machine_learning Namespace Reference

A* search algorithm More...

Classes
class	adaline

Functions
int	save_u_matrix (const char *fname, const std::vector< std::vector< std::valarray< double > > > &W)
double	update_weights (const std::valarray< double > &X, std::vector< std::vector< std::valarray< double > > > *W, std::vector< std::valarray< double > > *D, double alpha, int R)
void	kohonen_som (const std::vector< std::valarray< double > > &X, std::vector< std::vector< std::valarray< double > > > *W, double alpha_min)
void	update_weights (const std::valarray< double > &x, std::vector< std::valarray< double > > *W, std::valarray< double > *D, double alpha, int R)
void	kohonen_som_tracer (const std::vector< std::valarray< double > > &X, std::vector< std::valarray< double > > *W, double alpha_min)
template<typename T >
std::ostream &	operator<< (std::ostream &out, std::vector< std::valarray< T > > const &A)
template<typename T >
std::ostream &	operator<< (std::ostream &out, const std::pair< T, T > &A)
template<typename T >
std::ostream &	operator<< (std::ostream &out, const std::valarray< T > &A)
template<typename T >
std::valarray< T >	insert_element (const std::valarray< T > &A, const T &ele)
template<typename T >
std::valarray< T >	pop_front (const std::valarray< T > &A)
template<typename T >
std::valarray< T >	pop_back (const std::valarray< T > &A)
template<typename T >
void	equal_shuffle (std::vector< std::vector< std::valarray< T > > > &A, std::vector< std::vector< std::valarray< T > > > &B)
template<typename T >
void	uniform_random_initialization (std::vector< std::valarray< T > > &A, const std::pair< size_t, size_t > &shape, const T &low, const T &high)
template<typename T >
void	unit_matrix_initialization (std::vector< std::valarray< T > > &A, const std::pair< size_t, size_t > &shape)
template<typename T >
void	zeroes_initialization (std::vector< std::valarray< T > > &A, const std::pair< size_t, size_t > &shape)
template<typename T >
T	sum (const std::vector< std::valarray< T > > &A)
template<typename T >
std::pair< size_t, size_t >	get_shape (const std::vector< std::valarray< T > > &A)
template<typename T >
std::vector< std::vector< std::valarray< T > > >	minmax_scaler (const std::vector< std::vector< std::valarray< T > > > &A, const T &low, const T &high)
template<typename T >
size_t	argmax (const std::vector< std::valarray< T > > &A)
template<typename T >
std::vector< std::valarray< T > >	apply_function (const std::vector< std::valarray< T > > &A, T(*func)(const T &))
template<typename T >
std::vector< std::valarray< T > >	operator* (const std::vector< std::valarray< T > > &A, const T &val)
template<typename T >
std::vector< std::valarray< T > >	operator/ (const std::vector< std::valarray< T > > &A, const T &val)
template<typename T >
std::vector< std::valarray< T > >	transpose (const std::vector< std::valarray< T > > &A)
template<typename T >
std::vector< std::valarray< T > >	operator+ (const std::vector< std::valarray< T > > &A, const std::vector< std::valarray< T > > &B)
template<typename T >
std::vector< std::valarray< T > >	operator- (const std::vector< std::valarray< T > > &A, const std::vector< std::valarray< T > > &B)
template<typename T >
std::vector< std::valarray< T > >	multiply (const std::vector< std::valarray< T > > &A, const std::vector< std::valarray< T > > &B)
template<typename T >
std::vector< std::valarray< T > >	hadamard_product (const std::vector< std::valarray< T > > &A, const std::vector< std::valarray< T > > &B)

Variables
constexpr double	MIN_DISTANCE = 1e-4

Detailed Description

A* search algorithm

Machine Learning algorithms.

for std::vector

Machine learning algorithms.

A* is an informed search algorithm, or a best-first search, meaning that it is formulated in terms of weighted graphs: starting from a specific starting node of a graph (initial state), it aims to find a path to the given goal node having the smallest cost (least distance travelled, shortest time, etc.). It evaluates by maintaining a tree of paths originating at the start node and extending those paths one edge at a time until it reaches the final state. The weighted edges (or cost) is evaluated on two factors, G score (cost required from starting node or initial state to current state) and H score (cost required from current state to final state). The F(state), then is evaluated as: F(state) = G(state) + H(state).

To solve the given search with shortest cost or path possible is to inspect values having minimum F(state).

Author

Ashish Daulatabad for std::reverse function for std::array, representing EightPuzzle board for assert for std::function STL for IO operations for std::map STL for std::shared_ptr for std::set STL for std::vector STL

Machine learning algorithms

for std::transform and std::sort for assert for std::pow and std::sqrt for std::cout for std::accumulate for std::unordered_map

Machine learning algorithms

Function Documentation

apply_function()

template<typename T >

std::vector< std::valarray< T > > machine_learning::apply_function	(	const std::vector< std::valarray< T > > &	A,
		T(*)(const T &)	func )

Function which applys supplied function to every element of 2D vector

Template Parameters

T	typename of the vector

Parameters

A	2D vector on which function will be applied
func	Function to be applied

Returns

new resultant vector

                                                              {
    std::vector<std::valarray<double>> B =
        A;                  // New vector to store resultant vector
    for (auto &b : B) {     // For every row in vector
        b = b.apply(func);  // Apply function to that row
    }
    return B;  // Return new resultant 2D vector
}

argmax()

template<typename T >

size_t machine_learning::argmax

(

const std::vector< std::valarray< T > > &

A

)

Function to get index of maximum element in 2D vector

Template Parameters

T	typename of the vector

Parameters

A	2D vector for which maximum index is required

Returns

index of maximum element

                                                  {
    const auto shape = get_shape(A);
    // As this function is used on predicted (or target) vector, shape should be
    // (1, X)
    if (shape.first != 1) {
        std::cerr << "ERROR (" << __func__ << ") : ";
        std::cerr << "Supplied vector is ineligible for argmax" << std::endl;
        std::exit(EXIT_FAILURE);
    }
    // Return distance of max element from first element (i.e. index)
    return std::distance(std::begin(A[0]),
                         std::max_element(std::begin(A[0]), std::end(A[0])));
}

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equal_shuffle()

template<typename T >

void machine_learning::equal_shuffle	(	std::vector< std::vector< std::valarray< T > > > &	A,
		std::vector< std::vector< std::valarray< T > > > &	B )

Function to equally shuffle two 3D vectors (used for shuffling training data)

Template Parameters

T	typename of the vector

Parameters

A	First 3D vector
B	Second 3D vector

                                                            {
    // If two vectors have different sizes
    if (A.size() != B.size()) {
        std::cerr << "ERROR (" << __func__ << ") : ";
        std::cerr
            << "Can not equally shuffle two vectors with different sizes: ";
        std::cerr << A.size() << " and " << B.size() << std::endl;
        std::exit(EXIT_FAILURE);
    }
    for (size_t i = 0; i < A.size(); i++) {  // For every element in A and B
        // Genrating random index < size of A and B
        std::srand(std::chrono::system_clock::now().time_since_epoch().count());
        size_t random_index = std::rand() % A.size();
        // Swap elements in both A and B with same random index
        std::swap(A[i], A[random_index]);
        std::swap(B[i], B[random_index]);
    }
    return;
}

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get_shape()

template<typename T >

std::pair< size_t, size_t > machine_learning::get_shape

(

const std::vector< std::valarray< T > > &

A

)

Function to get shape of given 2D vector

Template Parameters

T	typename of the vector

Parameters

A	2D vector for which shape is required

Returns

shape as pair

                                                                      {
    const size_t sub_size = (*A.begin()).size();
    for (const auto &a : A) {
        // If supplied vector don't have same shape in all rows
        if (a.size() != sub_size) {
            std::cerr << "ERROR (" << __func__ << ") : ";
            std::cerr << "Supplied vector is not 2D Matrix" << std::endl;
            std::exit(EXIT_FAILURE);
        }
    }
    return std::make_pair(A.size(), sub_size);  // Return shape as pair
}

