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Neural Network for Recognition of Handwritten Digits

, 5 Dec 2006
A convolutional neural network achieves 99.26% accuracy on a modified NIST database of hand-written digits.
// NeuralNetwork.h: interface for the NeuralNetwork class.

#if !defined(AFX_NEURALNETWORK_H__186C10A1_9662_4C1C_B5CB_21F2F361D268__INCLUDED_)
#define AFX_NEURALNETWORK_H__186C10A1_9662_4C1C_B5CB_21F2F361D268__INCLUDED_

#if _MSC_VER > 1000
#pragma once
#endif // _MSC_VER > 1000

#include <math.h>
#include <vector>

using namespace std;

#define SIGMOID(x) (1.7159*tanh(0.66666667*x))
#define DSIGMOID(S) (0.66666667/1.7159*(1.7159+(S))*(1.7159-(S)))  // derivative of the sigmoid as a function of the sigmoid's output

// forward declarations

class NNLayer;
class NNWeight;
class NNNeuron;
class NNConnection;

// helpful typedef's

typedef std::vector< NNLayer* >  VectorLayers;
typedef std::vector< NNWeight* >  VectorWeights;
typedef std::vector< NNNeuron* >  VectorNeurons;
typedef std::vector< NNConnection > VectorConnections;
typedef std::basic_string<TCHAR>  tstring;

class NeuralNetwork  
	volatile double m_etaLearningRatePrevious;
	volatile double m_etaLearningRate;

	volatile UINT m_cBackprops;  // counter used in connection with Weight sanity check
	void PeriodicWeightSanityCheck();

	void Calculate(double* inputVector, UINT count, 
		double* outputVector = NULL, UINT oCount = 0,
		std::vector< std::vector< double > >* pNeuronOutputs = NULL );

	void Backpropagate(double *actualOutput, double *desiredOutput, UINT count,
		std::vector< std::vector< double > >* pMemorizedNeuronOutputs );

	void EraseHessianInformation();
	void DivideHessianInformationBy( double divisor );
	void BackpropagateSecondDervatives( double* actualOutputVector, double* targetOutputVector, UINT count );

	void Serialize(CArchive &ar);

	virtual ~NeuralNetwork();
	void Initialize();

	VectorLayers m_Layers;


class NNLayer

	void PeriodicWeightSanityCheck();  // check if weights are "reasonable"
	void Calculate();
	void Backpropagate( std::vector< double >& dErr_wrt_dXn /* in */, 
		std::vector< double >& dErr_wrt_dXnm1 /* out */, 
		std::vector< double >* thisLayerOutput,  // memorized values of this layer's output
		std::vector< double >* prevLayerOutput,  // memorized values of previous layer's output
		double etaLearningRate );

	void EraseHessianInformation();
	void DivideHessianInformationBy( double divisor );
	void BackpropagateSecondDerivatives( std::vector< double >& dErr_wrt_dXn /* in */, 
		std::vector< double >& dErr_wrt_dXnm1 /* out */);

	void Serialize(CArchive& ar );

	NNLayer( LPCTSTR str, NNLayer* pPrev = NULL );
	virtual ~NNLayer();

	VectorWeights m_Weights;
	VectorNeurons m_Neurons;

	tstring label;
	NNLayer* m_pPrevLayer;

	bool m_bFloatingPointWarning;  // flag for one-time warning (per layer) about potential floating point overflow

	void Initialize();


class NNConnection
	NNConnection(UINT neuron = ULONG_MAX, UINT weight = ULONG_MAX):NeuronIndex( neuron ), WeightIndex( weight ) {};
	virtual ~NNConnection() {};
	UINT NeuronIndex, WeightIndex;

class NNWeight
	NNWeight( LPCTSTR str, double val = 0.0 );
	virtual ~NNWeight();

	tstring label;
	double value;
	double diagHessian;

	void Initialize();


class NNNeuron
	NNNeuron( LPCTSTR str );
	virtual ~NNNeuron();

	void AddConnection( UINT iNeuron, UINT iWeight );
	void AddConnection( NNConnection const & conn );

	tstring label;
	double output;

	VectorConnections m_Connections;

///	VectorWeights m_Weights;
///	VectorNeurons m_Neurons;
	void Initialize();


#endif // !defined(AFX_NEURALNETWORK_H__186C10A1_9662_4C1C_B5CB_21F2F361D268__INCLUDED_)

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About the Author

Mike O'Neill
United States United States
Mike O'Neill is a patent attorney in Southern California, where he specializes in computer and software-related patents. He programs as a hobby, and in a vain attempt to keep up with and understand the technology of his clients.

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