# Create CIFAR-10 Deep Learning Model With ANNdotNET GUI Tool

With ANNdotNET 1.2 the user is able to create and train deep learning models for image classification. Image classification module provides minimum of GUI actions in order to fully prepare data set. In this post, we are going to create and train deep learning model for CIFAR-10 data set, and see how it easy to do that with ANNdotNET v1.2.

In order to prepare data we have to download CIFAR-10 data set from official web site . The CIFAR-10 data set is provided in 6 binary batch files that should be extracted and persisted on your local machine. Number 10 in the name means that data set is created for 10 labels.The following image shows 10 labels of CIFAR-10 data set each label with few sample images.

The data set contains 60 000 (50 000 for training and validation, and 10 000 for test) tinny colored images dimensions of 32×32. There is also bigger version of the data set CIFAR-100 with 100 labels. Our task is to create deep learning model capable of recognizing only one of 10 predefined labels from each image.

## Data preparation

In order to prepare images, we need to do the following:

The following image shows extracted data set persisted in 10 label folders. The bird folder is opened and shows all images labeled for bird. The test folder contains all images created for testing the model once the model is trained.

In order to properly save all images, we need to create simple C# Console application which should extract and save all 60 000 images. Complete C# program can be downloaded from here.

In order to successfully extract the images, we have to see how those images are stored in binary files. From the official site we can see that there are 5 for training and 1 for test binary files: data_batch_1.bin, data_batch_2.bin, …, data_batch_5.bin, as well as test_batch.bin.

Each of these files is formatted as follows so that the first byte of the array is label index, and the next 3072 bytes represent the image. Each batch contains 10 000 images.

Important to know is that images are stored in CHW format which means that 1d image array is created so that the first 1024 bytes are the red channel values, the next 1024 the green, and the final 1024 the blue. The values are stored in row-major order, so the first 32 bytes are the red channel values of the first row of the image. To end this, all those information have been carried out when implementing the Extractor application. The most important methods are reshaping the 1D byte array into [3, height, width] image tensor, and creating the image from the byte tensor. The following implementation shows how 1D byte array is transformed into 3channel bitmap tensor.

static int[][][] reshape(int channel, int height, int width,  byte[] img)
{
var data = new int[channel][][];
int counter = 0;
for(int c = 0; c < channel; c++)
{
data[c] = new int[height][];
for (int y = 0; y < height; y++)
{
data[c][y] = new int[width];
for (int x = 0; x < width; x++)
{
data[c][y][x] = img[counter];
counter++;
}
}
}
return data;
}

Once the 1D byte array is transformed into tensor, the image can be created and persisted on disk. The following method iterates through all 10000 images in one batch file, extract them and persist on disk.

public static void extractandSave(byte[] batch, string destImgFolder, ref int imgCounter)
{
var nStep = 3073;//1 for label and 3072 for image
//
for (int i = 0; i < batch.Length; i += nStep)
{
var l = (int)batch[i];
var img = new ArraySegment<byte>(batch, i + 1, nStep - 1).ToArray();
// data in CIFAR-10 dataset is in CHW format, which means CHW: RR...R, GG..G, BB..B;

// while HWC: RGB, RGB, ... RGB
var reshaped = reshape(3, 32, 32, img);
var image = ArrayToImg(reshaped);
//check if folder exist
var currentFolder = destImgFolder + classNames[l];

if (!Directory.Exists(currentFolder))
Directory.CreateDirectory(currentFolder);

//save image to specified folder
image.Save(currentFolder + "\\" + imgCounter.ToString() + ".png");

imgCounter++;
}
}

Run Cifar-Extractor console application and the process of downloading, extracting and saving images will be finished in few minutes. The most important is that CIFAR-10 data set will be stored in c://sc/datasets/cifar-10 path. This is important later, when we create image classifier.

Now that we have 60000 tiny images on disk arranged by labels we can start creating deep learning model.

## Create new image classification project file in ANNdotNET

Open the latest ANNdotNET v1.2 and select New-> Image Classification project. Enter CIFAR project name and press save button. The following image shows CIFAR new ann-project:

Once we have new project, we can start defining image labels by pressing Add button. For each 10 labels we need to add new label item in the list. In each item the following fields should be defined:

• Image label
• Path to images with the label.
• Query – in case we need to get all images within the specified path with certain part of the name. In case all images withing the specified path are images that indicate one label, query should be empty string.

Beside Label item, image transformation should be defined in order to define the size of the images, as well as how many images create validation/test data set.

Assuming the CIFAR-10 data set is extracted at c:/sc/datasets/cifar-10 folder, the following image shows how label items should be defined:

In case label item should be removed from the list, this is done by selecting the item, and then pressing Remove button. Beside image properties, we should defined how many images belong to validation data set. As can be seen 20% of all extracted images will be created validation data set. Notice that images from the test folder are not part of those two data set. they will be used for testing phase once the model is trained. Now that we done with data preparation we can move to the next step: creating mlconifg file.

