] * -1.294219e-06
                                   + kernels[32] * -5.37961e-07
                            ;
                    decisions[3] = -0.720663029823
                                   + kernels[6] * 1.4362e-08
                                   + kernels[7] * 6.177e-09
                                   + kernels[9] * 1.25e-08
                                   + kernels[10] * 2.05478e-07
                                   + kernels[12] * 2.501e-08
                                   + kernels[15] * 4.363e-07
                                   + kernels[16] * 9.147e-09
                                   + kernels[18] * -1.82182e-07
                                   + kernels[20] * -4.93707e-07
                                   + kernels[21] * -3.3084e-08
                            ;
                    decisions[4] = -1.605747746589
                                   + kernels[6] * 6.182e-09
                                   + kernels[7] * 1.3853e-08
                                   + kernels[8] * 2.12e-10
                                   + kernels[9] * 1.1243e-08
                                   + kernels[10] * 7.80681e-07
                                   + kernels[15] * 8.347e-07
                                   + kernels[17] * 1.64985e-07
                                   + kernels[23] * -4.25014e-07
                                   + kernels[25] * -1.134803e-06
                                   + kernels[34] * -2.52038e-07
                            ;
                    decisions[5] = -0.934328303475
                                   + kernels[19] * 3.3529e-07
                                   + kernels[20] * 1.121946e-06
                                   + kernels[21] * 3.44683e-07
                                   + kernels[22] * -6.23056e-07
                                   + kernels[24] * -1.4612e-07
                                   + kernels[28] * -1.24025e-07
                                   + kernels[29] * -4.31701e-07
                                   + kernels[31] * -9.2146e-08
                                   + kernels[33] * -3.8487e-07
                            ;
                    votes[decisions[0] > 0 ? 0 : 1] += 1;
                    votes[decisions[1] > 0 ? 0 : 2] += 1;
                    votes[decisions[2] > 0 ? 0 : 3] += 1;
                    votes[decisions[3] > 0 ? 1 : 2] += 1;
                    votes[decisions[4] > 0 ? 1 : 3] += 1;
                    votes[decisions[5] > 0 ? 2 : 3] += 1;
                    int val = votes[0];
                    int idx = 0;

                    for (int i = 1; i < 4; i++) {
                        if (votes[i] > val) {
                            val = votes[i];
                            idx = i;
                        }
                    }

                    return idx;
                }

                /**
                * Convert class idx to readable name
                */
                const char* predictLabel(float *x) {
                    switch (predict(x)) {
                        case 0:
                            return "no";
                        case 1:
                            return "stop";
                        case 2:
                            return "play";
                        case 3:
                            return "yes";
                        default:
                            return "Houston we have a problem";
                    }
                }

            protected:
                /**
                * Compute kernel between feature vector and support vector.
                * Kernel type: poly
                */
                float compute_kernel(float *x, ...) {
                    va_list w;
                    va_start(w, 64);
                    float kernel = 0.0;

                    for (uint16_t i = 0; i < 64; i++) {
                        kernel += x[i] * va_arg(w, double);
                    }

                    return pow((0.1 * kernel) + 0.0, 2);
                }
            };
        }
    }
}

Step 3. Deploy to your microcontroller

Now we have all the pieces we need to perform word classification on our Arduino board.

Download the Arduino Nano 33 BLE Sense - Audio classification sketch, open it in the Arduino IDE and paste the plain C code you got in the console inside the Classifier.h file (delete all its contents before!).

Fine: it's time to deploy!

Hit the upload button: if everything went fine, open the serial monitor and pronounce one of the words you recorded during Step 1.

Hopefully, you will read the word on the serial monitor.

Here's a quick demo (please forgive me for the bad video quality).

If you liked this tutorial and it helped you successfully implement word classification on your Arduino Nano 33 BLE Sense, please share it on your social media so others can benefit too.

If you have troubles or questions, don't hesitate to leave a comment: I will be happy to help you.

L'articolo Better word classification with Arduino Nano 33 BLE Sense and Machine Learning proviene da Eloquent Arduino Blog.

