mysom.py

# The main source of this code belongs to miniSOM library https://github.com/JustGlowing/minisom
# Modified by Ahmad Pouramini and Benyamin Hosseiny
# Modified parts:
# Converging based on delta_W (Weight matrix) (maximun difference or mean difference)
# Various decay fuctions such as exponential and geometrical


from math import sqrt
import matplotlib.pyplot as plt
import numpy as np

from numpy import (array, unravel_index, nditer, linalg, random, subtract,
                   power, exp, pi, zeros, arange, outer, meshgrid, dot, max, abs,
                   logical_and, mean, std, cov, argsort, linspace, transpose)
from collections import defaultdict, Counter
from warnings import warn
from sys import stdout
from time import time

# for unit tests
from numpy.testing import assert_almost_equal, assert_array_almost_equal
from numpy.testing import assert_array_equal
import unittest

"""
    Minimalistic implementation of the Self Organizing Maps (SOM).
"""


def _incremental_index_verbose(m):
    """Yields numbers from 0 to m-1 printing the status on the stdout."""
    progress = f'\r [ {0:{len(str(m))}} / {m} ] {0:3.0f}% ? it/s'
    stdout.write(progress)
    beginning = time()
    for i in range(m):
        yield i
        it_per_sec = (time() - beginning) / (i+1)
        progress = f'\r [ {i+1:{len(str(m))}} / {m} ]'
        progress += f' {100*(i+1)/m:3.0f}%'
        progress += f' {it_per_sec:4.5f} it/s'
        stdout.write(progress)


def fast_norm(x):
    """Returns norm-2 of a 1-D numpy array.

    * faster than linalg.norm in case of 1-D arrays (numpy 1.9.2rc1).
    """
    return sqrt(dot(x, x.T))


def asymptotic_decay(learning_rate, t, max_iter):
    """Decay function of the learning process.
    Parameters
    ----------
    learning_rate : float
        current learning rate.

    t : int
        current iteration.

    max_iter : int
        maximum number of iterations for the training.
    """
    return learning_rate / (1+t/(max_iter/2))


class MiniSom(object):
    def __init__(self, x, y, input_len, sigma=1.0, learning_rate=0.5,
                 decay_function=asymptotic_decay,
                 neighborhood_function='gaussian', random_seed=None):
        """Initializes a Self Organizing Maps.

        A rule of thumb to set the size of the grid for a dimensionality
        reduction task is that it should contain 5*sqrt(N) neurons
        where N is the number of samples in the dataset to analyze.

        E.g. if your dataset has 150 samples, 5*sqrt(150) = 61.23
        hence a map 8-by-8 should perform well.

        Parameters
        ----------
        x : int
            x dimension of the SOM.

        y : int
            y dimension of the SOM.

        input_len : int
            Number of the elements of the vectors in input.

        sigma : float, optional (default=1.0)
            Spread of the neighborhood function, needs to be adequate
            to the dimensions of the map.
            (at the iteration t we have sigma(t) = sigma / (1 + t/T)
            where T is #num_iteration/2)
            learning_rate, initial learning rate
            (at the iteration t we have
            learning_rate(t) = learning_rate / (1 + t/T)
            where T is #num_iteration/2)

        decay_function : function (default=None)
            Function that reduces learning_rate and sigma at each iteration
            the default function is:
                        learning_rate / (1+t/(max_iterarations/2))

            A custom decay function will need to to take in input
            three parameters in the following order:

            1. learning rate
            2. current iteration
            3. maximum number of iterations allowed


            Note that if a lambda function is used to define the decay
            MiniSom will not be pickable anymore.

        neighborhood_function : function, optional (default='gaussian')
            Function that weights the neighborhood of a position in the map
            possible values: 'gaussian', 'mexican_hat', 'bubble'

        random_seed : int, optional (default=None)
            Random seed to use.
        """
        if sigma >= x or sigma >= y:
            warn('Warning: sigma is too high for the dimension of the map.')