## Create mlconfig in ANNdotNET

By selecting New MLConfig command the new mlconfig file is created within the project explorer. Moreover by pressing F2 key on selected mlconfig tree item, we can easily change the name into “CIRAF-10-ConvNet”. The reason why we gave such name is because we are going to use convolution neural networks.

In order to define mlconfig file we need to define the following:

• Network configuration using Visual Network Designer
• Define Learning parameters
• Define training parameters

## Create Network configuration

By using Visual Network Designer (VND) we can quickly create network model. For this CIFAR-10 data set we are going to create 11 layers model with 4 Constitutional, 2 Pooling, 1 DropOut and 3 Dense layer, all followed by Scale layer:

Scale (1/255)->Conv2D(32,[3,3])->Conv2D(32,[3,3])->Pooling2d([2,2],2)->Conv2D(64,[3,3])->Conv2D(64,[3,3])->Pooling2d([2,2],2)->DropOut(0.5)->Dense(64, TanH)->Dense(32, TanH)->Dense(10,Softmax)

This network can be created so that we select appropriate layer from the VND combo box and click on Add button. The first layer is Scale layer, since we need to normalize the input values to be in interval (0,1). Then we created two sequence of Convolution, Pooling layers. Once we done with that, we can add two Dense layers with 64 and 32 neurons with TanH activation function. The last layer is output layer that must follow the output dimension, and Softmax activation function.

Once network model is defined, we can move to the next step: Setting learning and training parameters.

Learning parameters can be defined through the Learning parameters interface: For this model we can select:

• AdamLearner with 0.005 rate and 0.9 momentum value. Loss function is Classification Error, and the evaluation function is Classification Accuracy

In order to define the training parameters we switch to Training tab page and setup:

• Number of epoch
• Minibatch size
• Progress frequency
• Randomize minibatch during training

Now we have enough information to start model training. The training process is started by selecting Run command from the application ribbon. In order to get good model we need to train the model at least few thousands epoch. The following image shows trained model with training history charts.

The model is trained with exactly of 4071 epochs, with network parameters mentioned above. As can be seen from the upper chart, mini-batch loss function was CrossEntropyWithSoftmax, while the evaluation function was classification accuracy.  The bottom chart shows performance of the training and validation data sets for each 4071 epoch. We can also recognize that validation data set has roughly the same accuracy as training data set which indicates the model is trained well.  More details about model performance can be seen on the next image:

Upper charts of the image above show actual and predicted values for training (left) and validation (right). Most of the point values are blue and overlap the orange which indicates that most of value are correctly predicted. The charts can be zoomed and view details of each value.The bottom part of the evaluation show performance parameters of the model for corresponded data set. As can be seen the trained model has 0.91 overall accuracy for training data set and 0.826 overall accuracy for validation data set, which indicate pretty good accuracy of the model. Moreover, the next two images shows confusion matrix for the both data sets, which in details shows how model predict all 10 labels.

The last part of the post is testing model for test data set. For that purpose we selected 10 random images from each label of the test set, and evaluate the model. The following images shows the model correctly predicted all 10 images.

## Conclusion

ANNdotNET v1.2 image classification module offers complete data preparation and model development for image classification. The user can prepare data for training, create network model with Neural Network Designer, and perform set of statistical tools against trained model in order to validate and evaluate model. The important note is that the data set of images must be stored on specific location in order to use this trained model shown in the blog post. The trained model, as well as mlcofig files, can be load directly into ANNdotNET project explorer by doublick on CIFAR-10.zip feed example.

ANNdotNET as open source project provides outstanding way in complete development of deep learning model.

# CNTK on .NET platform – my session at ATD 14

Advanced Technology Days 14, ATD14, is a two days conference organized by the Microsoft and MS Community in Zagreb the Capital of Croatia. My session about Microsoft Cognitive Toolkit, CNTK on .NET platform held on second day, and I was very happy to talk about this, since only two months ago .NET Core support has finally implemented in the library.

There were more demos that I had time to preset them, so at the end of this blog you can find link for all demos and presentation file. Also the information about data sets need to be downloaded prior to run examples are placed in the code.
The last demo about ANNdotNET you can find on https://bhrnjica.net/anndotnet
The demos and presentation file can be found at this location: https://1drv.ms/f/s!AgPZDj-_uxGLhY1pCCODeT03qK_T3A

See you next time,

# How to visualize CNTK network in C#

When building deep learning models, it is often required to check the model for consistency and proper parameters definition. In ANNdotNET, ml network models are designed using Visual Network Designer (VND), so it is easy to see the network configuration. Beside VND, in ANNdotNET there are several visualization features on different level: network preparation, model training phase, post training evaluation, performance analysis, and export results. In this blog post we will learn how to use those features when working with deep learning models

## Visualization during network preparation and model training

When preparing network and training parameters, we need information about data sets, input format and output type. This information is relevant for selecting what type of network model to configure, what types of layers we will use, and what learner to select. For example the flowing image shows  network configuration containing of 2 embedding layers, 3 dense layers and 2 dropout layers. This network configuration is used to train CNTK model for mushroom data set. As can be seen network layers are arranged as listbox items, and the user has possibility to see, on the highest level, how neural networks looks like, which layers are included in the network, and how many dimensions each layer is defined. This is very helpful, since it provides the way of building network very quickly and accurately, and it requires much less times in comparisons to use traditional way of coding the network in python, or other programming language.

