first version

.gitignore

@@ -1 +1,3 @@
 .idea
+__pycache__/
+*.pyc

dist.py

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+import math
+
+
+def euclid_squared(a, b):
+ return sum((x_a - x_b) ** 2 for x_a, x_b in zip(a, b))
+
+
+def euclid(a, b):
+ return math.sqrt(euclid_squared(a, b))

lbg.py

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+#
+# Python 3!
+#
+
+import dist
+from functools import reduce
+from collections import defaultdict
+
+_size_data = 0
+_dim = 0
+
+
+def generate_codebook(data, size_codebook, epsilon=0.00001):
+ global _size_data, _dim
+
+ _size_data = len(data)
+ assert _size_data > 0
+
+ _dim = len(data[0])
+ assert _dim > 0
+
+ codebook = []
+ codebook_abs_weights = [_size_data]
+ codebook_rel_weights = [1.0]
+
+ # calculate initial codevector: average vector of whole input data
+ c0 = avg_vec_of_vecs(data, _dim, _size_data)
+ codebook.append(c0)
+
+ while len(codebook) < size_codebook:
+ avg_dist = avg_distortion_c0(c0, data)
+
+ codebook, codebook_abs_weights, codebook_rel_weights = split_codebook(data, codebook,
+ codebook_abs_weights,
+ codebook_rel_weights,
+ epsilon, avg_dist)
+
+ return codebook, codebook_abs_weights, codebook_rel_weights
+
+
+def split_codebook(data, codebook, abs_weights, rel_weights, epsilon, initial_avg_dist):
+ # split codevectors
+ new_codevectors = []
+ for c in codebook:
+ c1 = new_codevector(c, epsilon)
+ c2 = new_codevector(c, -epsilon)
+ new_codevectors.extend((c1, c2))
+
+ codebook = new_codevectors
+ len_codebook = len(codebook)
+ abs_weights = [0] * len_codebook
+ rel_weights = [0.0] * len_codebook
+
+ # print('> splitting to size', len_codebook)
+
+ avg_dist = 0
+ err = epsilon + 1
+ num_iter = 0
+ while err > epsilon:
+ # find closest codevectors for each vector in data
+ closest_c_list = [None] * _size_data
+ vecs_near_c = defaultdict(list)
+ vec_idxs_near_c = defaultdict(list)
+ for i, vec in enumerate(data):
+ min_dist = None
+ closest_c_index = None
+ for i_c, c in enumerate(codebook):
+ d = dist.euclid_squared(vec, c)
+ if min_dist is None or d < min_dist: # found new closest codevector
+ min_dist = d
+ closest_c_list[i] = c
+ closest_c_index = i_c
+ vecs_near_c[closest_c_index].append(vec)
+ vec_idxs_near_c[closest_c_index].append(i)
+
+ # update codebook
+ for i_c in range(len_codebook):
+ vecs = vecs_near_c.get(i_c) or []
+ num_vecs_near_c = len(vecs)
+ if num_vecs_near_c > 0:
+ new_c = avg_vec_of_vecs(vecs, _dim)
+ codebook[i_c] = new_c
+ for i in vec_idxs_near_c[i_c]:
+ closest_c_list[i] = new_c
+ abs_weights[i_c] = num_vecs_near_c
+ rel_weights[i_c] = num_vecs_near_c / _size_data
+
+ # recalculate average distortion value
+ prev_avg_dist = avg_dist if avg_dist > 0 else initial_avg_dist
+ avg_dist = avg_distortion_c_list(closest_c_list, data)
+ err = (prev_avg_dist - avg_dist) / prev_avg_dist
+ # print(closest_c_list)
+ # print('> iteration', num_iter, 'avg_dist', avg_dist, 'prev_avg_dist', prev_avg_dist, 'err', err)
+
+ num_iter += 1
+
+ return codebook, abs_weights, rel_weights
+
+
+def avg_vec_of_vecs(vecs, dim=None, size=None):
+ size = size or len(vecs)
+ dim = dim or len(vecs[0])
+ avg_vec = [0.0] * dim
+ for vec in vecs:
+ for i, x in enumerate(vec):
+ avg_vec[i] += x / size
+
+ return avg_vec
+
+
+def new_codevector(c, e):
+ return [x * (1.0 + e) for x in c]
+
+
+def avg_distortion_c0(c0, data, size=None):
+ size = size or _size_data
+ return reduce(lambda s, d: s + d / size,
+ (dist.euclid_squared(c0, vec)
+ for vec in data),
+ 0.0)
+
+
+def avg_distortion_c_list(c_list, data, size=None):
+ size = size or _size_data
+ return reduce(lambda s, d: s + d / size,
+ (dist.euclid_squared(c_i, data[i])
+ for i, c_i in enumerate(c_list)),
+ 0.0)

lbg_test.ipynb

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+{
+ "cells": [
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "generating codebook for size 1\noutput:\n> [0.375, -0.375, 0.6624999999999999], abs_weight=8, rel_weight=1.000000\ngenerating codebook for size 2\noutput:\n> [0.5, 1.625, 3.4499999999999997], abs_weight=4, rel_weight=0.500000\n> [0.25, -2.375, -2.125], abs_weight=4, rel_weight=0.500000\ngenerating codebook for size 4\noutput:\n> [-0.25, 2.0, 5.3], abs_weight=2, rel_weight=0.250000\n> [1.25, 1.25, 1.6], abs_weight=2, rel_weight=0.250000\n> [1.0, -2.5, -2.833333333333333], abs_weight=3, rel_weight=0.375000\n> [-2.0, -2.0, 0.0], abs_weight=1, rel_weight=0.125000\ngenerating codebook for size 8\noutput:\n> [1.0, 2.0, 5.6], abs_weight=1, rel_weight=0.125000\n> [-1.5, 2.0, 5.0], abs_weight=1, rel_weight=0.125000\n> [1.0, 1.0, 2.0], abs_weight=1, rel_weight=0.125000\n> [1.5, 1.5, 1.2], abs_weight=1, rel_weight=0.125000\n> [1.0, -2.5, -4.5], abs_weight=1, rel_weight=0.125000\n> [1.0, -2.5, -2.0], abs_weight=2, rel_weight=0.250000\n> [-2.00002, -2.00002, 0.0], abs_weight=0, rel_weight=0.000000\n> [-2.0, -2.0, 0.0], abs_weight=1, rel_weight=0.125000\n"
+ ]
+ }
+ ],
+ "source": [
+ "import lbg\n",
+ "\n",
+ "testdata = [(-1.5, 2.0, 5.0),\n",
+ " (-2.0, -2.0, 0.0),\n",
+ " (1.0, 1.0, 2.0),\n",
+ " (1.5, 1.5, 1.2),\n",
+ " (1.0, 2.0, 5.6),\n",
+ " (1.0, -2.0, -2.0),\n",
+ " (1.0, -3.0, -2.0),\n",
+ " (1.0, -2.5, -4.5)]\n",
+ "\n",
+ "for cb_size in (1, 2, 4, 8):\n",
+ " print('generating codebook for size', cb_size)\n",
+ " cb, cb_abs_w, cb_rel_w = lbg.generate_codebook(testdata, cb_size)\n",
+ " print('output:')\n",
+ " for i, c in enumerate(cb):\n",
+ " print('> %s, abs_weight=%d, rel_weight=%f' % (c, cb_abs_w[i], cb_rel_w[i]))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 32,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "<matplotlib.collections.PathCollection at 0x109484748>"
+ ]
+ },
+ "execution_count": 32,
+ "output_type": "execute_result",
+ "metadata": {}
+ },
+ {
+ "data": {
+ "image/png": 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+ },
+ "output_type": "display_data",
+ "text": [
+ "<matplotlib.figure.Figure at 0x109447710>"
+ ],
+ "metadata": {}
+ }
+ ],
+ "source": [
+ "import random\n",
+ "import matplotlib.pyplot as plt\n",
+ "\n",
+ "import lbg\n",
+ "\n",
+ "%matplotlib inline\n",
+ "\n",
+ "N = 16\n",
+ "SIZE_CODEBOOK = 8\n",
+ "\n",
+ "random.seed(0)\n",
+ "population = [(random.gauss(0, 1), random.gauss(0, 1))\n",
+ " for _ in range(N)]\n",
+ "\n",
+ "plt.scatter([p[0] for p in population], [p[1] for p in population], marker='x', color='blue')\n",
+ "\n",
+ "cb, cb_abs_w, cb_rel_w = lbg.generate_codebook(population, SIZE_CODEBOOK)\n",
+ "plt.scatter([p[0] for p in cb], [p[1] for p in cb], s=[((w+1) ** 5) * 40 for w in cb_rel_w], marker='o', color='red')\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ ""
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ ""
+ ]
+ }
+ ],
+ "metadata": {},
+ "nbformat": 4,
+ "nbformat_minor": 0
+}