{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# MDS\n", "[大图](mds.html), [下载](origin_files/mds.ipynb)" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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3.605551 4.123106 14.212670 12.000000 14.866069 5.656854 \n", "\n", " 18 19 \n", "0 6.403124 12.083046 \n", "1 7.615773 14.317821 \n", "2 14.317821 14.560220 \n", "3 6.324555 7.810250 \n", "4 5.099020 9.433981 \n", "5 7.071068 5.385165 \n", "6 7.280110 2.000000 \n", "7 13.000000 16.970563 \n", "8 6.708204 13.341664 \n", "9 14.142136 16.643317 \n", "10 7.615773 3.000000 \n", "11 5.000000 5.656854 \n", "12 4.472136 3.605551 \n", "13 8.944272 4.123106 \n", "14 11.180340 14.212670 \n", "15 13.892444 12.000000 \n", "16 8.602325 14.866069 \n", "17 11.704700 5.656854 \n", "18 0.000000 7.000000 \n", "19 7.000000 0.000000 " ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import numpy as np\n", "import pandas as pd\n", "from matplotlib import pyplot as plt\n", "from matplotlib.collections import LineCollection\n", "\n", "from sklearn import manifold\n", "from sklearn.metrics import euclidean_distances\n", "from sklearn.decomposition import PCA\n", "\n", "n_samples = 20\n", "seed = np.random.RandomState(seed=3)\n", "X_true = seed.randint(0, 20, 2 * n_samples).astype(np.float)\n", "X_true = X_true.reshape((n_samples, 2))\n", "# Center the data\n", "X_true -= X_true.mean()\n", "\n", "similarities = euclidean_distances(X_true)\n", "pd.DataFrame(similarities)" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": true }, "outputs": [], "source": [ "mds = manifold.MDS(n_components=2, max_iter=3000, eps=1e-9, random_state=seed,\n", " dissimilarity=\"precomputed\", n_jobs=1)\n", "pos = mds.fit(similarities).embedding_\n", "\n", "nmds = manifold.MDS(n_components=2, metric=False, max_iter=3000, eps=1e-12,\n", " dissimilarity=\"precomputed\", random_state=seed, n_jobs=1,\n", " n_init=1)\n", "npos = nmds.fit_transform(similarities, init=pos)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "dissimilarity=\"precomputed\"表示输入的是已经计算好的距离矩阵 \n", "metric=False表示是分类数据，metric=True表示是连续数据 \n", "\n" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "1.6871996034640421e-07" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "mds.stress_#压力值，可以用来计算应当降为多少维" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# Rescale the data\n", "pos *= np.sqrt((X_true ** 2).sum()) / np.sqrt((pos ** 2).sum())\n", "npos *= np.sqrt((X_true ** 2).sum()) / np.sqrt((npos ** 2).sum())" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# Rotate the data\n", "pca = PCA(n_components=2)\n", "X_true = pca.fit_transform(X_true)\n", "\n", "pos = pca.fit_transform(pos)\n", "\n", "npos = pca.fit_transform(npos)\n", "\n" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = plt.figure(1)\n", "ax = plt.axes([0., 0., 1., 1.])\n", "\n", "s = 100\n", "plt.scatter(X_true[:, 0], X_true[:, 1], color='navy', s=s, lw=0,\n", " label='True Position')\n", "\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.scatter(pos[:, 0], pos[:, 1], color='turquoise', s=s, lw=0, label='MDS')\n", "\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.scatter(npos[:, 0], npos[:, 1], color='darkorange', s=s, lw=0, label='NMDS')\n", "plt.show()" ] } ], "metadata": { "celltoolbar": "Raw Cell Format", "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": "3.6.2" } }, "nbformat": 4, "nbformat_minor": 1 }