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| { | ||
| "cells": [], | ||
| "metadata": {}, | ||
| "nbformat": 4, | ||
| "nbformat_minor": 2 | ||
| } |
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| { | ||
| "cells": [ | ||
| { | ||
| "cell_type": "code", | ||
| "execution_count": 1, | ||
| "metadata": { | ||
| "collapsed": true | ||
| }, | ||
| "outputs": [], | ||
| "source": [ | ||
| "import numpy as np" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "code", | ||
| "execution_count": 2, | ||
| "metadata": { | ||
| "collapsed": true | ||
| }, | ||
| "outputs": [], | ||
| "source": [ | ||
| "# create synthetic batch of z and ASSUME that there are 10 examples per class in a batch of 50\n", | ||
| "classes=5\n", | ||
| "examples_per_class = 10\n", | ||
| "batch_size = classes*examples_per_class\n", | ||
| "z_dim = 5\n", | ||
| "\n", | ||
| "# here rows are embeddings, columns are dimensions of the embedding\n", | ||
| "z_batch = np.random.randn(batch_size,z_dim)" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "code", | ||
| "execution_count": 3, | ||
| "metadata": {}, | ||
| "outputs": [], | ||
| "source": [ | ||
| "# this is mu_j in the paper:\n", | ||
| "class_means = np.zeros((z_dim,classes)) \n", | ||
| "\n", | ||
| "for i in range(0,batch_size, examples_per_class):\n", | ||
| " \n", | ||
| " class_means[(int(i/examples_per_class))] = z_batch[i:i+examples_per_class].mean()\n", | ||
| " " | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "code", | ||
| "execution_count": 4, | ||
| "metadata": {}, | ||
| "outputs": [], | ||
| "source": [ | ||
| "# I expect you can combine this loop that calculates intra_spread with the one for mu_j above easily enough, \n", | ||
| "# to save computation\n", | ||
| "\n", | ||
| "cum_diff_sq = 0\n", | ||
| "\n", | ||
| "for i in range(class_means.shape[0]):\n", | ||
| " \n", | ||
| " z = z_batch[i*examples_per_class:i*examples_per_class+examples_per_class] # extract per class data\n", | ||
| " mu = class_means[i] # extract class[i] mean\n", | ||
| " mu_diff = mu-z # calculate difference between the data and its corresponding class mean\n", | ||
| " # next calculate the per row squared L2 norm (i.e. dot product)\n", | ||
| " mu_diff_norm = np.asarray([np.dot(mu_diff[i].T, mu_diff[i]) for i in range(mu_diff.shape[0])])\n", | ||
| " cum_diff_sq += mu_diff_norm.sum() # sum these squared norms over examples AND over classes\n", | ||
| "\n", | ||
| "intra_spread = cum_diff_sq/batch_size # divide by total number of datapoints in batch\n" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "code", | ||
| "execution_count": 5, | ||
| "metadata": {}, | ||
| "outputs": [], | ||
| "source": [ | ||
| "# for inter-spread you essentially need to find the min of all pairwise distances\n", | ||
| "# you might want to look into efficient ways to compute this (there might be a keras function already, mind)\n", | ||
| "# if you only have a few classes then maybe not a big deal.\n", | ||
| "\n", | ||
| "inter_separation = np.min([np.dot((class_means[i] - class_means[j]).T,(class_means[i] - class_means[j])) for i in range(class_means.shape[0]) for j in range(class_means.shape[0]) if i > j])\n", | ||
| "\n" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "code", | ||
| "execution_count": 6, | ||
| "metadata": {}, | ||
| "outputs": [], | ||
| "source": [ | ||
| "ii_loss = intra_spread - inter_separation" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "code", | ||
| "execution_count": null, | ||
| "metadata": {}, | ||
| "outputs": [], | ||
| "source": [] | ||
| }, | ||
| { | ||
| "cell_type": "code", | ||
| "execution_count": null, | ||
| "metadata": { | ||
| "collapsed": true | ||
| }, | ||
| "outputs": [], | ||
| "source": [] | ||
| } | ||
| ], | ||
| "metadata": { | ||
| "kernelspec": { | ||
| "display_name": "Python 3", | ||
| "language": "python", | ||
| "name": "python3" | ||
| }, | ||
| "language_info": { | ||
| "codemirror_mode": { | ||
| "name": "ipython", | ||
| "version": 3 | ||
| }, | ||
| "file_extension": ".py", | ||
| "mimetype": "text/x-python", | ||
| "name": "python", | ||
| "nbconvert_exporter": "python", | ||
| "pygments_lexer": "ipython3", | ||
| "version": "3.6.3" | ||
| } | ||
| }, | ||
| "nbformat": 4, | ||
| "nbformat_minor": 2 | ||
| } |
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