# 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.

# Input normalization as separate layer in CNTK with C#

In the previous post, we have seen how to calculate some of basis parameters of descriptive statistics, as well as how to normalize data by calculating  mean and standard deviation. In this blog post we are going to implement data normalization as regular neural network layer, which can simplify the training process and data preparation.

## What is Data normalization?

Simple said, data normalization is set of tasks which transform values of any feature in a data set into predefined number range. Usually this range is [-1,1] , [0,1] or some other specific ranges. Data normalization plays very important role in ML, since it can dramatically improve the training process, and simplify settings of network parameters.

There are two main types of data normalization:
– MinMax normalization – which transforms all values into range of [0,1],
– Gauss Normalization or Z score normalization, which transforms the value in such a way that the average value is zero, and std is 1.

Beside those types there are plenty of other methods which can be used. Usually those two are used when the size of the data set is known, otherwise we should use some of the other methods, like log scaling, dividing every value with some constant, etc. But why data need to be normalized? This is essential question in ML, and the simplest answer is to provide the equal influence to all features to change the output label. More about data normalization and scaling can be found on this link.

In this blog post we are going to implement CNTK neural network which contain a “Normalization layer” between input and first hidden layer. The schematic picture of the network looks like the following image:

As can be observed, the Normalization layer is placed between input and first hidden layer. Also the Normalization layer contains the same neurons as input layer and produced the  output with the same dimension as the input layer.

In order to implement Normalization layer the following requirements must be met:

• calculate average  $\mu$ and standard deviation $\sigma$ in training data set as well find maximum and minimum value of each feature.
• this must be done prior to neural network model creation, since we need those values in the normalization layer.
• within network model creation, the normalization layer should be define after input layer is defined.

# Calculation of mean and standard deviation for training data set

Before network creation, we should prepare mean and standard deviation parameters which will be used in the Normalization layer as constants. Hopefully, the CNTK has the static method in the Minibatch source class for this purpose “MinibatchSource.ComputeInputPerDimMeansAndInvStdDevs”. The method takes the whole training data set defined in the minibatch and calculate the parameters.

//calculate mean and std for the minibatchsource
// prepare the training data
var d = new DictionaryNDArrayView, NDArrayView>>();
using (var mbs = MinibatchSource.TextFormatMinibatchSource(
trainingDataPath , streamConfig, MinibatchSource.FullDataSweep,false))
{
d.Add(mbs.StreamInfo("feature"), new Tuple(null, null));
//compute mean and standard deviation of the population for inputs variables
MinibatchSource.ComputeInputPerDimMeansAndInvStdDevs(mbs, d, device);

}

Now that we have average and std values for each feature, we can create network with normalization layer. In this example we define simple feed forward NN with 1 input, 1 normalization, 1 hidden and 1 output layer.

private static Function createFFModelWithNormalizationLayer(Variable feature, int hiddenDim,int outputDim, Tuple avgStdConstants, DeviceDescriptor device)
{
//First the parameters initialization must be performed
var glorotInit = CNTKLib.GlorotUniformInitializer(
CNTKLib.DefaultParamInitScale,
CNTKLib.SentinelValueForInferParamInitRank,
CNTKLib.SentinelValueForInferParamInitRank, 1);

//*******Input layer is indicated as feature
var inputLayer = feature;

//*******Normalization layer
var mean = new Constant(avgStdConstants.Item1, "mean");
var std = new Constant(avgStdConstants.Item2, "std");
var normalizedLayer = CNTKLib.PerDimMeanVarianceNormalize(inputLayer, mean, std);

//*****hidden layer creation
//shape of one hidden layer should be inputDim x neuronCount
var shape = new int[] { hiddenDim, 4 };
var weightParam = new Parameter(shape, DataType.Float, glorotInit, device, "wh");
var biasParam = new Parameter(new NDShape(1, hiddenDim), 0, device, "bh");
var hidLay = CNTKLib.Times(weightParam, normalizedLayer) + biasParam;
var hidLayerAct = CNTKLib.ReLU(hidLay);

//******Output layer creation
//the last action is creation of the output layer
var shapeOut = new int[] { 3, hiddenDim };
var wParamOut = new Parameter(shapeOut, DataType.Float, glorotInit, device, "wo");
var bParamOut = new Parameter(new NDShape(1, 3), 0, device, "bo");
var outLay = CNTKLib.Times(wParamOut, hidLayerAct) + bParamOut;
return outLay;
}

# Complete Source Code Example

The whole source code about this example is listed below. The example show how to normalize input feature for Iris famous data set. Notice that when using such way of data normalization, we don’t need to handle  normalization for validation or testing data sets, because data normalization  is part of the network model.

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using CNTK;
namespace NormalizationLayerDemo
{
class Program
{
static string trainingDataPath = "./data/iris_training.txt";
static string validationDataPath = "./data/iris_validation.txt";
static void Main(string[] args)
{
DeviceDescriptor device = DeviceDescriptor.UseDefaultDevice();

//stream configuration to distinct features and labels in the file
var streamConfig = new StreamConfiguration[]
{
new StreamConfiguration("feature", 4),
new StreamConfiguration("flower", 3)
};

// build a NN model
//define input and output variable and connecting to the stream configuration
var feature = Variable.InputVariable(new NDShape(1, 4), DataType.Float, "feature");
var label = Variable.InputVariable(new NDShape(1, 3), DataType.Float, "flower");

//calculate mean and std for the minibatchsource
// prepare the training data
var d = new Dictionary();
using (var mbs = MinibatchSource.TextFormatMinibatchSource(
trainingDataPath , streamConfig, MinibatchSource.FullDataSweep,false))
{
d.Add(mbs.StreamInfo("feature"), new Tuple(null, null));
//compute mean and standard deviation of the population for inputs variables
MinibatchSource.ComputeInputPerDimMeansAndInvStdDevs(mbs, d, device);

}

//Build simple Feed Froward Neural Network with normalization layer
var ffnn_model = createFFModelWithNormalizationLayer(feature,5,3,d.ElementAt(0).Value, device);

//Loss and error functions definition
var trainingLoss = CNTKLib.CrossEntropyWithSoftmax(new Variable(ffnn_model), label, "lossFunction");
var classError = CNTKLib.ClassificationError(new Variable(ffnn_model), label, "classificationError");

// set learning rate for the network
var learningRatePerSample = new TrainingParameterScheduleDouble(0.01, 1);

//define learners for the NN model
var ll = Learner.SGDLearner(ffnn_model.Parameters(), learningRatePerSample);

//define trainer based on model, loss and error functions , and SGD learner
var trainer = Trainer.CreateTrainer(ffnn_model, trainingLoss, classError, new Learner[] { ll });

//Preparation for the iterative learning process

// create minibatch for training
var mbsTraining = MinibatchSource.TextFormatMinibatchSource(trainingDataPath, streamConfig, MinibatchSource.InfinitelyRepeat, true);

int epoch = 1;
while (epoch  a.sweepEnd))
{
reportTrainingProgress(feature, label, streamConfig, trainer, epoch, device);
epoch++;
}
}
}

private static void reportTrainingProgress(Variable feature, Variable label, StreamConfiguration[] streamConfig,  Trainer trainer, int epoch, DeviceDescriptor device)
{
// create minibatch for training
var mbsTrain = MinibatchSource.TextFormatMinibatchSource(trainingDataPath, streamConfig, MinibatchSource.FullDataSweep, false);
var trainD = mbsTrain.GetNextMinibatch(int.MaxValue, device);
//
var a1 = new UnorderedMapVariableMinibatchData();
var trainEvaluation = trainer.TestMinibatch(a1);

// create minibatch for validation
var mbsVal = MinibatchSource.TextFormatMinibatchSource(validationDataPath, streamConfig, MinibatchSource.FullDataSweep, false);
var valD = mbsVal.GetNextMinibatch(int.MaxValue, device);

