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 System.Threading.Tasks;
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++;
                }
            }
            Console.Read();
        }

        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();
            a1.Add(feature, trainD[mbsTrain.StreamInfo("feature")]);
            a1.Add(label, trainD[mbsTrain.StreamInfo("flower")]);
            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();
            a2.Add(feature, valD[mbsVal.StreamInfo("feature")]);
            a2.Add(label, valD[mbsVal.StreamInfo("flower")]);
            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:

2018-07-13_18-20-58

The data set files used in the example can be downloaded from here.

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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: