minisom.py

from math import sqrt

from numpy import (array, unravel_index, nditer, linalg, random, subtract, max,
                   power, exp, pi, zeros, ones, arange, outer, meshgrid, dot,
                   logical_and, mean, std, cov, argsort, linspace, transpose,
                   einsum, prod, nan, sqrt, hstack, diff, argmin, multiply)
from numpy import sum as npsum
from numpy.linalg import norm
from collections import defaultdict, Counter
from warnings import warn
from sys import stdout
from time import time
from datetime import timedelta
import pickle
import os

# 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 _build_iteration_indexes(data_len, num_iterations,
                             verbose=False, random_generator=None):
    """Returns an iterable with the indexes of the samples
    to pick at each iteration of the training.

    If random_generator is not None, it must be an instalce
    of numpy.random.RandomState and it will be used
    to randomize the order of the samples."""
    iterations = arange(num_iterations) % data_len
    if random_generator:
        random_generator.shuffle(iterations)
    if verbose:
        return _wrap_index__in_verbose(iterations)
    else:
        return iterations


def _wrap_index__in_verbose(iterations):
    """Yields the values in iterations printing the status on the stdout."""
    m = len(iterations)
    digits = len(str(m))
    progress = '\r [ {s:{d}} / {m} ] {s:3.0f}% - ? it/s'
    progress = progress.format(m=m, d=digits, s=0)
    stdout.write(progress)
    beginning = time()
    stdout.write(progress)
    for i, it in enumerate(iterations):
        yield it
        sec_left = ((m-i+1) * (time() - beginning)) / (i+1)
        time_left = str(timedelta(seconds=sec_left))[:7]
        progress = '\r [ {i:{d}} / {m} ]'.format(i=i+1, d=digits, m=m)
        progress += ' {p:3.0f}%'.format(p=100*(i+1)/m)
        progress += ' - {time_left} left '.format(time_left=time_left)
        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', topology='rectangular',
                 activation_distance='euclidean', 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 : string, optional (default='gaussian')
            Function that weights the neighborhood of a position in the map.
            Possible values: 'gaussian', 'mexican_hat', 'bubble', 'triangle'

        topology : string, optional (default='rectangular')
            Topology of the map.
            Possible values: 'rectangular', 'hexagonal'

        activation_distance : string, optional (default='euclidean')
            Distance used to activate the map.
            Possible values: 'euclidean', 'cosine', 'manhattan', 'chebyshev'

        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
        self._weights /= linalg.norm(self._weights, axis=-1, keepdims=True)

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

        if topology not in ['hexagonal', 'rectangular']:
            msg = '%s not supported only hexagonal and rectangular available'
            raise ValueError(msg % topology)
        self.topology = topology
        self._xx, self._yy = meshgrid(self._neigx, self._neigy)
        self._xx = self._xx.astype(float)
        self._yy = self._yy.astype(float)
        if topology == 'hexagonal':
            self._xx[::-2] -= 0.5
            if neighborhood_function in ['triangle']:
                warn('triangle neighborhood function does not ' +
                     'take in account hexagonal topology')

        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
                                                    or sigma < 1):
            warn('sigma should be an integer >=1 when triangle or bubble' +
                 'are used as neighborhood function')

        self.neighborhood = neig_functions[neighborhood_function]

        distance_functions = {'euclidean': self._euclidean_distance,
                              'cosine': self._cosine_distance,
                              'manhattan': self._manhattan_distance,
                              'chebyshev': self._chebyshev_distance}

        if activation_distance not in distance_functions:
            msg = '%s not supported. Distances available: %s'
            raise ValueError(msg % (activation_distance,
                                    ', '.join(distance_functions.keys())))

        self._activation_distance = distance_functions[activation_distance]

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

    def get_euclidean_coordinates(self):
        """Returns the position of the neurons on an euclidean
        plane that reflects the chosen topology in two meshgrids xx and yy.
        Neuron with map coordinates (1, 4) has coordinate (xx[1, 4], yy[1, 4])
        in the euclidean plane.

        Only useful if the topology chosen is not rectangular.
        """
        return self._xx.T, self._yy.T

    def convert_map_to_euclidean(self, xy):
        """Converts map coordinates into euclidean coordinates
        that reflects the chosen topology.