//
var a2 = new UnorderedMapVariableMinibatchData();
var valEvaluation = trainer.TestMinibatch(a2);

Console.WriteLine($"Epoch={epoch}, Train Error={trainEvaluation}, Validation Error={valEvaluation}"); } private static Function createFFModelWithNormalizationLayer(Variable feature, int hiddenDim,int outputDim, Tuple avgStdConstants, DeviceDescriptor device) { //First the parameters initialization must be performed var glorotInit = CNTKLib.GlorotUniformInitializer( CNTKLib.DefaultParamInitScale, CNTKLib.SentinelValueForInferParamInitRank, CNTKLib.SentinelValueForInferParamInitRank, 1); //*******Input layer is indicated as feature var inputLayer = feature; //*******Normalization layer var mean = new Constant(avgStdConstants.Item1, "mean"); var std = new Constant(avgStdConstants.Item2, "std"); var normalizedLayer = CNTKLib.PerDimMeanVarianceNormalize(inputLayer, mean, std); //*****hidden layer creation //shape of one hidden layer should be inputDim x neuronCount var shape = new int[] { hiddenDim, 4 }; var weightParam = new Parameter(shape, DataType.Float, glorotInit, device, "wh"); var biasParam = new Parameter(new NDShape(1, hiddenDim), 0, device, "bh"); var hidLay = CNTKLib.Times(weightParam, normalizedLayer) + biasParam; var hidLayerAct = CNTKLib.ReLU(hidLay); //******Output layer creation //the last action is creation of the output layer var shapeOut = new int[] { 3, hiddenDim }; var wParamOut = new Parameter(shapeOut, DataType.Float, glorotInit, device, "wo"); var bParamOut = new Parameter(new NDShape(1, 3), 0, device, "bo"); var outLay = CNTKLib.Times(wParamOut, hidLayerAct) + bParamOut; return outLay; } } } The output window should looks like: The data set files used in the example can be downloaded from here, and full source code demo from 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 System.Threading.Tasks; 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:

# Using ANNdotNET – GUI tool to create CNTK based model for Iris data set

In this tutorial we are going to create and train Iris model using ANNdotNET.  ANNdotNET is windows application for creating and training CNTK based models without leaving GUI.

All procedures from downloading the data set, to exporting model, can be achieved in 6 steps.

1. Step: Download the data set file from https://archive.ics.uci.edu/ml/machine-learning-databases/iris/iris.data.

2. Step: Open ANNdotNET application. Press New command, select Project 1 tree item and rename the project  into Iris Data Set.

2. Step: Select Data Command from Model Preparation ribbon group, Click File button from Import experimenal data dialog and select the recently downloaded file. Check Comma check box and press Import Data button.

3. Steps: Double click on Scaling for each column, and select MinMax normalization option from the popup ComboBox list. Double click on Type for the output column, and select Category, and 1:N for encoding. More information how to prepare data for ML you can find at https://bhrnjica.net/2018/03/01/data-preparation-tool-for-machine-learning/

4. Steps: Once the data is prepared Click Create Model Command and Model Settings panel is shown. Setup parameters as shown on the image below and click Run command.

5. Steps: Once the model is trained you can evaluate model by selecting Evaluate Command. Depending on the model type (regression, Binary or Multi class classification) The appropriate Evaluation dialog appears. Since this is multi class classification model, the Confusion matrix is shows, with micro and macron performance parameters.

6. Steps: For further analysis you can export model to Excel, or into ONNX. Also you can save the project which can later be opened and retrained again.

Note: Currently ANNdotNET is in alpha version, and more feature will come in near future.