ANNdotNET Network Settings page provides pretty much information about the network, input and output layers, what data set are defined, as well as whole network configuration arranged in layers. Beside network related information, the Network Settings tab page also provides the learning parameters for the network training. More about Visual Network Designer the ready can find on one of the previous blog post.

Since ANNdotNET implements MLEngine which is based on CNTK, so all CNTK related visualization features could be used. The CNTK  library provides rich set of visualizations. For example you can use Tensorboard in CNTK  for visualization not just computational graph, but also training history, model evaluation etc. Beside Tensorboard, CNTK provides logger module which uses Graphviz tool for visualizing network graph. The bad news of this is that all above features cannot be run on C#, since those implementation are available only in python.

This is one of the main reason why ANNdotNET provides rich set of visualizations for .NET platform. This includes: training history, model evaluation for training and validation data set, as well as model performance analysis. The following image show some of the visualization features: the training history (loss and evaluation) of minibatches during training of mushroom model:

Moreover, the following image shows evaluation of training and validation set for each iteration during training:

Those graphs are generated during training phase, so the user can see what is happening with the model.  This is of tremendous help, when deciding when to stop the training process, or are training parameters produce good model at all, or this can be helpful in case when can stop and change parameters values. In case we need to stop the training process immediately, ANNdotNET provides Stop command which stops training process at any time.

## Model performance visualization

Once the model is trained, ANNdotNET provides performance analysis tool for all three types of ML problems: regression, binary and multi class classification.

Since the mushrooms project is binary ML problem the following image shows the performance of the trained model:

## Using Graphviz to visualize CNTK network graph in C#

We have seen that ANNdotNET provides all types of visualizations CNTK models, and those features are provided by mouse click through the GUI interfaces. One more feature are coming to ANNdotNET v1.1 which uses Grpahviz to visualize CNTK network graph. The feature is implemented based on original CNTK python implementation with some modification and style.

In order to use Graphviz to visualize network computation graph the following requirements must be met:

• Install Graphviz on you machine.
• Register Graphviz path as system variable. (See image below)

Now that you have install Graphviz tool, you can generate nice image of your network model directly in ANNdotNET just by click on Graph button above the Visual Network Designer (see image 1).

Here is some of nice graphs which can be generate from ANNdotNET preclaculated models.

In case you like this nice visualization features go to http://github.com/bhrnjica/anndotnet, download the latest version from release section or just download the source code and try it with Visual Studio, but don’t forget to give a star.

In the next blog post I will show you how visualization of CNTK computational graph is implemented, so you will be able to use it in your custom solutions.

# Export options in ANNdotNET

ANNdotNET v1.0 has been release a few weeks ago, and the feedback is very positive. Also up to now there is no any blocking or serious bug in the release which makes me very happy. For this blog post we are going through Export options in ANNdotNET.

The ANNdotNET supposed to be an application which can offer whole life-cycle for  machine learning project: from the defining raw data set, cleaning and features engineering, to training and evaluation of the model. Also with different mlconfig files within the same project, the user has ability to create as many ml configurations as wants. Once the user select the best ml configuration, and the training and evaluation process completes, the next step in ML project life-cycle is the model deployment/export.

Currently, ANNdotNET defines three export options:

• Export model result to CSV file,
• Export model and model result to Excel, and
• Export model in CNTK file format.

With those three export option, we can achieve many ML scenarios.

## Export to CSV

Export to CSV provides exporting actual and predicted values of testing data set to comma separated txt file. In case the testing data set is not provided, the result of validation data set will exported. In case nor testing nor validation dataset are not provided the export process is terminated.

The export process starts by selecting appropriate mlconfig file. The network model must be trained prior to be exported.

Once the export process completes, the csv file is created on disk. We can import the exported result in Excel, and similar content will be shows as image below:

Exported result is shows in two columns. The actual and predicted values. In case the classification result is exported, in the header the information about class values are exported.

## Export to Excel

Export to Excel option is more than just exporting the result. In fact, it is deployment of the model into Excel environment. Beside exporting all defined data sets (training, Validation, and Test) the model is also exported. Predicted values are calculated by using ANNdotNET Excel Add-in, which the model evaluation looks like calling ordinary Excel formula.  More information how it works can be found here.

