源代码实现
web：https://github.com/JustGlowing/minisom/blob/master/minisom.py
直接附上代码：
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')
