# 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.

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

# CNTK 106 Tutorial – Time Series prediction with LSTM using C#

In this post will show how to implement CNTK 106 Tutorial in C#. This tutorial lecture is written in Python and there is no related example in C#. For this reason I decided to translate this very good tutorial into C#. The tutorial can be found at: CNTK 106: Part A – Time series prediction with LSTM (Basics)  and uses sin wave function in order to predict time series data. For this problem the Long Short Term Memory, LSTM, Recurrent Neural Network is used.

## Goal

The goal of this tutorial is prediction the simulated data of a continuous function ( sin wave). From $N$ previous values of the $y=sin(t)$ function where $y$ is the observed amplitude signal at time $t$, prediction of  $M$ values of $y$ is going to predict for the corresponding future time points.

The excitement of this tutorial is using the LSTM recurrent neural network which is nicely suited for this kind of problems. As you probably know LSTM is special recurrent neural network which has ability to learn from its experience during the training. More information about this fantastic version of recurrent neural network can be found here.

The blog post is divided into several sub-sections:

1. Simulated data part
2. LSTM Network
3. Model training and evaluation

Since the simulated data set is huge, the original tutorial has two running mode which is described by the variable isFast. In case of fast mode, the variable is set to True, and this mode will be used in this tutorial. Later, the reader may change the value to False in order to see much better training model, but the training time will be much longer. The Demo for this this blog post exposes variables of the batch size and iteration number to the user, so the user may defined those numbers as he/she want.

## Data generation

In order to generate simulated sin wave data, we are going to implement several helper methods. Let $N$ and $M$  be a ordered set of past values and future (desired predicted values) of the sine wave, respectively. The two methods are implemented:

1. generateWaveDataset()

The generateWaveDataset takes the periodic function,set of independent values (which is corresponded the time for this case) and generate the wave function, by providing the time steps and time shift. The method is related to the generate_data() python methods from the original tutorial.

```static Dictionary<string, (float[][] train, float[][] valid, float[][] test)> loadWaveDataset(Func<double, double> fun, float[] x0, int timeSteps, int timeShift)
{
////fill data
float[] xsin = new float[x0.Length];//all data
for (int l = 0; l < x0.Length; l++)
xsin[l] = (float)fun(x0[l]);

//split data on training and testing part
var a = new float[xsin.Length - timeShift];
var b = new float[xsin.Length - timeShift];

for (int l = 0; l < xsin.Length; l++)
{
//
if (l < xsin.Length - timeShift) a[l] = xsin[l]; // if (l >= timeShift)
b[l - timeShift] = xsin[l];
}

//make arrays of data
var a1 = new List<float[]>();
var b1 = new List<float[]>();
for (int i = 0; i < a.Length - timeSteps + 1; i++)
{
//features
var row = new float[timeSteps];
for (int j = 0; j < timeSteps; j++)
row[j] = a[i + j];
//create features row
//label row
b1.Add(new float[] { b[i + timeSteps - 1] });
}

//split data into train, validation and test data set
var xxx = splitData(a1.ToArray(), 0.1f, 0.1f);
var yyy = splitData(b1.ToArray(), 0.1f, 0.1f);

var retVal = new Dictionary<string, (float[][] train, float[][] valid, float[][] test)>();
return retVal;
}
```

Once the data is generated, three datasets should be created: train, validate and test dataset, which are generated by splitting the dataset generated by the above method. The following splitData method splits the original sin wave dataset into three datasets,

```static (float[][] train, float[][] valid, float[][] test) splitData(float[][] data, float valSize = 0.1f, float testSize = 0.1f)
{
//calculate
var posTest = (int)(data.Length * (1 - testSize));
var posVal = (int)(posTest * (1 - valSize));

return (data.Skip(0).Take(posVal).ToArray(), data.Skip(posVal).Take(posTest - posVal).ToArray(), data.Skip(posTest).ToArray());
}
```

In order to visualize the data, the Windows Forms project is created. Moreover, the ZedGraph .NET class library is used in order to visualize the data. The following picture shows the generated data.