        self._random_generator = random.RandomState(random_seed)

        self._learning_rate = learning_rate
        self._sigma = sigma
        self._input_len = input_len
        # random initialization
        self._weights = self._random_generator.rand(x, y, input_len)*2-1

        for i in range(x):
            for j in range(y):
                # normalization
                norm = fast_norm(self._weights[i, j])
                self._weights[i, j] = self._weights[i, j] / norm

        self._activation_map = zeros((x, y))
        self._neigx = arange(x)
        self._neigy = arange(y)  # used to evaluate the neighborhood function
        self._decay_function = decay_function

        neig_functions = {'gaussian': self._gaussian,
                          'mexican_hat': self._mexican_hat,
                          'bubble': self._bubble,
                          'triangle': self._triangle}

        if neighborhood_function not in neig_functions:
            msg = '%s not supported. Functions available: %s'
            raise ValueError(msg % (neighborhood_function,
                                    ', '.join(neig_functions.keys())))

        if neighborhood_function in ['triangle',
                                     'bubble'] and divmod(sigma, 1)[1] != 0:
            warn('sigma should be an integer when triangle or bubble' +
                 'are used as neighborhood function')

        self.neighborhood = neig_functions[neighborhood_function]

    def get_weights(self):
        """Returns the weights of the neural network"""
        return self._weights

    def _activate(self, x):
        """Updates matrix activation_map, in this matrix
           the element i,j is the response of the neuron i,j to x"""
        s = subtract(x, self._weights)  # x - w
        it = nditer(self._activation_map, flags=['multi_index'])
        while not it.finished:
            # || x - w ||
            self._activation_map[it.multi_index] = fast_norm(s[it.multi_index])
            it.iternext()

    def activate(self, x):
        """Returns the activation map to x"""
        self._activate(x)
        return self._activation_map

    def _gaussian(self, c, sigma):
        """Returns a Gaussian centered in c"""
        d = 2*pi*sigma*sigma
        ax = exp(-power(self._neigx-c[0], 2)/d)
        ay = exp(-power(self._neigy-c[1], 2)/d)
        return outer(ax, ay)  # the external product gives a matrix

    def _mexican_hat(self, c, sigma):
        """Mexican hat centered in c"""
        xx, yy = meshgrid(self._neigx, self._neigy)
        p = power(xx-c[0], 2) + power(yy-c[1], 2)
        d = 2*pi*sigma*sigma
        return exp(-p/d)*(1-2/d*p)

    def _bubble(self, c, sigma):
        """Constant function centered in c with spread sigma.
           sigma should be an odd value,
        """
        ax = logical_and(self._neigx > c[0]-sigma,
                         self._neigx < c[0]+sigma)
        ay = logical_and(self._neigy > c[1]-sigma,
                         self._neigy < c[1]+sigma)
        return outer(ax, ay)*1.

    def _triangle(self, c, sigma):
        """Triangular function centered in c with spread sigma."""
        triangle_x = (-abs(c[0] - self._neigx)) + sigma
        triangle_y = (-abs(c[1] - self._neigy)) + sigma
        triangle_x[triangle_x < 0] = 0.
        triangle_y[triangle_y < 0] = 0.
        return outer(triangle_x, triangle_y)

    def _check_iteration_number(self, num_iteration):
        if num_iteration < 1:
            raise ValueError('num_iteration must be > 1')

    def _check_input_len(self, data):
        """Checks that the data in input is of the correct shape."""
        data_len = len(data[0])
        if self._input_len != data_len:
            msg = 'Received %d features, expected %d.' % (data_len,
                                                          self._input_len)
            raise ValueError(msg)

    def winner(self, x):
        """Computes the coordinates of the winning neuron for the sample x"""
        self._activate(x)
        return unravel_index(self._activation_map.argmin(),
                             self._activation_map.shape)

    def update(self, x, win, eta, sig):
        """Updates the weights of the neurons.

        Parameters
        ----------
        x : np.array
            Current pattern to learn
        win : tuple
            Position of the winning neuron for x (array or tuple)
         """
        # improves the performances
        g = self.neighborhood(win, sig) * eta
        it = nditer(g, flags=['multi_index'])

        while not it.finished:
            # eta * neighborhood_function * (x-w)
            x_w = (x - self._weights[it.multi_index])
            self._weights[it.multi_index] += g[it.multi_index] * x_w
            # normalization
            norm = fast_norm(self._weights[it.multi_index])
            self._weights[it.multi_index] = self._weights[it.multi_index] / norm
            it.iternext()

    def quantization(self, data):
        """Assigns a code book (weights vector of the winning neuron)
        to each sample in data."""
        self._check_input_len(data)
        q = zeros(data.shape)
        for i, x in enumerate(data):
            q[i] = self._weights[self.winner(x)]
        return q

    def random_weights_init(self, data):
        """Initializes the weights of the SOM
        picking random samples from data"""
        self._check_input_len(data)
        it = nditer(self._activation_map, flags=['multi_index'])
        while not it.finished:
            rand_i = self._random_generator.randint(len(data))
            self._weights[it.multi_index] = data[rand_i]
            norm = fast_norm(self._weights[it.multi_index])
            self._weights[it.multi_index] = self._weights[it.multi_index]/norm
            it.iternext()

    def pca_weights_init(self, data):
        """Initializes the weights to span the first two principal components.

        This initialization doesn't depend on random processes and
        makes the training process converge faster.

        It is strongly reccomended to normalize the data before initializing
        the weights and use the same normalization for the training data.
        """
        if self._input_len == 1:
            msg = 'The data needs at least 2 features for pca initialization'
            raise ValueError(msg)
        self._check_input_len(data)
        if len(self._neigx) == 1 or len(self._neigy) == 1:
            msg = 'PCA initialization inappropriate:' + \
                  'One of the dimensions of the map is 1.'
            warn(msg)
        pc_length, pc = linalg.eig(cov(transpose(data)))
        pc_order = argsort(pc_length)
        for i, c1 in enumerate(linspace(-1, 1, len(self._neigx))):
            for j, c2 in enumerate(linspace(-1, 1, len(self._neigy))):
                self._weights[i, j] = c1*pc[pc_order[0]] + c2*pc[pc_order[1]]

    def train_random(self, data, num_iteration, verbose=False):
        """Trains the SOM picking samples at random from data"""
        self._check_iteration_number(num_iteration)
        self._check_input_len(data)
        iterations = range(num_iteration)
        if verbose:
            iterations = _incremental_index_verbose(num_iteration)

        for iteration in iterations:
            # pick a random sample
            rand_i = self._random_generator.randint(len(data))
            eta = self._decay_function(self._learning_rate, iteration, num_iteration)
            # sigma and learning rate decrease with the same rule
            sig = self._decay_function(self._sigma, iteration, num_iteration)

            self.update(data[rand_i], self.winner(data[rand_i]),
                        eta, sig)

    def train_batch(self, data, num_iteration, verbose=False):
        """Trains using all the vectors in data sequentially"""
        self._check_iteration_number(num_iteration)
        self._check_input_len(data)
        iterations = range(num_iteration)
        if verbose:
            iterations = _incremental_index_verbose(num_iteration)

        for iteration in iterations:
            idx = iteration % (len(data)-1)
            eta = self._decay_function(self._learning_rate, iteration, num_iteration)
            # sigma and learning rate decrease with the same rule
            sig = self._decay_function(self._sigma, iteration, num_iteration)

            self.update(data[idx], self.winner(data[idx]),
                        eta, sig)

    def train_delta(self, data, delta, max_iteration, verbose=False, decay_lr=None, decay_sigma=None, delta_func='mean'):
        """Trains using all the vectors in data sequentially"""
        # num_iteration = len(data)
        self._check_iteration_number(max_iteration)
        self._check_input_len(data)
        iterations = range(max_iteration)
        if verbose:
            iterations = _incremental_index_verbose(max_iteration)

        delta_w = 1
        eta = self._learning_rate
        sig = self._sigma
        for iteration in iterations:
            # pick a random sample
            old_weights = self._weights.copy()
            
            if decay_lr != None:
              eta = decay_lr(self._learning_rate, iteration, max_iteration)
            else:
              eta = self._decay_function(self._learning_rate, iteration, max_iteration)
            if decay_sigma != None:
              sig = decay_sigma(self._sigma, iteration, max_iteration)             
            else:
              sig = self._decay_function(self._sigma, iteration, max_iteration)

            rand_i = self._random_generator.randint(len(data))
            self.update(data[rand_i], self.winner(data[rand_i]), eta, sig)

            # max_new = np.max(self._weights)
            if delta_func == 'mean':
              delta_w = np.mean(np.abs(old_weights - self._weights))
            else:
              delta_w = np.max(np.abs(old_weights - self._weights))
            #delta_w = np.max(np.abs(old_weights - self._weights))
            if verbose:
              print(f"iteration= {iteration} delta = {delta_w}")
            plt.plot(iteration, delta_w, 'bo')
            plt.xlabel('iteration')
            plt.ylabel('delta_w')

            if delta_w < delta:
                break

    def distance_map(self):
        """Returns the distance map of the weights.
        Each cell is the normalised sum of the distances between
        a neuron and its neighbours."""
        um = zeros((self._weights.shape[0], self._weights.shape[1]))
        it = nditer(um, flags=['multi_index'])
        while not it.finished:
            for ii in range(it.multi_index[0]-1, it.multi_index[0]+2):
                for jj in range(it.multi_index[1]-1, it.multi_index[1]+2):
                    if (ii >= 0 and ii < self._weights.shape[0] and
                            jj >= 0 and jj < self._weights.shape[1]):
                        w_1 = self._weights[ii, jj, :]
                        w_2 = self._weights[it.multi_index]
                        um[it.multi_index] += fast_norm(w_1-w_2)
            it.iternext()
        um = um/um.max()
        return um

    def activation_response(self, data):
        """
            Returns a matrix where the element i,j is the number of times
            that the neuron i,j have been winner.
        """
        self._check_input_len(data)
        a = zeros((self._weights.shape[0], self._weights.shape[1]))
        for x in data:
            a[self.winner(x)] += 1
        return a

    def quantization_error(self, data):
        """Returns the quantization error computed as the average
        distance between each input sample and its best matching unit."""
        self._check_input_len(data)
        error = 0
        for x in data:
            error += fast_norm(x-self._weights[self.winner(x)])
        return error/len(data)

    def win_map(self, data):
        """Returns a dictionary wm where wm[(i,j)] is a list
        with all the patterns that have been mapped in the position i,j."""
        self._check_input_len(data)
        winmap = defaultdict(list)
        for x in data:
            winmap[self.winner(x)].append(x)
        return winmap

    def labels_map(self, data, labels):
        """Returns a dictionary wm where wm[(i,j)] is a dictionary
        that contains the number of samples from a given label
        that have been mapped in position i,j.

        Parameters
        ----------
        data : data matrix

        label : list or array that contains the label of each sample in data.
        """
        self._check_input_len(data)
        winmap = defaultdict(list)
        for x, l in zip(data, labels):
            winmap[self.winner(x)].append(l)
        for position in winmap:
            winmap[position] = Counter(winmap[position])
        return winmap


class TestMinisom(unittest.TestCase):
    def setUp(self):
        self.som = MiniSom(5, 5, 1)
        for i in range(5):
            for j in range(5):
                # checking weights normalization
                assert_almost_equal(1.0, linalg.norm(self.som._weights[i, j]))
        self.som._weights = zeros((5, 5))  # fake weights
        self.som._weights[2, 3] = 5.0
        self.som._weights[1, 1] = 2.0

    def test_decay_function(self):
        assert self.som._decay_function(1., 2., 3.) == 1./(1.+2./(3./2))

    def test_fast_norm(self):
        assert fast_norm(array([1, 3])) == sqrt(1+9)

    def test_check_input_len(self):
        with self.assertRaises(ValueError):
            self.som.train_batch([[1, 2]], 1)

        with self.assertRaises(ValueError):
            self.som.random_weights_init(array([[1, 2]]))

        with self.assertRaises(ValueError):
            self.som._check_input_len(array([[1, 2]]))

        self.som._check_input_len(array([[1]]))
        self.som._check_input_len([[1]])

    def test_unavailable_neigh_function(self):
        with self.assertRaises(ValueError):
            MiniSom(5, 5, 1, neighborhood_function='boooom')

    def test_gaussian(self):
        bell = self.som._gaussian((2, 2), 1)
        assert bell.max() == 1.0
        assert bell.argmax() == 12  # unravel(12) = (2,2)

    def test_mexican_hat(self):
        bell = self.som._mexican_hat((2, 2), 1)
        assert bell.max() == 1.0
        assert bell.argmax() == 12  # unravel(12) = (2,2)

    def test_bubble(self):
        bubble = self.som._bubble((2, 2), 1)
        assert bubble[2, 2] == 1
        assert sum(sum(bubble)) == 1

    def test_triangle(self):
        bubble = self.som._triangle((2, 2), 1)
        assert bubble[2, 2] == 1
        assert sum(sum(bubble)) == 1

    def test_win_map(self):
        winners = self.som.win_map([[5.0], [2.0]])
        assert winners[(2, 3)][0] == [5.0]
        assert winners[(1, 1)][0] == [2.0]

    def test_labels_map(self):
        labels_map = self.som.labels_map([[5.0], [2.0]], ['a', 'b'])
        assert labels_map[(2, 3)]['a'] == 1
        assert labels_map[(1, 1)]['b'] == 1

    def test_activation_reponse(self):
        response = self.som.activation_response([[5.0], [2.0]])
        assert response[2, 3] == 1
        assert response[1, 1] == 1

    def test_activate(self):
        assert self.som.activate(5.0).argmin() == 13.0  # unravel(13) = (2,3)

    def test_quantization_error(self):
        assert self.som.quantization_error([[5], [2]]) == 0.0
        assert self.som.quantization_error([[4], [1]]) == 1.0

    def test_quantization(self):
        q = self.som.quantization(array([[4], [2]]))
        assert q[0] == 5.0
        assert q[1] == 2.0

    def test_random_seed(self):
        som1 = MiniSom(5, 5, 2, sigma=1.0, learning_rate=0.5, random_seed=1)
        som2 = MiniSom(5, 5, 2, sigma=1.0, learning_rate=0.5, random_seed=1)
        # same initialization
        assert_array_almost_equal(som1._weights, som2._weights)
        data = random.rand(100, 2)
        som1 = MiniSom(5, 5, 2, sigma=1.0, learning_rate=0.5, random_seed=1)
        som1.train_random(data, 10)
        som2 = MiniSom(5, 5, 2, sigma=1.0, learning_rate=0.5, random_seed=1)
        som2.train_random(data, 10)
        # same state after training
        assert_array_almost_equal(som1._weights, som2._weights)

    def test_train_batch(self):
        som = MiniSom(5, 5, 2, sigma=1.0, learning_rate=0.5, random_seed=1)
        data = array([[4, 2], [3, 1]])
        q1 = som.quantization_error(data)
        som.train_batch(data, 10)
        assert q1 > som.quantization_error(data)

        data = array([[1, 5], [6, 7]])
        q1 = som.quantization_error(data)
        som.train_batch(data, 10, verbose=True)
        assert q1 > som.quantization_error(data)

    def test_train_random(self):
        som = MiniSom(5, 5, 2, sigma=1.0, learning_rate=0.5, random_seed=1)
        data = array([[4, 2], [3, 1]])
        q1 = som.quantization_error(data)
        som.train_random(data, 10)
        assert q1 > som.quantization_error(data)

        data = array([[1, 5], [6, 7]])
        q1 = som.quantization_error(data)
        som.train_random(data, 10, verbose=True)
        assert q1 > som.quantization_error(data)

    def test_random_weights_init(self):
        som = MiniSom(2, 2, 2, random_seed=1)
        som.random_weights_init(array([[1.0, .0]]))
        for w in som._weights:
            assert_array_equal(w[0], array([1.0, .0]))

    def test_pca_weights_init(self):
        som = MiniSom(2, 2, 2)
        som.pca_weights_init(array([[1.,  0.], [0., 1.], [1., 0.], [0., 1.]]))
        expected = array([[[0., -1.41421356], [1.41421356, 0.]],
                          [[-1.41421356, 0.], [0., 1.41421356]]])
        assert_array_almost_equal(som._weights, expected)

    def test_distance_map(self):
        som = MiniSom(2, 2, 2, random_seed=1)
        som._weights = array([[[1.,  0.], [0., 1.]], [[1., 0.], [0., 1.]]])
        assert_array_equal(som.distance_map(), array([[1., 1.], [1., 1.]]))