(Gaussian) Naive Bayes

Naive Bayes classifiers are simple models based on the probability theory that can be used for classification.

They originate from the assumption of independence among the input variables. Even though this assumption doesn't hold true in the vast majority of the cases, they often perform very good at many classification tasks, so they're quite popular.

Gaussian Naive Bayes stack another (mostly wrong) assumption: that the variables exhibit a Gaussian probability distribution.

I (and many others like me) will never understand how it is possible that so many wrong assumptions lead to such good performances!

Nevertheless, what is important to us is that sklearn implements GaussianNB, so we easily train such a classifier.
The most interesting part is that GaussianNB can be tuned with just a single parameter: var_smoothing.

Don't ask me what it does in theory: in practice you change it and your accuracy can boost. This leads to an easy tuning process that doesn't involves expensive grid search.

import sklearn.datasets as d
from sklearn.model_selection import train_test_split
from sklearn.preprocessing import normalize
from sklearn.naive_bayes import GaussianNB

def pick_best(X_train, X_test, y_train, y_test):
    best = (None, 0)
    for var_smoothing in range(-7, 1):
        clf = GaussianNB(var_smoothing=pow(10, var_smoothing))
        clf.fit(X_train, y_train)
        y_pred = clf.predict(X_test)
        accuracy = (y_pred == y_test).sum()
        if accuracy > best[1]:
            best = (clf, accuracy)
    print('best accuracy', best[1] / len(y_test))
    return best[0]

iris = d.load_iris()
X = normalize(iris.data)
y = iris.target
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.3)
clf = pick_best(X_train, X_test, y_train, y_test)

This simple procedure will train a bunch of classifiers with a different var_smoothing factor and pick the best performing one.

EloquentML integration

Once you have your trained classifier, porting it to C is as easy as always:

from micromlgen import port

clf = pick_best()
print(port(clf))

Always remember to run

pip install --upgrade micromlgen

port is a magic method able to port many classifiers: it will automatically detect the proper converter for you.

What does the exported code looks like?

#pragma once
namespace Eloquent {
    namespace ML {
        namespace Port {
            class GaussianNB {
                public:
                    /**
                    * Predict class for features vector
                    */
                    int predict(float *x) {
                        float votes[3] = { 0.0f };
                        float theta[4] = { 0 };
                        float sigma[4] = { 0 };
                        theta[0] = 0.801139789889; theta[1] = 0.54726920354; theta[2] = 0.234408773313; theta[3] = 0.039178084094;
                        sigma[0] = 0.000366881742; sigma[1] = 0.000907992556; sigma[2] = 0.000740960787; sigma[3] = 0.000274925514;
                        votes[0] = 0.333333333333 - gauss(x, theta, sigma);
                        theta[0] = 0.748563871324; theta[1] = 0.349390892644; theta[2] = 0.536186138345; theta[3] = 0.166747384117;
                        sigma[0] = 0.000529727082; sigma[1] = 0.000847956504; sigma[2] = 0.000690057342; sigma[3] = 0.000311828658;
                        votes[1] = 0.333333333333 - gauss(x, theta, sigma);
                        theta[0] = 0.704497203305; theta[1] = 0.318862439835; theta[2] = 0.593755956917; theta[3] = 0.217288784452;
                        sigma[0] = 0.000363782089; sigma[1] = 0.000813846722; sigma[2] = 0.000415475678; sigma[3] = 0.000758478249;
                        votes[2] = 0.333333333333 - gauss(x, theta, sigma);
                        // return argmax of votes
                        uint8_t classIdx = 0;
                        float maxVotes = votes[0];

                        for (uint8_t i = 1; i < 3; i++) {
                            if (votes[i] > maxVotes) {
                                classIdx = i;
                                maxVotes = votes[i];
                            }
                        }

                        return classIdx;
                    }

                protected:
                    /**
                    * Compute gaussian value
                    */
                    float gauss(float *x, float *theta, float *sigma) {
                        float gauss = 0.0f;

                        for (uint16_t i = 0; i < 4; i++) {
                            gauss += log(sigma[i]);
                            gauss += pow(x[i] - theta[i], 2) / sigma[i];
                        }

                        return gauss;
                    }
                };
            }
        }
    }

As you can see, we need a couple of "weight vectors":

• theta is the mean of each feature
• sigma is the standard deviation

The computation is quite thin: just a couple of operations; the class with the highest score is then selected.

