From 1650f2129d8e251499a9bd8e533c8b5b1be53b73 Mon Sep 17 00:00:00 2001 From: Tuan Vu Date: Sun, 3 Jul 2016 00:21:45 -0700 Subject: [PATCH] KD tree --- .../quiz-KD-trees-checkpoint.ipynb | 519 ++++++++++++++++++ .../Screen Shot 2016-07-02 at 11.56.04 PM.png | Bin 0 -> 83742 bytes .../Screen Shot 2016-07-02 at 11.56.09 PM.png | Bin 0 -> 25010 bytes .../Screen Shot 2016-07-02 at 11.56.17 PM.png | Bin 0 -> 48598 bytes .../Screen Shot 2016-07-03 at 12.10.42 AM.png | Bin 0 -> 49037 bytes .../Screen Shot 2016-07-03 at 12.14.16 AM.png | Bin 0 -> 55471 bytes .../Screen Shot 2016-07-03 at 12.16.20 AM.png | Bin 0 -> 34718 bytes .../Screen Shot 2016-07-03 at 12.16.46 AM.png | Bin 0 -> 48422 bytes .../lecture/week2/quiz-KD-trees.ipynb | 519 ++++++++++++++++++ 9 files changed, 1038 insertions(+) create mode 100644 machine_learning/4_clustering_and_retrieval/lecture/week2/.ipynb_checkpoints/quiz-KD-trees-checkpoint.ipynb create mode 100644 machine_learning/4_clustering_and_retrieval/lecture/week2/images/Screen Shot 2016-07-02 at 11.56.04 PM.png create mode 100644 machine_learning/4_clustering_and_retrieval/lecture/week2/images/Screen Shot 2016-07-02 at 11.56.09 PM.png create mode 100644 machine_learning/4_clustering_and_retrieval/lecture/week2/images/Screen Shot 2016-07-02 at 11.56.17 PM.png create mode 100644 machine_learning/4_clustering_and_retrieval/lecture/week2/images/Screen Shot 2016-07-03 at 12.10.42 AM.png create mode 100644 machine_learning/4_clustering_and_retrieval/lecture/week2/images/Screen Shot 2016-07-03 at 12.14.16 AM.png create mode 100644 machine_learning/4_clustering_and_retrieval/lecture/week2/images/Screen Shot 2016-07-03 at 12.16.20 AM.png create mode 100644 machine_learning/4_clustering_and_retrieval/lecture/week2/images/Screen Shot 2016-07-03 at 12.16.46 AM.png create mode 100644 machine_learning/4_clustering_and_retrieval/lecture/week2/quiz-KD-trees.ipynb diff --git a/machine_learning/4_clustering_and_retrieval/lecture/week2/.ipynb_checkpoints/quiz-KD-trees-checkpoint.ipynb b/machine_learning/4_clustering_and_retrieval/lecture/week2/.ipynb_checkpoints/quiz-KD-trees-checkpoint.ipynb new file mode 100644 index 0000000..a83df8c --- /dev/null +++ b/machine_learning/4_clustering_and_retrieval/lecture/week2/.ipynb_checkpoints/quiz-KD-trees-checkpoint.ipynb @@ -0,0 +1,519 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# KD-trees" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Question 1\n", + "\n", + "\n", + "\n", + "*Screenshot taken from [Coursera](https://www.coursera.org/learn/ml-clustering-and-retrieval/exam/YV0W4/representations-and-metrics)*\n", + "\n", + "" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Question 2\n", + "\n", + "\n", + "\n", + "*Screenshot taken from [Coursera](https://www.coursera.org/learn/ml-clustering-and-retrieval/exam/YV0W4/representations-and-metrics)*\n", + "\n", + "" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Answer**" + ] + }, + { + "cell_type": "code", + "execution_count": 74, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[-1.58, -2.01],\n", + " [ 0.91, 3.98],\n", + " [-0.73, 4. ],\n", + " [-4.22, 1.16],\n", + " [ 4.19, -2.02],\n", + " [-0.33, 2.15]])" + ] + }, + "execution_count": 74, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "import numpy as np\n", + "\n", + "x1 = np.array([-1.58, 0.91, -0.73, -4.22, 4.19, -0.33])\n", + "x2 = np.array([-2.01, 3.98, 4.00, 1.16, -2.02, 2.15])\n", + "\n", + "x = np.vstack((x1, x2)).T\n", + "x" + ] + }, + { + "cell_type": "code", + "execution_count": 89, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "-0.01499999999999968" + ] + }, + "execution_count": 89, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Mid range of x1\n", + "x1_midrange = (x1.max() + x1.min())/2\n", + "x1_midrange" + ] + }, + { + "cell_type": "code", + "execution_count": 90, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def get_mid_range(data, column=0):\n", + " \"\"\" Get midrange of data by column\n", + " - x1: column=0\n", + " - x2: column=1\n", + " \"\"\"\n", + " midrange = (data[:, column].max() + data[:, column].min())/2\n", + " return midrange \n", + "\n", + "def split_by(x, value, column=0):\n", + " \"\"\" Split x array by value and column\n", + " - x1: column=0\n", + " - x2: column=1\n", + " \"\"\"\n", + " split1 = x[x[:, column] <= value]\n", + " split2 = x[x[:, column] > value]\n", + " return split1, split2" + ] + }, + { + "cell_type": "code", + "execution_count": 91, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[-1.58, -2.01],\n", + " [-0.73, 4. ],\n", + " [-4.22, 1.16],\n", + " [-0.33, 2.15]])" + ] + }, + "execution_count": 91, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "x1_midrange = get_mid_range(x)\n", + "x1_split1, x1_split2 = split_by(x, x1_midrange)\n", + "\n", + "# Split values of x1\n", + "x1_split1" + ] + }, + { + "cell_type": "code", + "execution_count": 92, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[ 0.91, 3.98],\n", + " [ 4.19, -2.02]])" + ] + }, + "execution_count": 92, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Split values of x1\n", + "x1_split2" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Question 3\n", + "\n", + "\n", + "\n", + "*Screenshot taken from [Coursera](https://www.coursera.org/learn/ml-clustering-and-retrieval/exam/YV0W4/representations-and-metrics)*\n", + "\n", + "" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Answer**" + ] + }, + { + "cell_type": "code", + "execution_count": 93, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0.995\n" + ] + } + ], + "source": [ + "# Mid range of x2 for the 1st split\n", + "# x1_split1_x2_midrange = (x1_split1[:, 1].max() + x1_split1[:, 1].min())/2\n", + "x1_split1_x2_midrange = get_mid_range(x1_split1, column=1)\n", + "\n", + "print x1_split1_x2_midrange" + ] + }, + { + "cell_type": "code", + "execution_count": 94, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0.98\n" + ] + } + ], + "source": [ + "# # Mid range of x2 for 2nd split\n", + "x1_split2_x2_midrange = get_mid_range(x1_split2, column=1)\n", + "print x1_split2_x2_midrange" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Question 4\n", + "\n", + "\n", + "\n", + "*Screenshot taken from [Coursera](https://www.coursera.org/learn/ml-clustering-and-retrieval/exam/YV0W4/representations-and-metrics)*\n", + "\n", + "" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Answer**" + ] + }, + { + "cell_type": "code", + "execution_count": 95, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[-1.58, -2.01]])" + ] + }, + "execution_count": 95, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "x1_split1_x2_split1, x1_split1_x2_split2 = split_by(x1_split1, x2_x1_split1_midrange, column=1)\n", + "x1_split1_x2_split1" + ] + }, + { + "cell_type": "code", + "execution_count": 97, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[-0.73, 4. ],\n", + " [-4.22, 1.16],\n", + " [-0.33, 2.15]])" + ] + }, + "execution_count": 97, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# node still has 3 data points\n", + "# continue to split\n", + "\n", + "x1_split1_x2_split2 " + ] + }, + { + "cell_type": "code", + "execution_count": 98, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "2.5800000000000001" + ] + }, + "execution_count": 98, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "x1_split1_x2_split2_midrange = get_mid_range(x1_split1_x2_split2, column=1)\n", + "x1_split1_x2_split2_midrange" + ] + }, + { + "cell_type": "code", + "execution_count": 99, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[-4.22, 1.16],\n", + " [-0.33, 2.15]])" + ] + }, + "execution_count": 99, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "x1_split1_x2_split2_x2_split1, x1_split1_x2_split2_x2_split2 = split_by(x1_split1_x2_split2, \n", + " x1_split1_x2_split2_midrange, \n", + " column=1)\n", + "x1_split1_x2_split2_x2_split1\n", + "# Continue to split" + ] + }, + { + "cell_type": "code", + "execution_count": 100, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[-0.73, 4. ]])" + ] + }, + "execution_count": 100, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "x1_split1_x2_split2_x2_split2" + ] + }, + { + "cell_type": "code", + "execution_count": 102, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "1.6549999999999998" + ] + }, + "execution_count": 102, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "x1_split1_x2_split2_x2_split1_midrange = get_mid_range(x1_split1_x2_split2_x2_split1, column=1)\n", + "x1_split1_x2_split2_x2_split1_midrange" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "- After split x1_split1_x2_split2_x2_split1 by 1.654, then we will have 2 more leaves. Data point 4: [-4.22, 1.16] will be the leaves contain the query point (-3, 1.5)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Question 5\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "*Screenshot taken from [Coursera](https://www.coursera.org/learn/ml-clustering-and-retrieval/exam/YV0W4/representations-and-metrics)*\n", + "\n", + "" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Answer**" + ] + }, + { + "cell_type": "code", + "execution_count": 86, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[ 4.19, -2.02]])" + ] + }, + "execution_count": 86, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "x1_split2_x2_split1, x1_split2_x2_split2 = split_by(x1_split2, x1_split2_x2_midrange, column=1)\n", + "x1_split2_x2_split1" + ] + }, + { + "cell_type": "code", + "execution_count": 87, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[ 0.91, 3.98]])" + ] + }, + "execution_count": 87, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "x1_split2_x2_split2" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 2", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.11" + }, + "toc": { + "toc_cell": false, + "toc_number_sections": false, + "toc_threshold": "8", + "toc_window_display": false + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/machine_learning/4_clustering_and_retrieval/lecture/week2/images/Screen Shot 2016-07-02 at 11.56.04 PM.png 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b/machine_learning/4_clustering_and_retrieval/lecture/week2/quiz-KD-trees.ipynb new file mode 100644 index 0000000..a83df8c --- /dev/null +++ b/machine_learning/4_clustering_and_retrieval/lecture/week2/quiz-KD-trees.ipynb @@ -0,0 +1,519 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# KD-trees" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Question 1\n", + "\n", + "\n", + "\n", + "*Screenshot taken from [Coursera](https://www.coursera.org/learn/ml-clustering-and-retrieval/exam/YV0W4/representations-and-metrics)*\n", + "\n", + "" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Question 2\n", + "\n", + "\n", + "\n", + "*Screenshot taken from [Coursera](https://www.coursera.org/learn/ml-clustering-and-retrieval/exam/YV0W4/representations-and-metrics)*\n", + "\n", + "" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Answer**" + ] + }, + { + "cell_type": "code", + "execution_count": 74, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[-1.58, -2.01],\n", + " [ 0.91, 3.98],\n", + " [-0.73, 4. ],\n", + " [-4.22, 1.16],\n", + " [ 4.19, -2.02],\n", + " [-0.33, 2.15]])" + ] + }, + "execution_count": 74, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "import numpy as np\n", + "\n", + "x1 = np.array([-1.58, 0.91, -0.73, -4.22, 4.19, -0.33])\n", + "x2 = np.array([-2.01, 3.98, 4.00, 1.16, -2.02, 2.15])\n", + "\n", + "x = np.vstack((x1, x2)).T\n", + "x" + ] + }, + { + "cell_type": "code", + "execution_count": 89, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "-0.01499999999999968" + ] + }, + "execution_count": 89, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Mid range of x1\n", + "x1_midrange = (x1.max() + x1.min())/2\n", + "x1_midrange" + ] + }, + { + "cell_type": "code", + "execution_count": 90, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def get_mid_range(data, column=0):\n", + " \"\"\" Get midrange of data by column\n", + " - x1: column=0\n", + " - x2: column=1\n", + " \"\"\"\n", + " midrange = (data[:, column].max() + data[:, column].min())/2\n", + " return midrange \n", + "\n", + "def split_by(x, value, column=0):\n", + " \"\"\" Split x array by value and column\n", + " - x1: column=0\n", + " - x2: column=1\n", + " \"\"\"\n", + " split1 = x[x[:, column] <= value]\n", + " split2 = x[x[:, column] > value]\n", + " return split1, split2" + ] + }, + { + "cell_type": "code", + "execution_count": 91, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[-1.58, -2.01],\n", + " [-0.73, 4. ],\n", + " [-4.22, 1.16],\n", + " [-0.33, 2.15]])" + ] + }, + "execution_count": 91, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "x1_midrange = get_mid_range(x)\n", + "x1_split1, x1_split2 = split_by(x, x1_midrange)\n", + "\n", + "# Split values of x1\n", + "x1_split1" + ] + }, + { + "cell_type": "code", + "execution_count": 92, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[ 0.91, 3.98],\n", + " [ 4.19, -2.02]])" + ] + }, + "execution_count": 92, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Split values of x1\n", + "x1_split2" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Question 3\n", + "\n", + "\n", + "\n", + "*Screenshot taken from [Coursera](https://www.coursera.org/learn/ml-clustering-and-retrieval/exam/YV0W4/representations-and-metrics)*\n", + "\n", + "" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Answer**" + ] + }, + { + "cell_type": "code", + "execution_count": 93, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0.995\n" + ] + } + ], + "source": [ + "# Mid range of x2 for the 1st split\n", + "# x1_split1_x2_midrange = (x1_split1[:, 1].max() + x1_split1[:, 1].min())/2\n", + "x1_split1_x2_midrange = get_mid_range(x1_split1, column=1)\n", + "\n", + "print x1_split1_x2_midrange" + ] + }, + { + "cell_type": "code", + "execution_count": 94, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0.98\n" + ] + } + ], + "source": [ + "# # Mid range of x2 for 2nd split\n", + "x1_split2_x2_midrange = get_mid_range(x1_split2, column=1)\n", + "print x1_split2_x2_midrange" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Question 4\n", + "\n", + "\n", + "\n", + "*Screenshot taken from [Coursera](https://www.coursera.org/learn/ml-clustering-and-retrieval/exam/YV0W4/representations-and-metrics)*\n", + "\n", + "" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Answer**" + ] + }, + { + "cell_type": "code", + "execution_count": 95, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[-1.58, -2.01]])" + ] + }, + "execution_count": 95, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "x1_split1_x2_split1, x1_split1_x2_split2 = split_by(x1_split1, x2_x1_split1_midrange, column=1)\n", + "x1_split1_x2_split1" + ] + }, + { + "cell_type": "code", + "execution_count": 97, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[-0.73, 4. ],\n", + " [-4.22, 1.16],\n", + " [-0.33, 2.15]])" + ] + }, + "execution_count": 97, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# node still has 3 data points\n", + "# continue to split\n", + "\n", + "x1_split1_x2_split2 " + ] + }, + { + "cell_type": "code", + "execution_count": 98, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "2.5800000000000001" + ] + }, + "execution_count": 98, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "x1_split1_x2_split2_midrange = get_mid_range(x1_split1_x2_split2, column=1)\n", + "x1_split1_x2_split2_midrange" + ] + }, + { + "cell_type": "code", + "execution_count": 99, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[-4.22, 1.16],\n", + " [-0.33, 2.15]])" + ] + }, + "execution_count": 99, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "x1_split1_x2_split2_x2_split1, x1_split1_x2_split2_x2_split2 = split_by(x1_split1_x2_split2, \n", + " x1_split1_x2_split2_midrange, \n", + " column=1)\n", + "x1_split1_x2_split2_x2_split1\n", + "# Continue to split" + ] + }, + { + "cell_type": "code", + "execution_count": 100, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[-0.73, 4. ]])" + ] + }, + "execution_count": 100, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "x1_split1_x2_split2_x2_split2" + ] + }, + { + "cell_type": "code", + "execution_count": 102, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "1.6549999999999998" + ] + }, + "execution_count": 102, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "x1_split1_x2_split2_x2_split1_midrange = get_mid_range(x1_split1_x2_split2_x2_split1, column=1)\n", + "x1_split1_x2_split2_x2_split1_midrange" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "- After split x1_split1_x2_split2_x2_split1 by 1.654, then we will have 2 more leaves. Data point 4: [-4.22, 1.16] will be the leaves contain the query point (-3, 1.5)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Question 5\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "*Screenshot taken from [Coursera](https://www.coursera.org/learn/ml-clustering-and-retrieval/exam/YV0W4/representations-and-metrics)*\n", + "\n", + "" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Answer**" + ] + }, + { + "cell_type": "code", + "execution_count": 86, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[ 4.19, -2.02]])" + ] + }, + "execution_count": 86, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "x1_split2_x2_split1, x1_split2_x2_split2 = split_by(x1_split2, x1_split2_x2_midrange, column=1)\n", + "x1_split2_x2_split1" + ] + }, + { + "cell_type": "code", + "execution_count": 87, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[ 0.91, 3.98]])" + ] + }, + "execution_count": 87, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "x1_split2_x2_split2" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 2", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.11" + }, + "toc": { + "toc_cell": false, + "toc_number_sections": false, + "toc_threshold": "8", + "toc_window_display": false + } + }, + "nbformat": 4, + "nbformat_minor": 0 +}