## Network modeling

As mentioned on the beginning of the blog post, we are going to create LSTM recurrent neural network, with 1 LSTM cell for each input. We have N inputs and each input is a value in our continuous function. The N outputs from the LSTM are the input into a dense layer that produces a single output. Between LSTM and dense layer we insert a dropout layer that randomly drops 20% of the values coming from the LSTM to prevent overfitting the model to the training dataset. We want use use the dropout layer during training but when using the model to make predictions we don’t want to drop values.

The description above can be illustrated on the following picture:

The implementation of the LSTM can be sumarize in one method, but the real implementation can be viewed in the demo sample which is attached with this blog post.
The following methods implements LSTM network depicted on the image above. The arguments for the method are already defined.

```public static Function CreateModel(Variable input, int outDim, int LSTMDim, int cellDim, DeviceDescriptor device, string outputName)
{

Func<Variable, Function> pastValueRecurrenceHook = (x) => CNTKLib.PastValue(x);

//creating LSTM cell for each input variable
Function LSTMFunction = LSTMPComponentWithSelfStabilization<float>(
input,
new int[] { LSTMDim },
new int[] { cellDim },
pastValueRecurrenceHook,
pastValueRecurrenceHook,
device).Item1;

//after the LSTM sequence is created return the last cell in order to continue generating the network
Function lastCell = CNTKLib.SequenceLast(LSTMFunction);

//implement drop out for 10%
var dropOut = CNTKLib.Dropout(lastCell,0.2, 1);

//create last dense layer before output
var outputLayer =  FullyConnectedLinearLayer(dropOut, outDim, device, outputName);

return outputLayer;
}
```

## Training the network

In order to train the model, the nextBatch() method is implemented that produces batches to feed the training function. Note that because CNTK supports variable sequence length, we must feed the batches as list of sequences. This is a convenience function to generate small batches of data often referred to as minibatch.

```private static IEnumerable<(float[] X, float[] Y)> nextBatch(float[][] X, float[][] Y, int mMSize)
{

float[] asBatch(float[][] data, int start, int count)
{
var lst = new List<float>();
for (int i = start; i < start + count; i++) { if (i >= data.Length)
break;

}
return lst.ToArray();
}

for (int i = 0; i <= X.Length - 1; i += mMSize) { var size = X.Length - i; if (size > 0 && size > mMSize)
size = mMSize;

var x = asBatch(X, i, size);
var y = asBatch(Y, i, size);

yield return (x, y);
}
}
```

Note: Since the this tutorial is implemented as WinForms C# project which can visualize training and testing datasets, as well as it  can show the best found model during the training process, there are lot of other implemented methods which are not mentioned here, but can be found in the demo source code attached in this blog post.

## Key Insight

When working with LSTM the user should pay attention on the following:

Since LSTM must work with axes with unknown dimensions, the variables should be defined on different way as we could saw in the previous blog posts. So the input and the output variable are initialized with the following code listing:

```// build the model
var feature = Variable.InputVariable(new int[] { inDim }, DataType.Float, featuresName, null, false /*isSparse*/);
var label = Variable.InputVariable(new int[] { ouDim }, DataType.Float, labelsName, new List<CNTK.Axis>() { CNTK.Axis.DefaultBatchAxis() }, false);
```

As specified in the original tutorial: “Specifying the dynamic axes enables the recurrence engine handle the time sequence data in the expected order. Please take time to understand how to work with both static and dynamic axes in CNTK as described here, the dynamic axes is key point in LSTM.
Now the implementation is continue with the defining learning rate, momentum, the learner and the trainer.

```
var lstmModel = LSTMHelper.CreateModel(feature, ouDim, hiDim, cellDim, device, "timeSeriesOutput");

Function trainingLoss = CNTKLib.SquaredError(lstmModel, label, "squarederrorLoss");
Function prediction = CNTKLib.SquaredError(lstmModel, label, "squarederrorEval");

// prepare for training
TrainingParameterScheduleDouble learningRatePerSample = new TrainingParameterScheduleDouble(0.0005, 1);
TrainingParameterScheduleDouble momentumTimeConstant = CNTKLib.MomentumAsTimeConstantSchedule(256);

IList<Learner> parameterLearners = new List<Learner>() {
Learner.MomentumSGDLearner(lstmModel.Parameters(), learningRatePerSample, momentumTimeConstant, /*unitGainMomentum = */true)  };

//create trainer
var trainer = Trainer.CreateTrainer(lstmModel, trainingLoss, prediction, parameterLearners);
```