Benchmarks

Following there's a recap of a couple benchmarks I run on an Arduino Nano 33 Ble Sense.

We can see that the accuracy is on par with a linear SVM, reaching up to 97% on some datasets. Its semplicity shines with high-dimensional datasets (breast cancer) where execution time is half of the LinearSVC: I can see this pattern repeating with other real-world, medium-sized datasets.

This is it, you can find the example project on Github.

L'articolo EloquentML grows its family of classifiers: Gaussian Naive Bayes on Arduino proviene da Eloquent Arduino Blog.

A few weeks ago I was wandering over arxiv.org looking for insipiration relative to Machine learning on microcontrollers when I found exactly what I was looking for.

SEFR: A Fast Linear-Time Classifier for Ultra-Low Power Devices is a paper from Hamidreza Keshavarz, Mohammad Saniee Abadeh, Reza Rawassizadeh where the authors develop a binary classifier that is:

• fast during training
• fast during prediction
• requires minimal memory

It has been specifically designed for embedded machine learning, so no optimization is required to run in on microcontrollers: it is tiny by design. In short, it uses a combination of the averages of the features as weights plus a bias to distinguish between positive and negative class. If you read the paper you will sure understand it: it's very straightforward.

How to use

The authors both provided a C and Python implementation on Github you can read. I ported the C version "manually" to my Eloquent ML library and created a Python package called sefr copy-pasting from the original repo.

Here's a Python example.

from sefr import SEFR
from sklearn.datasets import load_iris
from sklearn.preprocessing import normalize
from sklearn.model_selection import train_test_split

if __name__ == '__main__':
    iris = load_iris()
    X = normalize(iris.data)
    y = iris.target
    X = X[y < 2]
    y = y[y < 2]
    X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.3)
    clf = SEFR()
    clf.fit(X_train, y_train)
    print('accuracy', (clf.predict(X_test) == y_test).sum() / len(y_test))

How good is it?

Considering that the model only needs 1 weight per feature, I think this results are impressive!

Micromlgen integration

The Python porting was done so I could integrate it easily in my micromlgen package.

How to use it?

from sefr import SEFR
from sklearn.datasets import load_iris
from micromlgen import port

if __name__ == '__main__':
    iris = load_iris()
    X = iris.data
    y = iris.target
    X = X[y < 2]
    y = y[y < 2]
    clf = SEFR()
    clf.fit(X_train, y_train)
    print(port(clf))

The produced code is so compact I will report it here.

#pragma once
namespace Eloquent {
    namespace ML {
        namespace Port {
            class SEFR {
                public:
                    /**
                    * Predict class for features vector
                    */
                    int predict(float *x) {
                        return dot(x,   0.084993602632  , -0.106163278477  , 0.488989863684  , 0.687022900763 ) <= 2.075 ? 0 : 1;
                    }

                protected:
                    /**
                    * Compute dot product between features vector and classifier weights
                    */
                    float dot(float *x, ...) {
                        va_list w;
                        va_start(w, 4);
                        float kernel = 0.0;

                        for (uint16_t i = 0; i < 4; i++) {
                            kernel += x[i] * va_arg(w, double);
                        }

                        return kernel;
                    }
                };
            }
        }
    }

In your sketch:

#include "IrisSEFR.h"
#include "IrisTest.h"

void setup() {
    Serial.begin(115200);
}

void loop() {
    Eloquent::ML::Port::SEFR clf;
    Eloquent::ML::Test::IrisTestSet testSet;

    testSet.test(clf);
    Serial.println(testSet.dump());
    delay(5000);
}

You have to clone the Github example to compile the code.

That's all for today, I hope you will try this classifier and find a project it fits in: I'm very impressed by the easiness of implementation yet the accuracy it can achieve on benchmark datasets.