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hadamard_product()

template<typename T >

std::vector< std::valarray< T > > machine_learning::hadamard_product	(	const std::vector< std::valarray< T > > &	A,
		const std::vector< std::valarray< T > > &	B )

Function to get hadamard product of two 2D vectors

Template Parameters

T	typename of the vector

Parameters

A	First 2D vector
B	Second 2D vector

Returns

new resultant vector

                                        {
    const auto shape_a = get_shape(A);
    const auto shape_b = get_shape(B);
    // If vectors are not eligible for hadamard product
    if (shape_a.first != shape_b.first || shape_a.second != shape_b.second) {
        std::cerr << "ERROR (" << __func__ << ") : ";
        std::cerr << "Vectors have different shapes ";
        std::cerr << shape_a << " and " << shape_b << std::endl;
        std::exit(EXIT_FAILURE);
    }
    std::vector<std::valarray<T>> C;  // Vector to store result
    for (size_t i = 0; i < A.size(); i++) {
        C.push_back(A[i] * B[i]);  // Elementwise multiplication
    }
    return C;  // Return new resultant 2D vector
}

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insert_element()

template<typename T >

std::valarray< T > machine_learning::insert_element	(	const std::valarray< T > &	A,
		const T &	ele )

Function to insert element into 1D vector

Template Parameters

T	typename of the 1D vector and the element

Parameters

A	1D vector in which element will to be inserted
ele	element to be inserted

Returns

new resultant vector

                                                                     {
    std::valarray<T> B;      // New 1D vector to store resultant vector
    B.resize(A.size() + 1);  // Resizing it accordingly
    for (size_t i = 0; i < A.size(); i++) {  // For every element in A
        B[i] = A[i];                         // Copy element in B
    }
    B[B.size() - 1] = ele;  // Inserting new element in last position
    return B;               // Return resultant vector
}

kohonen_som()

void machine_learning::kohonen_som	(	const std::vector< std::valarray< double > > &	X,
		std::vector< std::vector< std::valarray< double > > > *	W,
		double	alpha_min )

Apply incremental algorithm with updating neighborhood and learning rates on all samples in the given datset.

Parameters

[in]	X	data set
[in,out]	W	weights matrix
[in]	alpha_min	terminal value of alpha

                                   {
    size_t num_samples = X.size();  // number of rows
    // size_t num_features = X[0].size();  // number of columns
    size_t num_out = W->size();  // output matrix size
    size_t R = num_out >> 2, iter = 0;
    double alpha = 1.f;
 
    std::vector<std::valarray<double>> D(num_out);
    for (int i = 0; i < num_out; i++) D[i] = std::valarray<double>(num_out);
 
    double dmin = 1.f;        // average minimum distance of all samples
    double past_dmin = 1.f;   // average minimum distance of all samples
    double dmin_ratio = 1.f;  // change per step
 
    // Loop alpha from 1 to slpha_min
    for (; alpha > 0 && dmin_ratio > 1e-5; alpha -= 1e-4, iter++) {
        // Loop for each sample pattern in the data set
        for (int sample = 0; sample < num_samples; sample++) {
            // update weights for the current input pattern sample
            dmin += update_weights(X[sample], W, &D, alpha, R);
        }
 
        // every 100th iteration, reduce the neighborhood range
        if (iter % 300 == 0 && R > 1) {
            R--;
        }
 
        dmin /= num_samples;
 
        // termination condition variable -> % change in minimum distance
        dmin_ratio = (past_dmin - dmin) / past_dmin;
        if (dmin_ratio < 0) {
            dmin_ratio = 1.f;
        }
        past_dmin = dmin;
 
        std::cout << "iter: " << iter << "\t alpha: " << alpha << "\t R: " << R
                  << "\t d_min: " << dmin_ratio << "\r";
    }
 
    std::cout << "\n";
}

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kohonen_som_tracer()

void machine_learning::kohonen_som_tracer	(	const std::vector< std::valarray< double > > &	X,
		std::vector< std::valarray< double > > *	W,
		double	alpha_min )

Apply incremental algorithm with updating neighborhood and learning rates on all samples in the given datset.