Now the code is ready, and the 10 epochs should return acceptable result:

```
// train the model
for (int i = 1; i <= iteration; i++)
{
//get the next minibatch amount of data
foreach (var miniBatchData in nextBatch(featureSet.train, labelSet.train, batchSize))
{
var xValues = Value.CreateBatch<float>(new NDShape(1, inDim), miniBatchData.X, device);
var yValues = Value.CreateBatch<float>(new NDShape(1, ouDim), miniBatchData.Y, device);

//Combine variables and data in to Dictionary for the training
var batchData = new Dictionary<Variable, Value>();

//train minibarch data
trainer.TrainMinibatch(batchData, device);
}

if (this.InvokeRequired)
{
// Execute the same method, but this time on the GUI thread
this.Invoke(
new Action(() =>
{
//output training process
progressReport(trainer, lstmModel.Clone(), i, device);
}
));
}
else
{
//output training process
progressReport(trainer, lstmModel.Clone(), i, device);

}
}
```

## Model Evaluation

Model evaluation is implemented during the training process. In this way we can see the learning process and how the model is getting better and better.

Fore each minibatch the progress method is called which updates the charts for the training and testing data set.

```void progressReport(Trainer trainer, Function model, int iteration, DeviceDescriptor device)
{
textBox3.Text = iteration.ToString();
textBox4.Text = trainer.PreviousMinibatchLossAverage().ToString();
progressBar1.Value = iteration;

reportOnGraphs(trainer, model, iteration, device);
}

private void reportOnGraphs(Trainer trainer, Function model, int i, DeviceDescriptor device)
{
currentModelEvaluation(trainer, model, i, device);
currentModelTest(trainer, model, i, device);
}
```

The following picture shows the training process, where the model evaluation is shown simultaneously, for the training and testing data set.
Also the simulation of the Loss value during the training is simulated as well.

As can be see the blog post extends the original Tutorial with some handy tricks during the training process. Also this demo is good strarting point for development bether tool for LSTM Time Series training. The full source code of this blog post, which shows much more implementation than presented in the blog post can be found here.

# Advance Technology Days 13: Predavanje o C# 7.* kompajleru

Predavanje o novoj verziji C# 7 kompajlera prošla je vrlo uspješno, a mnogobrojna publika pokazala je da se ipak i ovakve teme mogu uraditi zanimljive i interesantne.

Sve prezentirano na predavanju moguće je preuzeti sa donjeg linka. Na linku je uključena prezentacijska datoteka i demo primjeri u C#:

Vidimo se na ATD14

# Deploy CNTK model to Excel using C#

In the last blog post, we saw how to save model state (checkpoint) in order to load it and train again. Also we have seen how to save model for the evaluation and testing. In fact we have seen how to prepare the model to be production ready.

Once we finish with the modelling process, we enter in to production phase, to install the model on place where we can use it for solving real world problems. This blog post is going to describe the process how deployed CNTK model can be exported to Excel like as AddIn and be used like ordinary Excel formula.

## Preparing and deploying CNTK model

From the previous posts we saw how to train and save the model. This will be our starting point for this post.

Assume we trained and saved the model for evaluation from the previous blog post with file name as “IrisModel.model”. The model calculates Iris flower based on 4 input parameters, as we saw earlier.

1. The first step is to create  .NET Class Library and install the following Nugget packages
1. CNTK CPU Only ver. 2.3
3. Include saved IrisModel.model file in the project as Content and should be copied in Debug folder of the application.

As we can see, for this export we need Excel Dna Addin, fantastic library for making anything as Excel Addin. It can be install as Nuget package, and more information can be found at http://excel-dna.net/.

The following picture shows above 3 actions.

1. Change the Class.cs name into IrisModel.cs, and implement two methods:
1. public static string IrisEval(object arg) and
2. private static float EvaluateModel(float[] vector).

The first method is direct Excel function which will be called in the excel, and the second method is similar from the previous blog post for model evaluation. The following code snippet shows the implementation for the methods:

```[ExcelFunction(Description = "IrisEval - Prediction for the Iris flower based on 4 input values.")]
public static string IrisEval(object arg)
{
try
{
//First convert object in to array
object[,] obj = (object[,])arg;

//create list to convert values
List<float> calculatedOutput = new List<float>();
//
foreach (var s in obj)
{
var ss = float.Parse(s.ToString(), CultureInfo.InvariantCulture);
}
if (calculatedOutput.Count != 4)
throw new Exception("Incorrect number of input variables. It must be 4!");
return EvaluateModel(calculatedOutput.ToArray());
}
catch (Exception ex)
{
return ex.Message;
}

}
private static string EvaluateModel(float[] vector)
{

//extract features and label from the model
Variable feature = ffnn_model.Arguments[0];
Variable label = ffnn_model.Output;

Value xValues = Value.CreateBatch<float>(new int[] { feature.Shape[0] }, vector, DeviceDescriptor.CPUDevice);
//Value yValues = - we don't need it, because we are going to calculate it

//map the variables and values
var inputDataMap = new Dictionary<Variable, Value>();
var outputDataMap = new Dictionary<Variable, Value>();

//evaluate the model
ffnn_model.Evaluate(inputDataMap, outputDataMap, DeviceDescriptor.CPUDevice);
//extract the result  as one hot vector
var outputData = outputDataMap[label].GetDenseData<float>(label);
var actualLabels = outputData.Select(l => l.IndexOf(l.Max())).ToList();
var flower = actualLabels.FirstOrDefault();
var strFlower = flower == 0 ? "setosa" : flower == 1 ? "versicolor" : "virginica";
return strFlower;
}<span style="display: inline-block; width: 0px; overflow: hidden; line-height: 0;" data-mce-type="bookmark" class="mce_SELRES_start"></span>
```

That is all we need for model evaluation in Excel.

Notice that the project must be build with the x64 architecture, and also installed Excel must be in x64 version.  This demo will not work in Excel 32 bits.

Rebuild the project and open Excel file with Iris Data set. You can use the file included in the demo project,  specially prepared for this blog post.

• Got to Excel – > Options -> Addins,

• Start typing the Excel  formula :
• IrisEval(A1:D1) and press Enter. And the magic happen.

Complete source code for this blog post can be found here.

# How to save CNTK model to file in C#

Final process of training is the model which should be used in the production as safe, reliable and accurate. Usually model training is frustrating and time consuming process, and it is not like we can see as demo to introduce with the library. Once the model is built with right combination of parameter values and network architecture, the process of modelling turn in to interesting and funny task, since it calculates the values just as we expect.

In most of the time, we have to save the current state of the model, and continue with training due to various reasons:

• to change the parameters of the learner
• to switch from one to another machine,
• or to share the state of the model with your team mate,
• to switch from CPU to GPU,
• etc

In all above cases the current state of the model should be saved, and continue the training process from the last stage of the model. Because, the training from the beginning is not a solution, since we already invest time and knowledge to achieve progress of the model building.

The CNTK supports two kind of persisting the model.

• saving the checkpoint of the model for later training.

In the first case, the model is prepare for the evaluation and production but cannot be trained again, because it is freed from all other information but for the evaluation. During the saving process, only one files is generated.

In the second case, beside a model file, another file is generated with the name “modelname.ckp”. The file contains all information needed for the continuation of training.  Once the trainer  checkpoint is persisted we can continue with model training even if we changed the following:

• the training data set with the same dimensions and data types
• the parameters of the learner,
• the learner

What we cannot change in order to continue with training is the the network model. In other words, the model must remain with the same number of layers, input and output dimensions.

Once the model is trained it can be persisted as separated file. As separate file, it can be loaded and evaluated with different dataset, but the number of the features and the label must remain the same as in case when was trained. Use this method when you want to share the model with someone else, or when you want to deploy the model in the production.

The model is saved simply by calling the CNTK method  Save:

```public void SaveTrainedModel(Function model, string fileName)
{
model.Save(fileName);
}
```

The model evaluation requires several steps:

• load the model from the file,
• extract the features and label from the model
• call evaluate method from the model, by passing the batch created from the features, label and the evaluation dataset.

```public Function LoadTrainedModel(string fileName, DeviceDescriptor device)
{
}
```

Once the model is loaded, features and label are extracted from the model on the following way:

```//load the mdoel from file
//extract features and label from the model
Variable feature = ffnn_model.Arguments[0];
Variable label = ffnn_model.Output;
```

The next step is creating the minibatch in order to pass the data to the evaluation.In this case we are going to create only one row for the Iris example of:

```//Example: 5.0f, 3.5f, 1.3f, 0.3f, setosa
float[] xVal = new float[4] { 5.0f, 3.5f, 1.3f, 0.3f };
Value xValues = Value.CreateBatch<float>(new int[] {feature.Shape[0] }, xVal, device);
//Value yValues = - we don't need it, because we are going to calculate it
```

Once we created the variable and values we can map them and pass to the model evaluation, and calculate the result:

```//map the variables and values
var inputDataMap = new Dictionary<Variable, Value>();
var outputDataMap = new Dictionary<Variable, Value>();
//evaluate the model
ffnn_model.Evaluate(inputDataMap, outputDataMap, device);
//extract the result  as one hot vector
var outputData = outputDataMap[label].GetDenseData<float>(label);
```

The evaluation result should be transformed to proper format, and compared with expected result:

```//transforms into class value
var actualLabels = outputData.Select(l => l.IndexOf(l.Max())).ToList();
var flower = actualLabels.FirstOrDefault();
var strFlower = flower == 0 ? "setosa" : flower == 1 ? "versicolor" : "versicolor";
Console.WriteLine(\$"Model Prediction: Input({xVal[0]},{xVal[1]},{xVal[2]},{xVal[3]}), Iris Flower={strFlower}");
Console.WriteLine(\$"Model Expectation: Input({xVal[0]},{xVal[1]},{xVal[2]},{xVal[3]}), Iris Flower= setosa");
```

## Training previous saved model

Training previously saved model is very simple, since it requires no special coding. Right after the trainer is created with all necessary stuff (network, learning rate, momentum and other),
you just need to call

``` trainer.RestoreFromCheckpoint(strIrisFilePath);
```

The above method is called, after you successfully saved the model state by calling

```trainer.SaveCheckpoint(strIrisFilePath);
```

The method is usually called at the end of the training process.
Complete source code from this blog post can be found here.

# How to setup learning rate per iteration in CTNK using C#

So far we have seen how to train and validate models in CNTK using C#. Also there many more details which should be revealed in order to better understand the CNTK library. One of the important feature not only in the CNTK but also in every DNN (deep neural networks) is the learning rate.

In ANN the learning rate is the number by which the derivative is multiply before it is subtracted by the weight. If the weight is decreased to much the loss function will be increased and the network will diverge. On the other hand if the weight is decreased to little the loss function will be changed little and the diverge progress will be to slow. So selecting the right value of the parameter is important. During the training process, the learning rate is usually defined as constant value. In CNTK the learning rate is defined as follow:

```// set learning rate for the network
var learningRate = new TrainingParameterScheduleDouble(0.2, 1);
```

From the code above the learning rate is assign to 0.2 value per sample. This means whole training process will be done with the learning rate of 0.2.
The CNTK support dynamic changing of the learning rate.
Assume we want to setup different the learning rates so that from the fist to the 100 iterations the learning rate would be 0.2. From the 100 to 500 iterations we want the learning rate would be 0.1. Moreover, after the 500 iterations are completed and to he end of the iteration process, we want to setup the learning rate to 0.05.

Above said can be expressed:

```lr1=0.2 , from 1 to 100 iterations

lr2= 0.1 from 100 to 500 iterations

lr3= 0.05 from 500 to the end of the searching process.
```

In case we want to setup the learning rate dynamically we need to use the PairSizeTDouble class in order to defined the learning rate. So for the above requirements the flowing code should be implemented:

```PairSizeTDouble p1 = new PairSizeTDouble(2, 0.2);
PairSizeTDouble p2 = new PairSizeTDouble(10, 0.1);
PairSizeTDouble p3 = new PairSizeTDouble(1, 0.05);

var vp = new VectorPairSizeTDouble() { p1, p2, p3 };
var learningRatePerSample = new CNTK.TrainingParameterScheduleDouble(vp, 50);
```

First we need to defined PairSizeTDouble object for every learning rate value, with the integer number which will be multiply.
Once we define the rates, make a array of rate values by creating the VectorPairSizeTDouble object. Then the array is passed as the first argument in the TrainingParameterScheduleDouble method. The second argument of the method is multiplication number. So in the first rate value, the 2 is multiple with 50 which is 100, and denotes the iteration number. Similar multiplication are done in the other rate values.

# Testing and Validation CNTK models using C#

…continue from the previous post.
Once the model is build and Loss and Validation functions are satisfied our expectation, we need to validate and test the model using the data which was not part of the training data set (unseen data). The model validation is very important because we want to see if our model is trained well,so that can evaluates unseen data approximately same as the training data. Otherwise the model which cannot predict the output is called overfitted model. Overfitting can happen when the model was trained long enough that shows very high performance for the training data set, but for the testing data evaluate bad results.
We will continue with the implementation from the prevision two posts, and implement model validation. After the model is trained, the model and the trainer are passed to the Evaluation method. The evaluation method loads the testing data and calculated the output using passed model. Then it compares calculated (predicted) values with the output from the testing data set and calculated the accuracy. The following source code shows the evaluation implementation.

```private static void EvaluateIrisModel(Function ffnn_model, Trainer trainer, DeviceDescriptor device)
{
var dataFolder = "Data";//files must be on the same folder as program
var trainPath = Path.Combine(dataFolder, "testIris_cntk.txt");
var featureStreamName = "features";
var labelsStreamName = "label";

//extract features and label from the model
var feature = ffnn_model.Arguments[0];
var label = ffnn_model.Output;

//stream configuration to distinct features and labels in the file
var streamConfig = new StreamConfiguration[]
{
new StreamConfiguration(featureStreamName, feature.Shape[0]),
new StreamConfiguration(labelsStreamName, label.Shape[0])
};

// prepare testing data
var testMinibatchSource = MinibatchSource.TextFormatMinibatchSource(
trainPath, streamConfig, MinibatchSource.InfinitelyRepeat, true);
var featureStreamInfo = testMinibatchSource.StreamInfo(featureStreamName);
var labelStreamInfo = testMinibatchSource.StreamInfo(labelsStreamName);

int batchSize = 20;
int miscountTotal = 0, totalCount = 20;
while (true)
{
var minibatchData = testMinibatchSource.GetNextMinibatch((uint)batchSize, device);
if (minibatchData == null || minibatchData.Count == 0)
break;
totalCount += (int)minibatchData[featureStreamInfo].numberOfSamples;

// expected labels are in the mini batch data.
var labelData = minibatchData[labelStreamInfo].data.GetDenseData<float>(label);
var expectedLabels = labelData.Select(l => l.IndexOf(l.Max())).ToList();

var inputDataMap = new Dictionary<Variable, Value>() {
{ feature, minibatchData[featureStreamInfo].data }
};

var outputDataMap = new Dictionary<Variable, Value>() {
{ label, null }
};

ffnn_model.Evaluate(inputDataMap, outputDataMap, device);
var outputData = outputDataMap[label].GetDenseData<float>(label);
var actualLabels = outputData.Select(l => l.IndexOf(l.Max())).ToList();

int misMatches = actualLabels.Zip(expectedLabels, (a, b) => a.Equals(b) ? 0 : 1).Sum();

miscountTotal += misMatches;
Console.WriteLine(\$"Validating Model: Total Samples = {totalCount}, Mis-classify Count = {miscountTotal}");

if (totalCount >= 20)
break;
}
Console.WriteLine(\$"---------------");
Console.WriteLine(\$"------TESTING SUMMARY--------");
float accuracy = (1.0F - miscountTotal / totalCount);
Console.WriteLine(\$"Model Accuracy = {accuracy}");
return;

}
```

The implemented method is called in the previous Training method.

``` EvaluateIrisModel(ffnn_model, trainer, device);

```

As can be seen the model validation has shown that the model predicts the data with high accuracy, which is shown on the following picture.

This was the latest post in series of blog posts about using Feed forward neural networks to train the Iris data using CNTK and C#.

The full source code for all three samples can be found here.