In the next weeks I'm thinking in implementing a multi-class version of this and see how it performs, so stay tuned!

L'articolo SEFR: A Fast Linear-Time Classifier for Ultra-Low Power Devices proviene da Eloquent Arduino Blog.

If you Google "esp32 video streaming" you will get a bunch of results that are essentialy copy-pasted from the official Espressif repo: many of them neither copy-pasted the code, just tell you to load the example sketch.

And if you try to read it and try to modify just a bit for your own use-case, you won't understand much.

This is the exact environment for an Eloquent component to live: make it painfully easy what's messy.

I still have to find a good naming scheme for my libraries since Arduino IDE doesn't allow nested imports, so forgive me if "ESP32CameraHTTPVideoStreamingServer.h" was the best that came to mind.

How easy is it to use?

1 line of code if used in conjuction with my other library EloquentVision.

#define CAMERA_MODEL_M5STACK_WIDE
#include "WiFi.h"
#include "EloquentVision.h"
#include "ESP32CameraHTTPVideoStreamingServer.h"

using namespace Eloquent::Vision;
using namespace Eloquent::Vision::Camera;

ESP32Camera camera;
HTTPVideoStreamingServer server(81);

/**
 *
 */
void setup() {
    Serial.begin(115200);
    WiFi.softAP("ESP32", "12345678");

    camera.begin(FRAMESIZE_QVGA, PIXFORMAT_JPEG);
    server.start();

    Serial.print("Camera Ready! Use 'http://");
    Serial.print(WiFi.softAPIP());
    Serial.println(":81' to stream");
}

void loop() {
}

HTTPVideoStreamingServer assumes you already initialized your camera. You can achieve this task in the way you prefer: ESP32Camera class makes this a breeze.

81 in the server constructor is the port you want the server to be listening to.

Once connected to WiFi or started in AP mode, all you have to do is call start(): that's it!

What else is it good for?

The main reason I wrote this piece of library is because one of you reader commented on the motion detection post asking if it would be possible to start the video streaming once motion is detected.

Of course it is.

It's just a matter of composing the Eloquent pieces.

// not workings AS-IS, needs refactoring

#define CAMERA_MODEL_M5STACK_WIDE
#include "WiFi.h"
#include "EloquentVision.h"
#include "ESP32CameraHTTPVideoStreamingServer.h"

#define FRAME_SIZE FRAMESIZE_QVGA
#define SOURCE_WIDTH 320
#define SOURCE_HEIGHT 240
#define CHANNELS 1
#define DEST_WIDTH 32
#define DEST_HEIGHT 24
#define BLOCK_VARIATION_THRESHOLD 0.3
#define MOTION_THRESHOLD 0.2

// we're using the Eloquent::Vision namespace a lot!
using namespace Eloquent::Vision;
using namespace Eloquent::Vision::Camera;
using namespace Eloquent::Vision::ImageProcessing;
using namespace Eloquent::Vision::ImageProcessing::Downscale;
using namespace Eloquent::Vision::ImageProcessing::DownscaleStrategies;

ESP32Camera camera;
HTTPVideoStreamingServer server(81);
// the buffer to store the downscaled version of the image
uint8_t resized[DEST_HEIGHT][DEST_WIDTH];
// the downscaler algorithm
// for more details see https://eloquentarduino.github.io/2020/05/easier-faster-pure-video-esp32-cam-motion-detection
Cross<SOURCE_WIDTH, SOURCE_HEIGHT, DEST_WIDTH, DEST_HEIGHT> crossStrategy;
// the downscaler container
Downscaler<SOURCE_WIDTH, SOURCE_HEIGHT, CHANNELS, DEST_WIDTH, DEST_HEIGHT> downscaler(&crossStrategy);
// the motion detection algorithm
MotionDetection<DEST_WIDTH, DEST_HEIGHT> motion;

/**
 *
 */
void setup() {
    Serial.begin(115200);
    WiFi.softAP("ESP32", "12345678");

    camera.begin(FRAMESIZE_QVGA, PIXFORMAT_GRAYSCALE);
    motion.setBlockVariationThreshold(BLOCK_VARIATION_THRESHOLD);

    Serial.print("Camera Ready! Use 'http://");
    Serial.print(WiFi.softAPIP());
    Serial.println(":81' to stream");
}

void loop() {
    camera_fb_t *frame = camera.capture();

    // resize image and detect motion
    downscaler.downscale(frame->buf, resized);
    motion.update(resized);
    motion.detect();

    if (motion.ratio() > MOTION_THRESHOLD) {
        Serial.print("Motion detected");
        // start the streaming server when motion is detected
        // shutdown after 20 seconds if no one connects
        camera.begin(FRAMESIZE_QVGA, PIXFORMAT_JPEG);
        delay(2000);
        Serial.print("Camera Server ready! Use 'http://");
        Serial.print(WiFi.softAPIP());
        Serial.println(":81' to stream");
        server.start();
        delay(20000);
        server.stop();
        camera.begin(FRAMESIZE_QVGA, PIXFORMAT_GRAYSCALE);
        delay(2000);
    }

    // probably we don't need 30 fps, save some power
    delay(300);
}

Does it look good?

Now the rationale behind Eloquent components should be starting to be clear to you: easy to use objects you can compose the way it fits to achieve the result you want.

Would you suggest me more piece of functionality you would like to see wrapped in an Eloquent component?

You can find the class code and the example sketch on the Github repo.

L'articolo Easy ESP32 camera HTTP video streaming server proviene da Eloquent Arduino Blog.

Why dimensionality reduction on Arduino microcontrollers?

Dimensionality reduction is a tecnique you see often in Machine Learning projects. By stripping away "unimportant" or redundant information, it generally helps speeding up the training process and achieving higher classification performances.

Since we now know we can run Machine Learning on Arduino boards and embedded microcontrollers, it can become a key tool at our disposal to squeeze out the most out of our boards.

In the specific case of resource-constrained devices as old Arduino boards (the UNO for example, with only 2 kb of RAM), it can become a decisive turn in unlocking even more application scenarios where the high dimensionality of the input features would not allow any model to fit.

Let's take the Gesture classification project as an example: among the different classifiers we trained, only one fitted on the Arduino UNO, since most of them required too much flash memory due to the high dimension of features (90) and support vectors (25 to 61).

In this post I will resume that example and see if dimensionality reduction can help reduce this gap.

If you are working on a project with many features, let me know in the comments so I can create a detailed list of real world examples.

How to export PCA (Principal Component Analysis) to plain C

Among the many algorithms available for dimensionality reduction, I decided to start with PCA (Principal Component Analysis) because it's one of the most widespread. In the next weeks I will probably work on porting other alternatives.

If you never used my Python package micromlgen I first invite you to read the introduction post to get familiar with it.

Always remember to install the latest version, since I publish frequent updates.

pip install --upgrade micromlgen

Now it is pretty straight-forward to convert a sklearn PCA transformer to plain C: you use the magic method port. In addition to converting SVM/RVM classifiers, it is now able to export PCA too.

from sklearn.decomposition import PCA
from sklearn.datasets import load_iris
from micromlgen import port

if __name__ == '__main__':
    X = load_iris().data
    pca = PCA(n_components=2, whiten=False).fit(X)

    print(port(pca))

How to deploy PCA to Arduino

To use the exported code, we first have to include it in our sketch. Save the contents to a file (I named it pca.h) in the same folder of your .ino project and include it.

#include "pca.h"

// this was trained on the IRIS dataset, with 2 principal components
Eloquent::ML::Port::PCA pca;

The pca object is now able to take an array of size N as input and return an array of size K as output, with K < N usually.

void setup() {
    float x_input[4] = {5.1, 3.5, 1.4, 0.2};
    float x_output[2];

    pca.transform(x_input, x_output);
}

That's it: now you can run your classifier on x_output.

#include "pca.h"
#include "svm.h"

Eloquent::ML::Port::PCA pca;
Eloquent::ML::Port::SVM clf;

void setup() {
    float x_input[4] = {5.1, 3.5, 1.4, 0.2};
    float x_output[2];
    int y_pred;

    pca.transform(x_input, x_output);

    y_pred = clf.predict(x_output);
}

A real world example

As I anticipated, let's take a look at how PCA dimensionality reduction can help in fitting classifiers that would otherwise be too large to fit on our microcontrollers.

This is the exact table from the Gesture classification project.

The dataset has 90 features (30 samples x 3 axes) and achieves 99% accuracy.

Let's pick the poly kernel with degree 2 and see how much we can decrease the number of components while still achieving a good accuracy.

We clearly see a couple of things:

1. we still achieve 99% accuracy even with only 40 out of 90 principal components
2. we get a satisfactory 90% accuracy even with only 15 components
3. (this is a bit unexpected) it looks like there's a sweet spot at 10 components where the accuracy skyrockets to 99% again. This could be just a contingency of this particular dataset, don't expect to replicate this results on your own dataset

What do these numbers mean to you? It means your board has to do many less computations to give you a prediction and will probably be able to host a more complex model.

Let's check out the figures with n_components = 10 compared with the ones without PCA.

A couple notes:

1. accuracy increased (on stayed the same) for all kernels
2. with one exception, flash size decreased in the range 20 - 50%
3. now we can fit 3 classifiers on our Arduino UNO instead of only one

I will probably spend some more time investingating the usefulness of PCA for Arduino Machine Learning projects, but for now that's it: it's a good starting point in my opinion.

There's a little example sketch on Github that applies PCA to the IRIS dataset.

Tell me what you think may be a clever application of dimensionality reduction in the world of microcontrollers and see if we can build something great together.

L'articolo Arduino dimensionality reduction (PCA) for Machine Learning projects proviene da Eloquent Arduino Blog.

What is anomaly / novelty detection useful for?

Detect noise or anomalies

As the name implies, anomaly detection can be used to monitor a stream of data and alert you when something unexpected happens.
Think of an Industrial IoT setup where you have a bunch of sensors monitoring the working state of a production plant: you want to know as soon as possible if something bad is gonna happen.

In this case, anomaly detection tells you if your machinery is acting in a different way from the normal state so you can take action.

Ignore irrelevant data

(This application was suggested from two of my readers)
Say you're developing a super simple word classification project: you want to distinguish door bell from fire alarm (as per one of the two readers).
So you train your SVM classifier and use micromlgen to run it on your Arduino microcontroller.

It works well, but we have a problem: you live in a noisy environment with many sounds, so not all of them will either be door bells or fire alarms. Since your classifier is binary, it has to classify all of the sounds as either A or B.

The solution will be novelty detection: before running the binary SVM, you run the OneClassSVM to filter known sounds (bell and alarm) from unknown ones (eg. dog barking).
If OneClassSVM predicts the sound as a novelty, you discard it since it's of no interest for you. If it predicts the sound as known, you run the binary SVM.

How to run anomaly / novelty detection on Arduino microcontroller via OneClassSVM

Porting a OneClassSVM from Python to plain C++ is as easy as a single command in the micromlgen package:

from sklearn.svm import OneClassSVM
from micromlgen import port

clf = OneClassSVM(kernel="rbf", nu=0.5, gamma=0.1)
clf.fit(X, y)
print(port(clf))

If you read my previous posts about micromlgen and SVM the above snippet should be familiar: with the latest release, port is able to export either SVC, LinearSVC, OneClassSVC and RVC (Relevant Vector Machines) to object oriented C++.

Now you can embed the generated code in your Arduino sketch.

#include "OneClassSVM.h"

Eloquent::ML::Port::OneClassSVM clf;

void setup() {
  Serial.begin(115200);
  delay(2000);

  for (int i = 0; i < DATASET_SIZE; i++)
    clf.predict(X[i]);
}

void loop() {}

I created an example sketch from a synthetic dataset for anomaly detection (copied from a scikit-learn example) you can run to get a feel of how it performs.

Go checkout the Github repo

L'articolo Anomaly detection on your Arduino microcontroller via One Class SVM proviene da Eloquent Arduino Blog.