Exported xlsx file can be opened, and the further analysis for the model and related data sets can be continued. The following image shows exported model for Concrete Slum Test example. Since only two data sets are defined (training and validation) those data sets are exported. As can be seen the predicted column is not filled, only the row is filled with the formula that must be evaluated by inserting equal sign “=” in front of the formula.

Once the formula is evaluated for the first row, we can use Excel trick to copy it on other rows.

The same situation is for other data sets separated in Excel Worksheets.

## Export to CNTK

The last option allows to export CNTK trained model in CNTK format. Also ONNX format will be supported as soon as being available on CNTK for C# library. This option is handy in situation where trained CNTK model being evaluated in other solutions.

For this blog post, there is a short video which the reader can see all three options in actions.

# Brief Introduction to ANNdotNET

ANNdotNET – is an open source project for deep learning on .NET platform (.NET Framework and .NET Core). The project is hosted at http://github.com/bhrnjica/anndotnet with more information at the https://bhrnjica.net/anndotnet.

The project comes in two versions: GUI and CMD tool. The main purpose of the project is focus on building deep learning models without to be distracted with debugging the source code and installing/updating missing packages and environments. The user should no worry which version of ML Engine the application is using. In other words, the ANNdotNET is ideal in several scenarios:

1. more focus on network development and training process using classic desktop approach, instead of focusing on coding,
2. less time spending on debugging source code, more focusing on different configuration and parameter variants,
3. ideal for engineers/users who are not familiar with supported programming languages,
4. in case the problem requires coding more advanced custom models, or training process, ANNdotNET CMD provides high level of API for such implementation,
5. all ml configurations files generated with GUI tool, can be handled with CMD tool and vice versa.

With ANNdotNET GUI Tool the user can prepare data for training, by performing several actions: data cleaning, feature selection, category encoding, missing values handling, and create training and validation dataset prior to start building deep neural network. Once the data is prepared, the user can create Machine Learning Configuration (mlconfig) file in order to start building and training deep neural network. All previous actions user can handle using GUI tool implemented in the application.

For persisting information about data preparation and transformation actions, the application uses annproject file type which consists information about raw dataset, metadata information and information about mlconfig files.

The machine learning configurations are stored in separated files with mlconfig file extension. For more information about files in ANNdotNET the reader may open this link. The following image shows how ANNdotNET handles annproject and corresponded machine learning configurations within the annproject:

As can be seen the annproject can be consisted of arbitrary number of mlconfigs, which is typical scenario when working on ML Project. User can switch between mlconfigs any time except when the application is in training or evaluation mode.

# ANNdotNET ML Engine

ANNdotNET introduces the ANNdotNET Machine Learning Engine (MLEngine) which is responsible for training and evaluation models defined in the mlconfig files.The ML Engine relies on Microsoft Cognitive Toolkit, CNTK open source library which is proved to be one of the best open source library for deep learning. Through all application ML Engine exposed all great features of the CNTK e.g. GPU support for training and evaluation, different kind of learners, but also extends CNTK features with more Evaluation functions (RMSE, MSE, Classification Accuracy, Coefficient of Determination, etc.), Extended Mini-batch Sources, Trainer and Evaluaton models.

ML Engine also contains the implementation of neural network layers which supposed to be high level CNTK API very similar as layer implementation in Keras and other python based deep learning APIs. With this implementation the ANNdotNET implements the Visual Neural Network Designer called ANNdotNET NNDesigner which allows the user to design neural network configuration of any size with any type of the layers. In the first release the following layers are implemented:

• Normalization Layer – takes the numerical features and normalizes its values before getting to the network. More information can be found here.
• Dense – classic neural network layer with activation function
• LSTM – LSTM layer with option for peephole and self-stabilization.
• Embedding – Embedding layer,
• Drop – drop layer.

More layer types will be added in the future release.

Designing the neural network can be simplify by using pre-defined layer. So on this way we can implement almost any network we usually implement through the source code.

# How to use ANNdotNET NNDesigner

Once the MLConfig is created user can open it and start building neural network. NNDesigner is placed in the Network Setting tab page. The following image shows the Network Setting tab page.

NNetwork Designer contains combo box with supported NN layers, and two action buttons for adding and removing layers in/from the network. Adding and removing layers is simple as adding and removing items in/from the list box. In order to add a layer, select the item from the combo box, and press Add button. In order to remove the layer form the network, click the layer in the listbox and press Remove button, then confirm deletion. In order to successfully create the network, the last layer in the list must be created with the same output dimension as the Output layer shown on the left side of the window, otherwise the warning messages will appear about this information once the training is stared.

Once the layer is added to the list it must be configured. The layer configuration depends of its type . The main parameter for each layer is output dimension and activation function, except the drop and normalization layer. The following text explains parameters for all supported layers:

Normalization layer – does not require any parameter. The following image shows the normalization item in the NNDesigner. You can insert only one normalization layer, and it is positioned at the first place.