        Only useful if the topology chosen is not rectangular.
        """
        return self._xx.T[xy], self._yy.T[xy]

    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."""
        self._activation_map = self._activation_distance(x, self._weights)

    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*sigma*sigma
        ax = exp(-power(self._xx-self._xx.T[c], 2)/d)
        ay = exp(-power(self._yy-self._yy.T[c], 2)/d)
        return (ax * ay).T  # the external product gives a matrix

    def _mexican_hat(self, c, sigma):
        """Mexican hat centered in c."""
        p = power(self._xx-self._xx.T[c], 2) + power(self._yy-self._yy.T[c], 2)
        d = 2*sigma*sigma
        return (exp(-p/d)*(1-2/d*p)).T

    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 _cosine_distance(self, x, w):
        num = (w * x).sum(axis=2)
        denum = multiply(linalg.norm(w, axis=2), linalg.norm(x))
        return 1 - num / (denum+1e-8)

    def _euclidean_distance(self, x, w):
        return linalg.norm(subtract(x, w), axis=-1)

    def _manhattan_distance(self, x, w):
        return linalg.norm(subtract(x, w), ord=1, axis=-1)

    def _chebyshev_distance(self, x, w):
        return max(subtract(x, w), axis=-1)

    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, t, max_iteration):
        """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).
        t : int
            Iteration index
        max_iteration : int
            Maximum number of training itarations.
        """
        eta = self._decay_function(self._learning_rate, t, max_iteration)
        # sigma and learning rate decrease with the same rule
        sig = self._decay_function(self._sigma, t, max_iteration)
        # improves the performances
        g = self.neighborhood(win, sig)*eta
        # w_new = eta * neighborhood_function * (x-w)
        self._weights += einsum('ij, ijk->ijk', g, x-self._weights)

    def quantization(self, data):
        """Assigns a code book (weights vector of the winning neuron)
        to each sample in data."""
        self._check_input_len(data)
        winners_coords = argmin(self._distance_from_weights(data), axis=1)
        return self._weights[unravel_index(winners_coords,
                                           self._weights.shape[:2])]

    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]
            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(self, data, num_iteration, random_order=False, verbose=False):
        """Trains the SOM.

        Parameters
        ----------
        data : np.array or list
            Data matrix.

        num_iteration : int
            Maximum number of iterations (one iteration per sample).
        random_order : bool (default=False)
            If True, samples are picked in random order.
            Otherwise the samples are picked sequentially.

        verbose : bool (default=False)
            If True the status of the training
            will be printed at each iteration.
        """
        self._check_iteration_number(num_iteration)
        self._check_input_len(data)
        random_generator = None
        if random_order:
            random_generator = self._random_generator
        iterations = _build_iteration_indexes(len(data), num_iteration,
                                              verbose, random_generator)
        for t, iteration in enumerate(iterations):
            self.update(data[iteration], self.winner(data[iteration]),
                        t, num_iteration)
        if verbose:
            print('\n quantization error:', self.quantization_error(data))

    def train_random(self, data, num_iteration, verbose=False):
        """Trains the SOM picking samples at random from data.

        Parameters
        ----------
        data : np.array or list
            Data matrix.

        num_iteration : int
            Maximum number of iterations (one iteration per sample).

        verbose : bool (default=False)
            If True the status of the training
            will be printed at each iteration.
        """
        self.train(data, num_iteration, random_order=True, verbose=verbose)

    def train_batch(self, data, num_iteration, verbose=False):
        """Trains the SOM using all the vectors in data sequentially.

        Parameters
        ----------
        data : np.array or list
            Data matrix.

        num_iteration : int
            Maximum number of iterations (one iteration per sample).

        verbose : bool (default=False)
            If True the status of the training
            will be printed at each iteration.
        """
        self.train(data, num_iteration, random_order=False, verbose=verbose)

    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. Note that this method uses
        the euclidean distance."""
        um = zeros((self._weights.shape[0],
                    self._weights.shape[1],
                    8))  # 2 spots more for hexagonal topology

        ii = [[0, -1, -1, -1, 0, 1, 1, 1]]*2
        jj = [[-1, -1, 0, 1, 1, 1, 0, -1]]*2

        if self.topology == 'hexagonal':
            ii = [[1, 1, 1, 0, -1, 0], [0, 1, 0, -1, -1, -1]]
            jj = [[1, 0, -1, -1, 0, 1], [1, 0, -1, -1, 0, 1]]

        for x in range(self._weights.shape[0]):
            for y in range(self._weights.shape[1]):
                w_2 = self._weights[x, y]
                e = y % 2 == 0   # only used on hexagonal topology
                for k, (i, j) in enumerate(zip(ii[e], jj[e])):
                    if (x+i >= 0 and x+i < self._weights.shape[0] and
                            y+j >= 0 and y+j < self._weights.shape[1]):
                        w_1 = self._weights[x+i, y+j]
                        um[x, y, k] = fast_norm(w_2-w_1)

        um = um.sum(axis=2)
        return um/um.max()

    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 _distance_from_weights(self, data):
        """Returns a matrix d where d[i,j] is the euclidean distance between
        data[i] and the j-th weight.
        """
        input_data = array(data)
        weights_flat = self._weights.reshape(-1, self._weights.shape[2])
        input_data_sq = power(input_data, 2).sum(axis=1, keepdims=True)
        weights_flat_sq = power(weights_flat, 2).sum(axis=1, keepdims=True)
        cross_term = dot(input_data, weights_flat.T)
        return sqrt(-2 * cross_term + input_data_sq + weights_flat_sq.T)

    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)
        return norm(data-self.quantization(data), axis=1).mean()

    def topographic_error(self, data):
        """Returns the topographic error computed by finding
        the best-matching and second-best-matching neuron in the map
        for each input and then evaluating the positions.

        A sample for which these two nodes are not adjacent counts as
        an error. The topographic error is given by the
        the total number of errors divided by the total of samples.

        If the topographic error is 0, no error occurred.
        If 1, the topology was not preserved for any of the samples."""
        self._check_input_len(data)
        if self.topology == 'hexagonal':
            msg = 'Topographic error not implemented for hexagonal topology.'
            raise NotImplementedError(msg)
        total_neurons = prod(self._activation_map.shape)
        if total_neurons == 1:
            warn('The topographic error is not defined for a 1-by-1 map.')
            return nan

        t = 1.42
        # b2mu: best 2 matching units
        b2mu_inds = argsort(self._distance_from_weights(data), axis=1)[:, :2]
        b2my_xy = unravel_index(b2mu_inds, self._weights.shape[:2])
        b2mu_x, b2mu_y = b2my_xy[0], b2my_xy[1]
        dxdy = hstack([diff(b2mu_x), diff(b2mu_y)])
        distance = norm(dxdy, axis=1)
        return (distance > t).mean()

    def win_map(self, data, return_indices=False):
        """Returns a dictionary wm where wm[(i,j)] is a list with:
        - all the patterns that have been mapped to the position (i,j),
          if return_indices=False (default)
        - all indices of the elements that have been mapped to the
          position (i,j) if return_indices=True"""
        self._check_input_len(data)
        winmap = defaultdict(list)
        for i, x in enumerate(data):
            winmap[self.winner(x)].append(i if return_indices else 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 : np.array or list
            Data matrix.

        label : np.array or list
            Labels for each sample in data.
        """
        self._check_input_len(data)
        if not len(data) == len(labels):
            raise ValueError('data and labels must have the same length.')
        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, 1))  # 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_euclidean_distance(self):
        x = zeros((1, 2))
        w = ones((2, 2, 2))
        d = self.som._euclidean_distance(x, w)
        assert_array_almost_equal(d, [[1.41421356, 1.41421356],
                                      [1.41421356, 1.41421356]])

    def test_cosine_distance(self):
        x = zeros((1, 2))
        w = ones((2, 2, 2))
        d = self.som._cosine_distance(x, w)
        assert_array_almost_equal(d, [[1., 1.],
                                      [1., 1.]])

    def test_manhattan_distance(self):
        x = zeros((1, 2))
        w = ones((2, 2, 2))
        d = self.som._manhattan_distance(x, w)
        assert_array_almost_equal(d, [[2., 2.],
                                      [2., 2.]])

    def test_chebyshev_distance(self):
        x = array([1, 3])
        w = ones((2, 2, 2))
        d = self.som._chebyshev_distance(x, w)
        assert_array_almost_equal(d, [[2., 2.],
                                      [2., 2.]])

    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_unavailable_distance_function(self):
        with self.assertRaises(ValueError):
            MiniSom(5, 5, 1, activation_distance='ridethewave')

    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_win_map_indices(self):
        winners = self.som.win_map([[5.0], [2.0]], return_indices=True)
        assert winners[(2, 3)] == [0]
        assert winners[(1, 1)] == [1]

    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
        with self.assertRaises(ValueError):
            self.som.labels_map([[5.0]], ['a', 'b'])

    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_distance_from_weights(self):
        data = arange(-5, 5).reshape(-1, 1)
        weights = self.som._weights.reshape(-1, self.som._weights.shape[2])
        distances = self.som._distance_from_weights(data)
        for i in range(len(data)):
            for j in range(len(weights)):
                assert(distances[i][j] == norm(data[i] - weights[j]))

    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_topographic_error(self):
        # 5 will have bmu_1 in (2,3) and bmu_2 in (2, 4)
        # which are in the same neighborhood
        self.som._weights[2, 4] = 6.0
        # 15 will have bmu_1 in (4, 4) and bmu_2 in (0, 0)
        # which are not in the same neighborhood
        self.som._weights[4, 4] = 15.0
        self.som._weights[0, 0] = 14.
        assert self.som.topographic_error([[5]]) == 0.0
        assert self.som.topographic_error([[15]]) == 1.0

        self.som.topology = 'hexagonal'
        with self.assertRaises(NotImplementedError):
            assert self.som.topographic_error([[5]]) == 0.0
        self.som.topology = 'rectangular'

    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(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(data, 10, random_order=True)
        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.]]))

        som = MiniSom(2, 2, 2, topology='hexagonal', random_seed=1)
        som._weights = array([[[1.,  0.], [0., 1.]], [[1., 0.], [0., 1.]]])
        assert_array_equal(som.distance_map(), array([[.5, 1.], [1., .5]]))

    def test_pickling(self):
        with open('som.p', 'wb') as outfile:
            pickle.dump(self.som, outfile)
        with open('som.p', 'rb') as infile:
            pickle.load(infile)
        os.remove('som.p')