{ "cells": [ { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "%matplotlib inline" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n# Sparse CCA Methods\n\nThis script shows how regularised methods can be used to extract sparse solutions to the CCA problem\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "import matplotlib.pyplot as plt\nimport numpy as np\nimport pandas as pd\n\nfrom cca_zoo.data import generate_covariance_data\nfrom cca_zoo.model_selection import GridSearchCV\nfrom cca_zoo.models import PMD, SCCA, ElasticCCA, CCA, PLS, SCCA_ADMM, SpanCCA" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "np.random.seed(42)\nn = 200\np = 100\nq = 100\nview_1_sparsity = 0.1\nview_2_sparsity = 0.1\nlatent_dims = 1\n\n(X, Y), (tx, ty) = generate_covariance_data(\n n,\n view_features=[p, q],\n latent_dims=latent_dims,\n view_sparsity=[view_1_sparsity, view_2_sparsity],\n correlation=[0.9],\n)\ntx /= np.sqrt(n)\nty /= np.sqrt(n)" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def plot_true_weights_coloured(ax, weights, true_weights, title=\"\"):\n ind = np.arange(len(true_weights))\n mask = np.squeeze(true_weights == 0)\n ax.scatter(ind[~mask], weights[~mask], c=\"b\")\n ax.scatter(ind[mask], weights[mask], c=\"r\")\n ax.set_title(title)\n\n\ndef plot_model_weights(wx, wy, tx, ty):\n fig, axs = plt.subplots(2, 2, sharex=True, sharey=True)\n plot_true_weights_coloured(axs[0, 0], tx, tx, title=\"true x weights\")\n plot_true_weights_coloured(axs[0, 1], ty, ty, title=\"true y weights\")\n plot_true_weights_coloured(axs[1, 0], wx, tx, title=\"model x weights\")\n plot_true_weights_coloured(axs[1, 1], wy, ty, title=\"model y weights\")\n plt.tight_layout()\n plt.show()" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "cca = CCA().fit([X, Y])\nplot_model_weights(cca.weights[0], cca.weights[1], tx, ty)" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "pls = PLS().fit([X, Y])\nplot_model_weights(pls.weights[0], pls.weights[1], tx, ty)" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "pmd = PMD(c=[0.5, 0.5]).fit([X, Y])\nplot_model_weights(pmd.weights[0], pmd.weights[1], tx, ty)" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "plt.figure()\nplt.title(\"Objective Convergence\")\nplt.plot(np.array(pmd.track[0][\"objective\"]).T)\nplt.ylabel(\"Objective\")\nplt.xlabel(\"#iterations\")" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "c1 = [0.1, 0.3, 0.7, 0.9]\nc2 = [0.1, 0.3, 0.7, 0.9]\nparam_grid = {\"c\": [c1, c2]}\npmd = GridSearchCV(PMD(), param_grid=param_grid, cv=3, verbose=True).fit([X, Y])" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "pd.DataFrame(pmd.cv_results_)" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "scca = SCCA(c=[1e-3, 1e-3]).fit([X, Y])\nplot_model_weights(scca.weights[0], scca.weights[1], tx, ty)\n\n# Convergence\nplt.figure()\nplt.title(\"Objective Convergence\")\nplt.plot(np.array(scca.track[0][\"objective\"]).T)\nplt.ylabel(\"Objective\")\nplt.xlabel(\"#iterations\")" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "scca_pos = SCCA(c=[1e-3, 1e-3], positive=[True, True]).fit([X, Y])\nplot_model_weights(scca_pos.weights[0], scca_pos.weights[1], tx, ty)\n\n# Convergence\nplt.figure()\nplt.title(\"Objective Convergence\")\nplt.plot(np.array(scca_pos.track[0][\"objective\"]).T)\nplt.ylabel(\"Objective\")\nplt.xlabel(\"#iterations\")" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "elasticcca = ElasticCCA(c=[10000, 10000], l1_ratio=[0.000001, 0.000001]).fit([X, Y])\nplot_model_weights(elasticcca.weights[0], elasticcca.weights[1], tx, ty)\n\n# Convergence\nplt.figure()\nplt.title(\"Objective Convergence\")\nplt.plot(np.array(elasticcca.track[0][\"objective\"]).T)\nplt.ylabel(\"Objective\")\nplt.xlabel(\"#iterations\")" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "scca_admm = SCCA_ADMM(c=[1e-3, 1e-3]).fit([X, Y])\nplot_model_weights(scca_admm.weights[0], scca_admm.weights[1], tx, ty)\n\n# Convergence\nplt.figure()\nplt.title(\"Objective Convergence\")\nplt.plot(np.array(scca_admm.track[0][\"objective\"]).T)\nplt.ylabel(\"Objective\")\nplt.xlabel(\"#iterations\")" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "spancca = SpanCCA(c=[10, 10], max_iter=2000, rank=20).fit([X, Y])\nplot_model_weights(spancca.weights[0], spancca.weights[1], tx, ty)\n\n# Convergence\nplt.figure()\nplt.title(\"Objective Convergence\")\nplt.plot(np.array(spancca.track[0][\"objective\"]).T)\nplt.ylabel(\"Objective\")\nplt.xlabel(\"#iterations\")" ] } ], "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": "3.7.9" } }, "nbformat": 4, "nbformat_minor": 0 }