Drop layer – requires percentage drop value which is integer value. The following image shows how drop layer looks in the NNDesigner. There is no any constrains for this layer.

Embedding layer – requires only output dimension to be configured. There is no any constrains for the layer. The following image shows how it looks in the NNDesigner:

Dense layer – requires output dimension and activation function to be configured. There is no any constrains for the layer.

LSTM layer – requires: output and cell dimension, activation function, and two Boolean parameters to enable peephole and self-stabilization variant in the layer. The following image shows how LSTM item looks in the NNDesigner.

The LSTM layer has some constrains which is already implemented in the code. In case two LSTM layers are added in the network, the network becomes the Stacked LSTM which should be treated differently. Also all LSTM layers are inserted as stack, and they cannot be inserted on different places in the list. The implementation of the Stacked LSTM layer will be shown later.

# Different network configurations

In this section, various network configuration will be listed, in order to show how easy is to use NNDesigner to create very complex neural network configurations. Network examples are implemented in pre-calculated examples which come with default ANNdotNET installation package.

# Feed Forward network

This example shows how to implement Feed Forward network, with one hidden and one output layer which is the last layer in the NNDesinger. The example is part of the ANNdotNET installation package.

# Feed Forward with Normalization layer

This example shows feed forward network with normalization layer as the first layer. The example of this configuration can be found in the installation package of the ANNdotNET.

# Feed Forward Network with Embedding layers

In this example embedding layers are used in order to reduce the dimensions of the input layer. Network is configured with 3 embedding layers, one hidden and output layer. The example is part of the ANNdotNET installation package.

# Deep Neural Network

This example shows deep neural network with three kind of layers: Embedding, Drop and Dense layers. The project is part of the ANNdotNET installation package.

# LSTM Deep Neural Network

This example shows how to configure LSTM based network. The network consist of normalization, embedding, drop, dense and LSTM layers. The project is part of the ANNdotNET installation package.

# Stacked LSTM Neural Network

This is example of Stacked LSTM network, consist of multiple LSTM layers connected into stack. The example is part of the installation package.

The complete list of examples can be seen at the ANNdotNET Start Page. In order to open the example, the user just need to click the link. Hope this project will be useful for many ml scenarios.

# Linear Regression with CNTK and C#

CNTK is Microsoft’s deep learning tool for training very large and complex neural network models. However, you can use CNTK for various other purposes. In some of the previous posts we have seen how to use CNTK to perform matrix multiplication, in order to calculate descriptive statistics parameters on data set.
In this blog post we are going to implement simple linear regression model, LR. The model contains only one neuron. The model also contains bias parameters, so in total the linear regression has only two parameters: w and b.
The image below shows LR model:

The reason why we use the CNTK to solve such a simple task is very straightforward. Learning on simple models like this one, we can see how the CNTK library works, and see some of not-so-trivial actions in CNTK.
The model shown above can be easily extend to logistic regression model, by adding activation function. Besides the linear regression which represent the neural network configuration without activation function, the Logistic Regression is the simplest neural network configuration which includes activation function.

The following image shows logistic regression model:
In case you want to see more info about how to create Logistic Regression with CNTK, you can see this official demo example.
Now that we made some introduction to the neural network models, we can start by defining the data set. Assume we have simple data set which represent the simple linear function $y=2x+1$. The generated data set is shown in the following table:

We already know that the linear regression parameters for presented data set are: $b_0=1$ and $b_1=2$, so we want to engage the CNTK library in order to get those values, or at least parameter values which are very close to them.

All task about how the develop LR model by using CNTK can be described in several steps:

Step 1: Create C# Console application in Visual Studio, change the current architecture to $x64$, and add the latest “CNTK.GPU “ NuGet package in the solution. The following image shows those action performed in Visual Studio.

Step 2: Start writing code by adding two variables: $X$ – feature, and label $Y$. Once the variables are defined, start with defining the training data set by creating batch. The following code snippet shows how to create variables and batch, as well as how to start writing CNTK based C# code.

First we need to add some using statements, and define the device where computation will be happen. Usually, we can defined CPU or GPU in case the machine contains NVIDIA compatible graphics card. So the demo starts with the following cod snippet:

using System;
using System.Linq;
using System.Collections.Generic;
using CNTK;
namespace LR_CNTK_Demo
{
class Program
{
static void Main(string[] args)
{
//Step 1: Create some Demo helpers
Console.Title = "Linear Regression with CNTK!";
Console.WriteLine("#### Linear Regression with CNTK! ####");
Console.WriteLine("");
//define device
var device = DeviceDescriptor.UseDefaultDevice();


Now define two variables, and data set presented in the previous table:

//Step 2: define values, and variables
Variable x = Variable.InputVariable(new int[] { 1 }, DataType.Float, "input");
Variable y = Variable.InputVariable(new int[] { 1 }, DataType.Float, "output");

//Step 2: define training data set from table above
var xValues = Value.CreateBatch(new NDShape(1, 1), new float[] { 1f, 2f, 3f, 4f, 5f }, device);
var yValues = Value.CreateBatch(new NDShape(1, 1), new float[] { 3f, 5f, 7f, 9f, 11f }, device);


Step 3: Create linear regression network model, by passing input variable and device for computation. As we already discussed, the model consists of one neuron and one bias parameter. The following method implements LR network model:

private static Function createLRModel(Variable x, DeviceDescriptor device)
{
//initializer for parameters
var initV = CNTKLib.GlorotUniformInitializer(1.0, 1, 0, 1);

//bias
var b = new Parameter(new NDShape(1,1), DataType.Float, initV, device, "b"); ;

//weights
var W = new Parameter(new NDShape(2, 1), DataType.Float, initV, device, "w");

//matrix product
var Wx = CNTKLib.Times(W, x, "wx");

//layer
var l = CNTKLib.Plus(b, Wx, "wx_b");

return l;
}


First, we create initializer, which will initialize startup values of network parameters. Then we defined bias and weight parameters, and join them in form of linear model “$wx+b$”, and returned as Function type. The createModel function is called in the main method. Once the model is created, we can exam it, and prove there are only two parameters in the model. The following code create the Linear Regression model, and print model parameters:

//Step 3: create linear regression model
var lr = createLRModel(x, device);
//Network model contains only two parameters b and w, so we query
//the model in order to get parameter values
var paramValues = lr.Inputs.Where(z => z.IsParameter).ToList();
var totalParameters = paramValues.Sum(c => c.Shape.TotalSize);
Console.WriteLine($"LRM has {totalParameters} params, {paramValues[0].Name} and {paramValues[1].Name}.");  In the previous code, we have seen how to extract parameters from the model. Once we have parameters, we can change its values, or just print those values for the further analysis. Step 4: Create Trainer, which will be used to train network parameters w and b. The following code snippet shows implementation of Trainer method. public Trainer createTrainer(Function network, Variable target) { //learning rate var lrate = 0.082; var lr = new TrainingParameterScheduleDouble(lrate); //network parameters var zParams = new ParameterVector(network.Parameters().ToList()); //create loss and eval Function loss = CNTKLib.SquaredError(network, target); Function eval = CNTKLib.SquaredError(network, target); //learners // var llr = new List(); var msgd = Learner.SGDLearner(network.Parameters(), lr); llr.Add(msgd); //trainer var trainer = Trainer.CreateTrainer(network, loss, eval, llr); // return trainer; }  First we defined learning rate the main neural network parameter. Then we create Loss and Evaluation functions. With those parameters we can create SGD learner. Once the SGD learner object is instantiated, the trainer is created by calling CreateTrainer static CNTK method, and passed it further as function return. The method createTrainer is called in the main method: //Step 4: create trainer var trainer = createTrainer(lr, y);  Step 5: Training process: Once the variables, data set, network model and trainer are defined, the training process can be started. //Ştep 5: training for (int i = 1; i <= 200; i++) { var d = new Dictionary(); d.Add(x, xValues); d.Add(y, yValues); // trainer.TrainMinibatch(d, true, device); // var loss = trainer.PreviousMinibatchLossAverage(); var eval = trainer.PreviousMinibatchEvaluationAverage(); // if (i % 20 == 0) Console.WriteLine($"It={i}, Loss={loss}, Eval={eval}");

if(i==200)
{
//print weights
var b0_name = paramValues[0].Name;
var b0 = new Value(paramValues[0].GetValue()).GetDenseData(paramValues[0]);
var b1_name = paramValues[1].Name;
var b1 = new Value(paramValues[1].GetValue()).GetDenseData(paramValues[1]);
Console.WriteLine($" "); Console.WriteLine($"Training process finished with the following regression parameters:");
Console.WriteLine($"b={b0[0][0]}, w={b1[0][0]}"); Console.WriteLine($" ");
}
}
}


As can be seen, in just 200 iterations, regression parameters got the values we almost expected $b_0=0.995$, and $w=2.005$. Since the training process is different than classic regression parameter determination, we cannot get exact values. In order to estimate regression parameters, the neural network uses iteration methods called Stochastic Gradient Decadent, SGD. On the other hand, classic regression uses regression analysis procedures by minimizing the least square error, and solve system equations where unknowns are b and w.
Once we implement all code above, we can start LR demo by pressing F5. Similar output window should be shown:

Hope this blog post can provide enough information to start with CNTK C# and Machine Learning. Source code for this blog post can be downloaded here.