Parameters

[in]	X	data set
[in,out]	W	weights matrix
[in]	alpha_min	terminal value of alpha

                                          {
    int num_samples = X.size();  // number of rows
    // int num_features = X[0].size();  // number of columns
    int num_out = W->size();  // number of rows
    int R = num_out >> 2, iter = 0;
    double alpha = 1.f;
 
    std::valarray<double> D(num_out);
 
    // Loop alpha from 1 to slpha_min
    do {
        // Loop for each sample pattern in the data set
        for (int sample = 0; sample < num_samples; sample++) {
            // update weights for the current input pattern sample
            update_weights(X[sample], W, &D, alpha, R);
        }
 
        // every 10th iteration, reduce the neighborhood range
        if (iter % 10 == 0 && R > 1) {
            R--;
        }
 
        alpha -= 0.01;
        iter++;
    } while (alpha > alpha_min);
}

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minmax_scaler()

template<typename T >

std::vector< std::vector< std::valarray< T > > > machine_learning::minmax_scaler	(	const std::vector< std::vector< std::valarray< T > > > &	A,
		const T &	low,
		const T &	high )

Function to scale given 3D vector using min-max scaler

Template Parameters

T	typename of the vector

Parameters

A	3D vector which will be scaled
low	new minimum value
high	new maximum value

Returns

new scaled 3D vector

                   {
    std::vector<std::vector<std::valarray<T>>> B =
        A;                               // Copying into new vector B
    const auto shape = get_shape(B[0]);  // Storing shape of B's every element
    // As this function is used for scaling training data vector should be of
    // shape (1, X)
    if (shape.first != 1) {
        std::cerr << "ERROR (" << __func__ << ") : ";
        std::cerr
            << "Supplied vector is not supported for minmax scaling, shape: ";
        std::cerr << shape << std::endl;
        std::exit(EXIT_FAILURE);
    }
    for (size_t i = 0; i < shape.second; i++) {
        T min = B[0][0][i], max = B[0][0][i];
        for (size_t j = 0; j < B.size(); j++) {
            // Updating minimum and maximum values
            min = std::min(min, B[j][0][i]);
            max = std::max(max, B[j][0][i]);
        }
        for (size_t j = 0; j < B.size(); j++) {
            // Applying min-max scaler formula
            B[j][0][i] =
                ((B[j][0][i] - min) / (max - min)) * (high - low) + low;
        }
    }
    return B;  // Return new resultant 3D vector
}

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multiply()

template<typename T >

std::vector< std::valarray< T > > machine_learning::multiply	(	const std::vector< std::valarray< T > > &	A,
		const std::vector< std::valarray< T > > &	B )

Function to multiply two 2D vectors

Template Parameters

T	typename of the vector

Parameters

A	First 2D vector
B	Second 2D vector

Returns

new resultant vector

                                                                           {
    const auto shape_a = get_shape(A);
    const auto shape_b = get_shape(B);
    // If vectors are not eligible for multiplication
    if (shape_a.second != shape_b.first) {
        std::cerr << "ERROR (" << __func__ << ") : ";
        std::cerr << "Vectors are not eligible for multiplication ";
        std::cerr << shape_a << " and " << shape_b << std::endl;
        std::exit(EXIT_FAILURE);
    }
    std::vector<std::valarray<T>> C;  // Vector to store result
    // Normal matrix multiplication
    for (size_t i = 0; i < shape_a.first; i++) {
        std::valarray<T> row;
        row.resize(shape_b.second);
        for (size_t j = 0; j < shape_b.second; j++) {
            for (size_t k = 0; k < shape_a.second; k++) {
                row[j] += A[i][k] * B[k][j];
            }
        }
        C.push_back(row);
    }
    return C;  // Return new resultant 2D vector
}

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operator*()

template<typename T >

std::vector< std::valarray< T > > machine_learning::operator*	(	const std::vector< std::valarray< T > > &	A,
		const T &	val )

Overloaded operator "*" to multiply given 2D vector with scaler

Template Parameters

T	typename of both vector and the scaler

Parameters

A	2D vector to which scaler will be multiplied
val	Scaler value which will be multiplied

Returns

new resultant vector

                                                      {
    std::vector<std::valarray<double>> B =
        A;               // New vector to store resultant vector
    for (auto &b : B) {  // For every row in vector
        b = b * val;     // Multiply row with scaler
    }
    return B;  // Return new resultant 2D vector
}

operator+()

template<typename T >

std::vector< std::valarray< T > > machine_learning::operator+	(	const std::vector< std::valarray< T > > &	A,
		const std::vector< std::valarray< T > > &	B )

Overloaded operator "+" to add two 2D vectors

Template Parameters

T	typename of the vector

Parameters

A	First 2D vector
B	Second 2D vector

Returns

new resultant vector

                                        {
    const auto shape_a = get_shape(A);
    const auto shape_b = get_shape(B);
    // If vectors don't have equal shape
    if (shape_a.first != shape_b.first || shape_a.second != shape_b.second) {
        std::cerr << "ERROR (" << __func__ << ") : ";
        std::cerr << "Supplied vectors have different shapes ";
        std::cerr << shape_a << " and " << shape_b << std::endl;
        std::exit(EXIT_FAILURE);
    }
    std::vector<std::valarray<T>> C;
    for (size_t i = 0; i < A.size(); i++) {  // For every row
        C.push_back(A[i] + B[i]);            // Elementwise addition
    }
    return C;  // Return new resultant 2D vector
}

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operator-()

template<typename T >

std::vector< std::valarray< T > > machine_learning::operator-	(	const std::vector< std::valarray< T > > &	A,
		const std::vector< std::valarray< T > > &	B )

Overloaded operator "-" to add subtract 2D vectors

Template Parameters

T	typename of the vector

Parameters

A	First 2D vector
B	Second 2D vector

Returns

new resultant vector

                                        {
    const auto shape_a = get_shape(A);
    const auto shape_b = get_shape(B);
    // If vectors don't have equal shape
    if (shape_a.first != shape_b.first || shape_a.second != shape_b.second) {
        std::cerr << "ERROR (" << __func__ << ") : ";
        std::cerr << "Supplied vectors have different shapes ";
        std::cerr << shape_a << " and " << shape_b << std::endl;
        std::exit(EXIT_FAILURE);
    }
    std::vector<std::valarray<T>> C;         // Vector to store result
    for (size_t i = 0; i < A.size(); i++) {  // For every row
        C.push_back(A[i] - B[i]);            // Elementwise substraction
    }
    return C;  // Return new resultant 2D vector
}

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operator/()

template<typename T >

std::vector< std::valarray< T > > machine_learning::operator/	(	const std::vector< std::valarray< T > > &	A,
		const T &	val )

Overloaded operator "/" to divide given 2D vector with scaler

Template Parameters

T	typename of the vector and the scaler

Parameters

A	2D vector to which scaler will be divided
val	Scaler value which will be divided

Returns

new resultant vector

                                                      {
    std::vector<std::valarray<double>> B =
        A;               // New vector to store resultant vector
    for (auto &b : B) {  // For every row in vector
        b = b / val;     // Divide row with scaler
    }
    return B;  // Return new resultant 2D vector
}

operator<<() [1/3]

template<typename T >

std::ostream & machine_learning::operator<<	(	std::ostream &	out,
		const std::pair< T, T > &	A )

Overloaded operator "<<" to print a pair

Template Parameters

T	typename of the pair

Parameters

out	std::ostream to output
A	Pair to be printed

                                                                {
    // Setting output precision to 4 in case of floating point numbers
    out.precision(4);
    // printing pair in the form (p, q)
    std::cout << "(" << A.first << ", " << A.second << ")";
    return out;
}

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operator<<() [2/3]

template<typename T >

std::ostream & machine_learning::operator<<	(	std::ostream &	out,
		const std::valarray< T > &	A )

Overloaded operator "<<" to print a 1D vector

Template Parameters

T	typename of the vector

Parameters

out	std::ostream to output
A	1D vector to be printed

                                                                 {
    // Setting output precision to 4 in case of floating point numbers
    out.precision(4);
    for (const auto &a : A) {   // For every element in the vector.
        std::cout << a << ' ';  // Print element
    }
    std::cout << std::endl;
    return out;
}

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operator<<() [3/3]

template<typename T >

std::ostream & machine_learning::operator<<	(	std::ostream &	out,
		std::vector< std::valarray< T > > const &	A )

Overloaded operator "<<" to print 2D vector

Template Parameters

T	typename of the vector

Parameters

out	std::ostream to output
A	2D vector to be printed

                                                             {
    // Setting output precision to 4 in case of floating point numbers
    out.precision(4);
    for (const auto &a : A) {       // For each row in A
        for (const auto &x : a) {   // For each element in row
            std::cout << x << ' ';  // print element
        }
        std::cout << std::endl;
    }
    return out;
}

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pop_back()

template<typename T >

std::valarray< T > machine_learning::pop_back

(

const std::valarray< T > &

A

)

Function to remove last element from 1D vector

Template Parameters

T	typename of the vector

Parameters

A	1D vector from which last element will be removed

Returns

new resultant vector

                                                 {
    std::valarray<T> B;      // New 1D vector to store resultant vector
    B.resize(A.size() - 1);  // Resizing it accordingly
    for (size_t i = 0; i < A.size() - 1;
         i++) {       // For every (except last) element in A
        B[i] = A[i];  // Copy element in B
    }
    return B;  // Return resultant vector
}

pop_front()

template<typename T >

std::valarray< T > machine_learning::pop_front

(

const std::valarray< T > &

A

)

Function to remove first element from 1D vector

Template Parameters

T	typename of the vector

Parameters

A	1D vector from which first element will be removed

Returns

new resultant vector

                                                  {
    std::valarray<T> B;      // New 1D vector to store resultant vector
    B.resize(A.size() - 1);  // Resizing it accordingly
    for (size_t i = 1; i < A.size();
         i++) {           // // For every (except first) element in A
        B[i - 1] = A[i];  // Copy element in B with left shifted position
    }
    return B;  // Return resultant vector
}

save_u_matrix()

int machine_learning::save_u_matrix	(	const char *	fname,
		const std::vector< std::vector< std::valarray< double > > > &	W )

Create the distance matrix or U-matrix from the trained 3D weiths matrix and save to disk.

Parameters

[in]	fname	filename to save in (gets overwriten without confirmation)
[in]	W	model matrix to save

Returns

0 if all ok

-1 if file creation failed

                                                                      {
    std::ofstream fp(fname);
    if (!fp) {  // error with fopen
        std::cerr << "File error (" << fname << "): " << std::strerror(errno)
                  << std::endl;
        return -1;
    }
 
    // neighborhood range
    unsigned int R = 1;
 
    for (int i = 0; i < W.size(); i++) {         // for each x
        for (int j = 0; j < W[0].size(); j++) {  // for each y
            double distance = 0.f;
 
            int from_x = std::max<int>(0, i - R);
            int to_x = std::min<int>(W.size(), i + R + 1);
            int from_y = std::max<int>(0, j - R);
            int to_y = std::min<int>(W[0].size(), j + R + 1);
            int l = 0, m = 0;
#ifdef _OPENMP
#pragma omp parallel for reduction(+ : distance)
#endif
            for (l = from_x; l < to_x; l++) {      // scan neighborhoor in x
                for (m = from_y; m < to_y; m++) {  // scan neighborhood in y
                    auto d = W[i][j] - W[l][m];
                    double d2 = std::pow(d, 2).sum();
                    distance += std::sqrt(d2);
                    // distance += d2;
                }
            }
 
            distance /= R * R;          // mean distance from neighbors
            fp << distance;             // print the mean separation
            if (j < W[0].size() - 1) {  // if not the last column
                fp << ',';              // suffix comma
            }
        }
        if (i < W.size() - 1) {  // if not the last row
            fp << '\n';          // start a new line
        }
    }
 
    fp.close();
    return 0;
}

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sum()

template<typename T >

T machine_learning::sum

(

const std::vector< std::valarray< T > > &

A

)

Function to get sum of all elements in 2D vector

Template Parameters

T	typename of the vector

Parameters

A	2D vector for which sum is required

Returns

returns sum of all elements of 2D vector

                                          {
    T cur_sum = 0;             // Initially sum is zero
    for (const auto &a : A) {  // For every row in A
        cur_sum += a.sum();    // Add sum of that row to current sum
    }
    return cur_sum;  // Return sum
}

transpose()

template<typename T >

std::vector< std::valarray< T > > machine_learning::transpose

(

const std::vector< std::valarray< T > > &

A

)

Function to get transpose of 2D vector

Template Parameters

T	typename of the vector

Parameters

A	2D vector which will be transposed

Returns

new resultant vector

                                        {
    const auto shape = get_shape(A);  // Current shape of vector
    std::vector<std::valarray<T>> B;  // New vector to store result
    // Storing transpose values of A in B
    for (size_t j = 0; j < shape.second; j++) {
        std::valarray<T> row;
        row.resize(shape.first);
        for (size_t i = 0; i < shape.first; i++) {
            row[i] = A[i][j];
        }
        B.push_back(row);
    }
    return B;  // Return new resultant 2D vector
}

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uniform_random_initialization()

template<typename T >

void machine_learning::uniform_random_initialization	(	std::vector< std::valarray< T > > &	A,
		const std::pair< size_t, size_t > &	shape,
		const T &	low,
		const T &	high )

Function to initialize given 2D vector using uniform random initialization

Template Parameters

T	typename of the vector

Parameters

A	2D vector to be initialized
shape	required shape
low	lower limit on value
high	upper limit on value

                                                                {
    A.clear();  // Making A empty
    // Uniform distribution in range [low, high]
    std::default_random_engine generator(
        std::chrono::system_clock::now().time_since_epoch().count());
    std::uniform_real_distribution<T> distribution(low, high);
    for (size_t i = 0; i < shape.first; i++) {  // For every row
        std::valarray<T>
            row;  // Making empty row which will be inserted in vector
        row.resize(shape.second);
        for (auto &r : row) {             // For every element in row
            r = distribution(generator);  // copy random number
        }
        A.push_back(row);  // Insert new row in vector
    }
    return;
}

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unit_matrix_initialization()

template<typename T >

void machine_learning::unit_matrix_initialization	(	std::vector< std::valarray< T > > &	A,
		const std::pair< size_t, size_t > &	shape )

Function to Intialize 2D vector as unit matrix

Template Parameters

T	typename of the vector

Parameters

A	2D vector to be initialized
shape	required shape

                                                                      {
    A.clear();  // Making A empty
    for (size_t i = 0; i < shape.first; i++) {
        std::valarray<T>
            row;  // Making empty row which will be inserted in vector
        row.resize(shape.second);
        row[i] = T(1);     // Insert 1 at ith position
        A.push_back(row);  // Insert new row in vector
    }
    return;
}

update_weights() [1/2]

void machine_learning::update_weights	(	const std::valarray< double > &	x,
		std::vector< std::valarray< double > > *	W,
		std::valarray< double > *	D,
		double	alpha,
		int	R )

Update weights of the SOM using Kohonen algorithm

Parameters

[in]	X	data point
[in,out]	W	weights matrix
[in,out]	D	temporary vector to store distances
[in]	alpha	learning rate \(0<\alpha\le1\)
[in]	R	neighborhood range

                                                                 {
    int j = 0, k = 0;
    int num_out = W->size();  // number of SOM output nodes
    // int num_features = x.size();  // number of data features
 
#ifdef _OPENMP
#pragma omp for
#endif
    // step 1: for each output point
    for (j = 0; j < num_out; j++) {
        // compute Euclidian distance of each output
        // point from the current sample
        (*D)[j] = (((*W)[j] - x) * ((*W)[j] - x)).sum();
    }
 
    // step 2:  get closest node i.e., node with snallest Euclidian distance to
    // the current pattern
    auto result = std::min_element(std::begin(*D), std::end(*D));
    // double d_min = *result;
    int d_min_idx = std::distance(std::begin(*D), result);
 
    // step 3a: get the neighborhood range
    int from_node = std::max(0, d_min_idx - R);
    int to_node = std::min(num_out, d_min_idx + R + 1);
 
    // step 3b: update the weights of nodes in the
    // neighborhood
#ifdef _OPENMP
#pragma omp for
#endif
    for (j = from_node; j < to_node; j++) {
        // update weights of nodes in the neighborhood
        (*W)[j] += alpha * (x - (*W)[j]);
    }
}

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update_weights() [2/2]

double machine_learning::update_weights	(	const std::valarray< double > &	X,
		std::vector< std::vector< std::valarray< double > > > *	W,
		std::vector< std::valarray< double > > *	D,
		double	alpha,
		int	R )

Update weights of the SOM using Kohonen algorithm

Parameters

[in]	X	data point - N features
[in,out]	W	weights matrix - PxQxN
[in,out]	D	temporary vector to store distances PxQ
[in]	alpha	learning rate \(0<\alpha\le1\)
[in]	R	neighborhood range

Returns

minimum distance of sample and trained weights

                             {
    int x = 0, y = 0;
    int num_out_x = static_cast<int>(W->size());       // output nodes - in X
    int num_out_y = static_cast<int>(W[0][0].size());  // output nodes - in Y
    // int num_features = static_cast<int>(W[0][0][0].size());  //  features =
    // in Z
    double d_min = 0.f;
 
#ifdef _OPENMP
#pragma omp for
#endif
    // step 1: for each output point
    for (x = 0; x < num_out_x; x++) {
        for (y = 0; y < num_out_y; y++) {
            (*D)[x][y] = 0.f;
            // compute Euclidian distance of each output
            // point from the current sample
            auto d = ((*W)[x][y] - X);
            (*D)[x][y] = (d * d).sum();
            (*D)[x][y] = std::sqrt((*D)[x][y]);
        }
    }
 
    // step 2:  get closest node i.e., node with snallest Euclidian distance
    // to the current pattern
    int d_min_x = 0, d_min_y = 0;
    get_min_2d(*D, &d_min, &d_min_x, &d_min_y);
 
    // step 3a: get the neighborhood range
    int from_x = std::max(0, d_min_x - R);
    int to_x = std::min(num_out_x, d_min_x + R + 1);
    int from_y = std::max(0, d_min_y - R);
    int to_y = std::min(num_out_y, d_min_y + R + 1);
 
    // step 3b: update the weights of nodes in the
    // neighborhood
#ifdef _OPENMP
#pragma omp for
#endif
    for (x = from_x; x < to_x; x++) {
        for (y = from_y; y < to_y; y++) {
            /* you can enable the following normalization if needed.
   personally, I found it detrimental to convergence */
            // const double s2pi = sqrt(2.f * M_PI);
            // double normalize = 1.f / (alpha * s2pi);
 
            /* apply scaling inversely proportional to distance from the
               current node */
            double d2 =
                (d_min_x - x) * (d_min_x - x) + (d_min_y - y) * (d_min_y - y);
            double scale_factor = std::exp(-d2 / (2.f * alpha * alpha));
 
            (*W)[x][y] += (X - (*W)[x][y]) * alpha * scale_factor;
        }
    }
    return d_min;
}

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zeroes_initialization()

template<typename T >

void machine_learning::zeroes_initialization	(	std::vector< std::valarray< T > > &	A,
		const std::pair< size_t, size_t > &	shape )

Function to Intialize 2D vector as zeroes

Template Parameters

T	typename of the vector

Parameters

A	2D vector to be initialized
shape	required shape

                                                                 {
    A.clear();  // Making A empty
    for (size_t i = 0; i < shape.first; i++) {
        std::valarray<T>
            row;  // Making empty row which will be inserted in vector
        row.resize(shape.second);  // By default all elements are zero
        A.push_back(row);          // Insert new row in vector
    }
    return;
}

Variable Documentation

MIN_DISTANCE

constexpr double machine_learning::MIN_DISTANCE = 1e-4

constexpr

Minimum average distance of image nodes