# Data Preparation Tool for Machine Learning

Regardless of machine learning library you use, the data preparation is the first and one of the most important step in developing predictive models. It is very often case that the data supposed to be used for the training is dirty with lot of unnecessary columns, full of missing values, un-formatted numbers etc. Before training the data must be cleaned and properly defined in order to get good model. This is known as data preparation. The data preparation consist of cleaning the data, defining features and labels, deriving the new features from the existing data, handling missing values, scaling the data etc.  It can be concluded that the total time we spend in ML modelling,the most of it is related to data preparation.

In this blog post I am going to present the simple tool which can significantly reduce the preparation time for ML. The tool simply loads the data in to GUI, and then the user can define all necessary information. Once the data is prepared user can store the data it to files which can be then directly imported into ML algorithm such as CNTK.

The following image shows the ML Data Preparation Tool main window.

From the image above, the data preparation can be achieved in several steps.

1. Load dirty data into ML Prep Tool, by pressing Import Data button
2. Transform the data by providing the flowing:
1. Type – each column can be:
1. Numeric – which holds continuous numeric values,
2. Binary – which indicates two class categorical data,
3. Category – which indicates categorical data with more than two classes,
4. String – which indicate the column will not be part of training and testing data set,
2. Encoding – in case of Binary and Category column type, the encoding must be defined. The flowing encoding is supported:
1. Binary Encoding with (0,1) – first binary values will be 0, and second binary values will be 1.
2. Binary encoding with (-1,1) – first binary values will be -1, and second binary values will be 1.
3. Category Level- which each class treats as numeric value. In case of 3 categories(R,G, B), encoding will be (0,1,2)
4. Category 1:N- implements One-Hot vector with N columns. In case of 3 categories(R,G, B), encoding will be R =  (1,0,0),G =  (0,1,0), B =  (0,0,1).
5. Category 1:N-1(0) – implements dummy coding with N-1 columns. In case of 3 categories(R, G, B), encoding will be R =  (1,0),G =  (0,1), B =  (0,0).
6. Category 1:N-1(-1) – implements dummy coding with N-1 columns. In case of 3 categories(R, G, B), encoding will be R =  (1,0),G =  (0,1), B =  (-1,-1).
3. Variable – defines features and label. Only one label, and at least one features can be defined. Also the column can be defined as Ignore variable, which will skip that column.  The following options are sported:
1. Input – which identifies the column as feature or predictor,
2. Output – which identifies the column as label or model output.
4. Scaling – defines column scaling. Two scaling options are supported:
1. MinMax,
2. Gauss Standardization,
5. Missing Values – defines the replacement for the missing value withing the column. There are several options related to numeric and two options (Random and Mode ) for categorical type.
3. Define the testing data set size by providing information of row numbers or percent.
4. Define export options
5. Press Export Button.

As can be seen this is straightforward workflow of data preparation.

Besides the general export options which can be achieved by selecting different delimiter options, you can export data set in to CNTK format, which is very handy if you play with CNTK.

After data transformations, the user need to check CNTK format int the export options and press Export in order to get CNTK training and testing files, which can be directly used in the code without any modifications.

Some of examples will be provided int he next blog post.

The project is hosted at GitHub, where the source code can be freely downloaded and used at this location: https://github.com/bhrnjica/MLDataPreparationTool .

In case you want only binaries, the release of version v1.0 is published here: https://github.com/bhrnjica/MLDataPreparationTool/releases/tag/v1.0

# Using CNTK and C# to train Mario to drive Kart

## Introduction

In this blog post I am going to explain one of possible way how to implement Deep Learning to play video game. For this purpose I used the following:

1. N64 Nintendo emulator which can be found here,
2. Mario Kart 64 ROM, which can be found on internet as well,
3. CNTK – Microsoft Cognitive Toolkit
4. .NET Framework and C#

The idea behind this machine learning project is to capture images together with action, while you play Mario Kart game. Then captured images are transformed into features of training data set, and action keys into label hot vectors respectively.  Since we need to capture images, the emulator should be positioned at fixed location and resized to fixed size during playing the game, testing algorithm to play game, and play the game. The flowing image shows N64 emulator graphics configuration settings.

Also the N64 emulator is positioned to Top-Left corned of screen, so it is easier to capture the images.

## Data collection for training data set

During image captures, game is played as you would play normally. Also no special agent, nor platform is required.

In .NET and C#, it is implemented image capture from the specific position of screen, as well as it is recorded which keys are pressed during game play. In order to record keys press, the code found here is modified and used.

The flowing image shows the position of N64 emulator with Mario Kart game (1), the window which shows the captured and transformed images (2), and .NET Console  application with the implementation (3).

The data is generated on the following way:

• each image is captured, resized to 100×74 pixels and gray scaled prior to be transformed and persisted to data set training file.
• before image is persisted the hotkey of action key press is recorded and connected to image.

So the training data is persisted into CNTK format which consist of:

1. |label – which represent 5 component hot vector, indicate: Forward, Break, Forward-Left, Forward-Right and None (1 0 0 0 0)
2. |features consist of 100×74 numbers which represent pixels of the images.

The following data sample shows how training data set are persisted in the txt file:

|label 1 0 0 0 0 |features 202 202 202 202 202 202 204 189 234 209 199...
|label 0 1 0 0 0 |features 201 201 201 201 201 201 201 201 203 18...
|label 0 0 1 0 0 |features 199 199 199 199 199 199 199 199 199 19...
|label 0 0 0 1 1 |features 199 199 199 199 199 199 199 199 199 19...

Since my training data is more than 300 000 MB of size, I provided just few BM sized file, but you can generate file as big as you wish with just playing the game, and running the flowing code from Program.cs file:

await GenerateData.Start();

## Model training to play the game

Once we generate the data, we can move to the next step: training RCNN model to play the game. For training model the CNTK is used. Since we play a game which the previous sequence will determined the next sequence in the game, the LSTM RNN is used. More information about CNTK and LSTM can be found in previous posts.

In my case I have collected nearly 15000 images during several round of playing the same level and route. Also for more accurate model much more images should be collected, nearly 100 000. The model is trained in one hour, with 500000 iterations. The source code about whole project can be found on GitHub page. (http://github.com/bhrnjica/LSTMBotGame )

By running the following code, the training process is started with provided training data:

CNTKDeepNN.Train(DeviceDescriptor.UseDefaultDevice());

## Playing the game with CNTK model

Once we trained the model, we move to the next step: playing a game.

The emulator should be positioned on the same position and with the same size as we had while generating training data.Once the model is trained and created, the playing game can be achieve by running:

var dev = DeviceDescriptor.UseDefaultDevice();
MarioKartPlay.PlayGame(dev);

How it looks like on my case, you can see on this you tube video:

# Step by step CNTK Object Detection on Custom Dataset with Python

Recently, I was playing with CNTK object detection API, and produced very interesting model which can recognize the Nokia3310 mobile phone. As you probably already know Nokia3310 is legendary mobile phone which was popular 15 years ago, and recently re-branded by Nokia.

In this blog post I will provide you with step by step introductions how to:

• prepare images for training
• generate training data for selected images by using VOOT tool,
• prepare Python code for object detection using FasterRCNN alogirithm implemented with CNTK,
• testing custom image in order to detect Nokia3310 on image.

# Preparing Image for model training

Finding appropriate images for our model is very easy. Just go to google.com and type “Nokia3310” and bum, there are plenty of images.

Find at least 20 images, and put into the Nokia3310 image folder. Once we collect enough image for the model, we can move to the next step.

# Generating data from the image data set using VOTT tool

In order to train image detection model by using FasterRCNN algoritm, we have to provide three kinds of data separated in three different files:

1. class_map file – which contains list of available objects which the model should recognize on the image,
2. train_image file – which contains the list of image file paths
3. train roi file – which contains “region of interest” data. The data is consisting of list of 4 numbers which represent the top, left, right and bottom coordinate producing rectangle of the object.

Seems pretty much job for simple object detection, but hopefully there is a tool which can generate all data for us. It is called  VoTT: Visual Object Tagging Tool, and it can be found at : https://github.com/Microsoft/VoTT.

## Generating Image data with VOTT

Here we will explain in detail how to generate image data by using VOTT tool.

1. Open VOTT tool, from File menu and select folder we previously collected with images.

2. Enter “nokia3310”  in Labels edit box and click Continue button. In case we have more than one

3. Then for each image, make a rectangle on each object which represents the Nokia3310.

4. Once you finish with tagging for one image, press Next, and do the same for all selected images.

5. Once the process of tagging is finished, then the export action can be performed.

6. With Export option data is generated for each rectangle we made, and the two files are generated for each image in data set. Also once the tagging process is completed VOTT tool generated three folders:

a) negative – contains images which have no any tagged rectangle (no nokia3310 on images),

b) positive – contains approximate 70% of all images which we tagged Nokia3310 object, and this folder will be used for training the model,

c) testImages – contains approximate 30% of all images which we tagged Nokia3310 object, and this folder will be used for evaluation and testing the model.

The VOOT classified all images in three folders. In case there are images with no tagging, images will be moved to negatives, all other images is separated into positive and testImages folder.

From each image two files are generated:

[imagename].bboxes.labels.tsv – which consist of all labels tagged in image file.

[imagename].bboxes.tsv – rectangle coordinates of all tags in the image.

## Processing VOTT generated data into CNTK training and testing dataset files

Once we have VOTT generated data, we need to transform them into cntk format. First we will generate: class_map file.txt

7. Create new “class_map file.txt”  file, and put the following text into it:

__background__	0
Nokia3310	1

As can be seen there is only one class which we want to detect, and ti is Nokia3310, (the __backgroud__ is reserved tag which is added by default and cannot be removed). Now we need to generate the second file:
8. Create new “train_image_file.txt” file, and put text similar with this one:

0 positive/img01.jpg 0
1 positive/img05.jpg 0
2 positive/img10.jpg 0
...

The content of the file is list of all images placed in positive folder, with ID on the left side and zero on the right side, separated by tabulator. Image path should be relative.
9. Create new “train_roi_file.txt”, and put data similar with this one:

0 |roiAndLabel 10	418	340	520 1
1 |roiAndLabel 631	75	731	298 1
2 |roiAndLabel 47	12	222	364 1
3 |roiAndLabel 137	67	186	184 1	188	69	234	180 1
...

As can be seen first four numbers are rectangle coordinates, which follow the 1 number indicates classValue. Since we have only one class 1 is always after 4 numbers. Also in case image contains more than one rectangle which is the case of line 3, after every four  numbers it goes class value.

This is procedure how can we make three files for training, needed to run CNTK object detection. Also for testing data we need image and ROI files. Whole data set and corresponded files can be found on GitHub page.

# Implementation of Object Detection

CNTK comes with example how to implement object detection which can be found at: https://github.com/Microsoft/CNTK/tree/master/Examples/Image/Detection

So I took the source code from there, and modify it for my case, and published at git hub which can be found here.

10. Before downloading source code, be sure the CNTK 2.3 is installed on your machine with Anaconda 4.1.1, in the environment with Python 3.5 version.

11. Clone the Github repository https://github.com/bhrnjica/ObjectDetection and open it in Visual Studio or Visual Studio Code.

12. First thing you should do is to download pre-trained “Alex net” model. You can easily download it, by running the download_model.py python code placed in PretrainedModels folder.

13. Process of training is started when you run Nokia3310_detection.py python file. Beside pre-trained model, no other resources are required in order to run the project. The folowing picture shows main parts of the solution.

Once the training process is finished, once image is evaluated and shown in order to evaluate how model is good in detecting the phone. Such image is shows at the beginning of the blog post.

All source code with image dataset you can download from GitHub at https://github.com/bhrnjica/ObjectDetection