# Descriptive statistics and data normalization with CNTK and C#

As you probably know CNTK is Microsoft Cognitive Toolkit for deep learning. It is open source library which is used by various Microsoft products. Also the CNTK is powerful library for developing custom ML solutions from various fields with different platforms and languages. What is also so powerful in the CNTK is the way of the implementation. In fact the library is implemented as series of computation graphs, which  is fully elaborated into the sequence of steps performed in a deep neural network training.

Each CNTK compute graph is created with set of nodes where each node represents numerical (mathematical) operation. The edges between nodes in the graph represent data flow between operations. Such a representation allows CNTK to schedule computation on the underlying hardware GPU or CPU. The CNTK can dynamically analyze the graphs in order to to optimize both latency and efficient use of resources. The most powerful part of this is the fact thet the CNTK can calculate derivation of any constructed set of operations, which can be used for efficient learning  process of the network parameters. The flowing image shows the core architecture of the CNTK.

On the other hand, any operation can be executed on CPU or GPU with minimal code changes. In fact we can implement method which can automatically takes GPU computation if available. The CNTK is the first .NET library which provide .NET developers to develop GPU aware .NET applications.

What this exactly mean is that with this powerful library you can develop complex math computation directly to GPU in .NET using C#, which currently is not possible when using standard .NET library.

For this blog post I will show how to calculate some of basic statistics operations on data set.

Say we have data set with 4 columns (features) and 20 rows (samples). The C# implementation of this 2D array is show on the following code snippet:

static float[][] mData = new float[][] {
new float[] { 5.1f, 3.5f, 1.4f, 0.2f},
new float[] { 4.9f, 3.0f, 1.4f, 0.2f},
new float[] { 4.7f, 3.2f, 1.3f, 0.2f},
new float[] { 4.6f, 3.1f, 1.5f, 0.2f},
new float[] { 6.9f, 3.1f, 4.9f, 1.5f},
new float[] { 5.5f, 2.3f, 4.0f, 1.3f},
new float[] { 6.5f, 2.8f, 4.6f, 1.5f},
new float[] { 5.0f, 3.4f, 1.5f, 0.2f},
new float[] { 4.4f, 2.9f, 1.4f, 0.2f},
new float[] { 4.9f, 3.1f, 1.5f, 0.1f},
new float[] { 5.4f, 3.7f, 1.5f, 0.2f},
new float[] { 4.8f, 3.4f, 1.6f, 0.2f},
new float[] { 4.8f, 3.0f, 1.4f, 0.1f},
new float[] { 4.3f, 3.0f, 1.1f, 0.1f},
new float[] { 6.5f, 3.0f, 5.8f, 2.2f},
new float[] { 7.6f, 3.0f, 6.6f, 2.1f},
new float[] { 4.9f, 2.5f, 4.5f, 1.7f},
new float[] { 7.3f, 2.9f, 6.3f, 1.8f},
new float[] { 5.7f, 3.8f, 1.7f, 0.3f},
new float[] { 5.1f, 3.8f, 1.5f, 0.3f},};


If you want to play with CNTK and math calculation you need some knowledge from Calculus, as well as vectors, matrix and tensors. Also in CNTK any operation is performed as matrix operation, which may simplify the calculation process for you. In standard way, you have to deal with multidimensional arrays during calculations. As my knowledge currently there is no .NET library which can perform math operation on GPU, which constrains the .NET platform for implementation of high performance applications.

If we want to compute average value, and standard deviation for each column, we can do that with CNTK very easy way. Once we compute those values we can used them for normalizing the data set by computing standard score (Gauss Standardization).

The Gauss standardization is calculated by the flowing term:

$nValue= \frac{X-\nu}{\sigma}$,
where X- is column values, $\nu$ – column mean, and $\sigma$– standard deviation of the column.

For this example we are going to perform three statistic operations,and the CNTK automatically provides us with ability to compute those values on GPU. This is very important in case you have data set with millions of rows, and computation can be performed in few milliseconds.

Any computation process in CNTK can be achieved in several steps:

1. Read data from external source or in-memory data,
2. Define Value and Variable objects.
3. Define Function for the calculation
4. Perform Evaluation of the function by passing the Variable and Value objects
5. Retrieve the result of the calculation and show the result.

All above steps are implemented in the following implementation:

using System;
using System.Collections.Generic;
using System.Diagnostics;
using System.Linq;
using System.Text;
using CNTK;
namespace DataNormalizationWithCNTK
{
class Program
{
static float[][] mData = new float[][] {
new float[] { 5.1f, 3.5f, 1.4f, 0.2f},
new float[] { 4.9f, 3.0f, 1.4f, 0.2f},
new float[] { 4.7f, 3.2f, 1.3f, 0.2f},
new float[] { 4.6f, 3.1f, 1.5f, 0.2f},
new float[] { 6.9f, 3.1f, 4.9f, 1.5f},
new float[] { 5.5f, 2.3f, 4.0f, 1.3f},
new float[] { 6.5f, 2.8f, 4.6f, 1.5f},
new float[] { 5.0f, 3.4f, 1.5f, 0.2f},
new float[] { 4.4f, 2.9f, 1.4f, 0.2f},
new float[] { 4.9f, 3.1f, 1.5f, 0.1f},
new float[] { 5.4f, 3.7f, 1.5f, 0.2f},
new float[] { 4.8f, 3.4f, 1.6f, 0.2f},
new float[] { 4.8f, 3.0f, 1.4f, 0.1f},
new float[] { 4.3f, 3.0f, 1.1f, 0.1f},
new float[] { 6.5f, 3.0f, 5.8f, 2.2f},
new float[] { 7.6f, 3.0f, 6.6f, 2.1f},
new float[] { 4.9f, 2.5f, 4.5f, 1.7f},
new float[] { 7.3f, 2.9f, 6.3f, 1.8f},
new float[] { 5.7f, 3.8f, 1.7f, 0.3f},
new float[] { 5.1f, 3.8f, 1.5f, 0.3f},};
static void Main(string[] args)
{
//define device where the calculation will executes
var device = DeviceDescriptor.UseDefaultDevice();

//print data to console
Console.WriteLine($"X1,\tX2,\tX3,\tX4"); Console.WriteLine($"-----,\t-----,\t-----,\t-----");
foreach (var row in mData)
{
Console.WriteLine($"{row[0]},\t{row[1]},\t{row[2]},\t{row[3]}"); } Console.WriteLine($"-----,\t-----,\t-----,\t-----");

//convert data into enumerable list
var data = mData.ToEnumerable<IEnumerable<float>>();

//assign the values
var vData = Value.CreateBatchOfSequences<float>(new int[] {4},data, device);
//create variable to describe the data
var features = Variable.InputVariable(vData.Shape, DataType.Float);

//define mean function for the variable
var mean =  CNTKLib.ReduceMean(features, new Axis(2));//Axis(2)- means calculate mean along the third axes which represent 4 features

//map variables and data
var inputDataMap = new Dictionary<Variable, Value>() { { features, vData } };
var meanDataMap = new Dictionary<Variable, Value>() { { mean, null } };

//mean calculation
mean.Evaluate(inputDataMap,meanDataMap,device);
//get result
var meanValues = meanDataMap[mean].GetDenseData<float>(mean);

Console.WriteLine($""); Console.WriteLine($"Average values for each features x1={meanValues[0][0]},x2={meanValues[0][1]},x3={meanValues[0][2]},x4={meanValues[0][3]}");

//Calculation of standard deviation
var std = calculateStd(features);
var stdDataMap = new Dictionary<Variable, Value>() { { std, null } };
//mean calculation
std.Evaluate(inputDataMap, stdDataMap, device);
//get result
var stdValues = stdDataMap[std].GetDenseData<float>(std);

Console.WriteLine($""); Console.WriteLine($"STD of features x1={stdValues[0][0]},x2={stdValues[0][1]},x3={stdValues[0][2]},x4={stdValues[0][3]}");

//Once we have mean and std we can calculate Standardized values for the data
var gaussNormalization = CNTKLib.ElementDivide(CNTKLib.Minus(features, mean), std);
var gaussDataMap = new Dictionary<Variable, Value>() { { gaussNormalization, null } };
//mean calculation
gaussNormalization.Evaluate(inputDataMap, gaussDataMap, device);

//get result
var normValues = gaussDataMap[gaussNormalization].GetDenseData<float>(gaussNormalization);
//print data to console
Console.WriteLine($"-------------------------------------------"); Console.WriteLine($"Normalized values for the above data set");
Console.WriteLine($""); Console.WriteLine($"X1,\tX2,\tX3,\tX4");
Console.WriteLine($"-----,\t-----,\t-----,\t-----"); var row2 = normValues[0]; for (int j = 0; j < 80; j += 4) { Console.WriteLine($"{row2[j]},\t{row2[j + 1]},\t{row2[j + 2]},\t{row2[j + 3]}");
}
Console.WriteLine(\$"-----,\t-----,\t-----,\t-----");
}

private static Function calculateStd(Variable features)
{
var mean = CNTKLib.ReduceMean(features,new Axis(2));
var remainder = CNTKLib.Minus(features, mean);
var squared = CNTKLib.Square(remainder);
//the last dimension indicate the number of samples
var n = new Constant(new NDShape(0), DataType.Float, features.Shape.Dimensions.Last()-1);
var elm = CNTKLib.ElementDivide(squared, n);
var sum = CNTKLib.ReduceSum(elm, new Axis(2));
var stdVal = CNTKLib.Sqrt(sum);
return stdVal;
}
}

public static class ArrayExtensions
{
public static IEnumerable<T> ToEnumerable<T>(this Array target)
{
foreach (var item in target)
yield return (T)item;
}
}
}


The output for the source code above should look like: