{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Indexing Variaton" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/vnd.plotly.v1+html": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import scipy\n", "import numpy as np\n", "from sklearn.neighbors import KernelDensity\n", "from sklearn.decomposition import PCA\n", "from sklearn.model_selection import GridSearchCV\n", "from sklearn.cluster import estimate_bandwidth\n", "from sklearn.cluster import MeanShift, estimate_bandwidth\n", "\n", "import pandas as pd\n", "\n", "from scipy import stats\n", "from scipy.stats import beta\n", "from math import sin\n", "from random import randint\n", "\n", "###########################################\n", "import matplotlib.pyplot as plt\n", "import matplotlib\n", "\n", "%matplotlib inline\n", "\n", "import itertools as it\n", "\n", "\n", "\n", "from matplotlib.collections import BrokenBarHCollection\n", "import pandas as pd\n", "\n", "import re\n", "\n", "import plotly\n", "import plotly.plotly as py\n", "import plotly.graph_objs as go\n", "from plotly.offline import download_plotlyjs, init_notebook_mode, plot, iplot\n", "from plotly.graph_objs import *\n", "\n", "from ipywidgets import interact, interactive, fixed, interact_manual\n", "import ipywidgets as widgets\n", "init_notebook_mode(connected=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In previous posts, we resorted to density estimates to attempt to weed out outliers, identify cases of mislabelling and classify unlabelled observations. \n", "\n", "We went on to explore how cluster-derived KDE vectors of the same variables would aggregate in feature space, allowing us to label them in bulk (see **5. Visualizing KDE**).\n", "\n", "Varying distances among clusters, resulting distinguishable cluster profiles, can be of interest, depending on the nature of the data we are considering. If those distances vary according to physical distance for example, it might be interesting to extract and visualize those locations.\n", "\n", "Let's begin by performing the same simulations, of three populations, of which two see their distributions overlap as a function of a variable X (also seen in **6. Conditional Variation**)." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "\n", "# We must first define the number of populations, the length of the haplotypes desired, and their respective population sizes\n", "L= 300\n", "\n", "import itertools as it\n", "n= 20\n", "n_samples= 20\n", "\n", "a_range= np.linspace(1.5,2.5,n_samples)\n", "a_set= [i for i in a_range for _ in range(n)]\n", "\n", "b_range= np.linspace(0.1,.6,n_samples)\n", "b_set= [i for i in b_range for _ in range(n)]\n", "\n", "L_set= [L] * n * n_samples\n", "\n", "traces= [x for x in it.product(range(n*11),range(n*11),range(n*11))]\n", "\n", "background= np.array([a_set,b_set,L_set]).T\n", "\n", "vector_lib= []\n", "for k in range(background.shape[0]):\n", " \n", " probs= beta.rvs(background[k,0], background[k,1], size=int(background[k,2]))\n", " probs[(probs > 1)]= 1\n", " probs= [1-x for x in probs]\n", " \n", " \n", " vector_lib.append(probs)\n", "\n", "vector_lib= np.array(vector_lib)\n", "\n" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "PC1: 0.047; PC2: 0.011; PC3: 0.011; PC4: 0.011; PC5: 0.01; PC6: 0.01; PC7: 0.01; PC8: 0.01; PC9: 0.01; PC10: 0.01; PC11: 0.009; PC12: 0.009; PC13: 0.009; PC14: 0.009; PC15: 0.009; PC16: 0.009; PC17: 0.009; PC18: 0.009; PC19: 0.009; PC20: 0.009; PC21: 0.008; PC22: 0.008; PC23: 0.008; PC24: 0.008; PC25: 0.008; PC26: 0.008; PC27: 0.008; PC28: 0.008; PC29: 0.008; PC30: 0.008; PC31: 0.008; PC32: 0.007; PC33: 0.007; PC34: 0.007; PC35: 0.007; PC36: 0.007; PC37: 0.007; PC38: 0.007; PC39: 0.007; PC40: 0.007; PC41: 0.007; PC42: 0.007; PC43: 0.007; PC44: 0.006; PC45: 0.006; PC46: 0.006; PC47: 0.006; PC48: 0.006; PC49: 0.006; PC50: 0.006\n", "features shape: (400, 50)\n" ] } ], "source": [ "n_comp = 50\n", "\n", "pca = PCA(n_components=n_comp, whiten=False,svd_solver='randomized')\n", "features = pca.fit_transform(vector_lib)\n", "\n", "var_comps= pca.explained_variance_ratio_\n", "print(\"; \".join(['PC{0}: {1}'.format(x+1,round(var_comps[x],3)) for x in range(n_comp)]))\n", "print('features shape: {}'.format(features.shape))" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "data": [ { "marker": { "line": { "width": 0 }, "opacity": 0.8, "size": 4, "symbol": "circle" }, "mode": "markers", "text": [ "a: 1.5; b: 0.1, L: 300.0; index = 0", "a: 1.5; b: 0.1, L: 300.0; index = 1", "a: 1.5; b: 0.1, L: 300.0; index = 2", "a: 1.5; b: 0.1, L: 300.0; index = 3", "a: 1.5; b: 0.1, L: 300.0; index = 4", "a: 1.5; b: 0.1, L: 300.0; index = 5", "a: 1.5; b: 0.1, L: 300.0; index = 6", "a: 1.5; b: 0.1, L: 300.0; index = 7", "a: 1.5; b: 0.1, L: 300.0; index = 8", "a: 1.5; b: 0.1, L: 300.0; index = 9", "a: 1.5; b: 0.1, L: 300.0; index = 10", "a: 1.5; b: 0.1, L: 300.0; index = 11", "a: 1.5; b: 0.1, L: 300.0; index = 12", "a: 1.5; b: 0.1, L: 300.0; index = 13", "a: 1.5; b: 0.1, L: 300.0; index = 14", "a: 1.5; b: 0.1, L: 300.0; index = 15", "a: 1.5; b: 0.1, L: 300.0; index = 16", "a: 1.5; b: 0.1, L: 300.0; index = 17", "a: 1.5; b: 0.1, L: 300.0; index = 18", "a: 1.5; b: 0.1, L: 300.0; index = 19", "a: 1.5526315789473684; b: 0.12631578947368421, L: 300.0; index = 20", "a: 1.5526315789473684; b: 0.12631578947368421, L: 300.0; index = 21", "a: 1.5526315789473684; b: 0.12631578947368421, L: 300.0; index = 22", "a: 1.5526315789473684; b: 0.12631578947368421, L: 300.0; index = 23", "a: 1.5526315789473684; b: 0.12631578947368421, L: 300.0; index = 24", "a: 1.5526315789473684; b: 0.12631578947368421, L: 300.0; index = 25", "a: 1.5526315789473684; b: 0.12631578947368421, L: 300.0; index = 26", "a: 1.5526315789473684; b: 0.12631578947368421, L: 300.0; index = 27", "a: 1.5526315789473684; b: 0.12631578947368421, L: 300.0; index = 28", "a: 1.5526315789473684; b: 0.12631578947368421, L: 300.0; index = 29", "a: 1.5526315789473684; b: 0.12631578947368421, L: 300.0; index = 30", "a: 1.5526315789473684; b: 0.12631578947368421, L: 300.0; index = 31", "a: 1.5526315789473684; b: 0.12631578947368421, L: 300.0; index = 32", "a: 1.5526315789473684; b: 0.12631578947368421, L: 300.0; index = 33", "a: 1.5526315789473684; b: 0.12631578947368421, L: 300.0; index = 34", "a: 1.5526315789473684; b: 0.12631578947368421, L: 300.0; index = 35", "a: 1.5526315789473684; b: 0.12631578947368421, L: 300.0; index = 36", "a: 1.5526315789473684; b: 0.12631578947368421, L: 300.0; index = 37", "a: 1.5526315789473684; b: 0.12631578947368421, L: 300.0; index = 38", "a: 1.5526315789473684; b: 0.12631578947368421, L: 300.0; index = 39", "a: 1.6052631578947367; b: 0.15263157894736842, L: 300.0; index = 40", "a: 1.6052631578947367; b: 0.15263157894736842, L: 300.0; index = 41", "a: 1.6052631578947367; b: 0.15263157894736842, L: 300.0; index = 42", "a: 1.6052631578947367; b: 0.15263157894736842, L: 300.0; index = 43", "a: 1.6052631578947367; b: 0.15263157894736842, L: 300.0; index = 44", "a: 1.6052631578947367; b: 0.15263157894736842, L: 300.0; index = 45", "a: 1.6052631578947367; b: 0.15263157894736842, L: 300.0; index = 46", "a: 1.6052631578947367; b: 0.15263157894736842, L: 300.0; index = 47", "a: 1.6052631578947367; b: 0.15263157894736842, L: 300.0; index = 48", "a: 1.6052631578947367; b: 0.15263157894736842, L: 300.0; index = 49", "a: 1.6052631578947367; b: 0.15263157894736842, L: 300.0; index = 50", "a: 1.6052631578947367; b: 0.15263157894736842, L: 300.0; index = 51", "a: 1.6052631578947367; b: 0.15263157894736842, L: 300.0; index = 52", "a: 1.6052631578947367; b: 0.15263157894736842, L: 300.0; index = 53", "a: 1.6052631578947367; b: 0.15263157894736842, L: 300.0; index = 54", "a: 1.6052631578947367; b: 0.15263157894736842, L: 300.0; index = 55", "a: 1.6052631578947367; b: 0.15263157894736842, L: 300.0; index = 56", "a: 1.6052631578947367; b: 0.15263157894736842, L: 300.0; index = 57", "a: 1.6052631578947367; b: 0.15263157894736842, L: 300.0; index = 58", "a: 1.6052631578947367; b: 0.15263157894736842, L: 300.0; index = 59", "a: 1.6578947368421053; b: 0.17894736842105263, L: 300.0; index = 60", "a: 1.6578947368421053; b: 0.17894736842105263, L: 300.0; index = 61", "a: 1.6578947368421053; b: 0.17894736842105263, L: 300.0; index = 62", "a: 1.6578947368421053; b: 0.17894736842105263, L: 300.0; index = 63", "a: 1.6578947368421053; b: 0.17894736842105263, L: 300.0; index = 64", "a: 1.6578947368421053; b: 0.17894736842105263, L: 300.0; index = 65", "a: 1.6578947368421053; b: 0.17894736842105263, L: 300.0; index = 66", "a: 1.6578947368421053; b: 0.17894736842105263, L: 300.0; index = 67", "a: 1.6578947368421053; b: 0.17894736842105263, L: 300.0; index = 68", "a: 1.6578947368421053; b: 0.17894736842105263, L: 300.0; index = 69", "a: 1.6578947368421053; b: 0.17894736842105263, L: 300.0; index = 70", "a: 1.6578947368421053; b: 0.17894736842105263, L: 300.0; index = 71", "a: 1.6578947368421053; b: 0.17894736842105263, L: 300.0; index = 72", "a: 1.6578947368421053; b: 0.17894736842105263, L: 300.0; index = 73", "a: 1.6578947368421053; b: 0.17894736842105263, L: 300.0; index = 74", "a: 1.6578947368421053; b: 0.17894736842105263, L: 300.0; index = 75", "a: 1.6578947368421053; b: 0.17894736842105263, L: 300.0; index = 76", "a: 1.6578947368421053; b: 0.17894736842105263, L: 300.0; index = 77", "a: 1.6578947368421053; b: 0.17894736842105263, L: 300.0; index = 78", "a: 1.6578947368421053; b: 0.17894736842105263, L: 300.0; index = 79", "a: 1.7105263157894737; b: 0.20526315789473684, L: 300.0; index = 80", "a: 1.7105263157894737; b: 0.20526315789473684, L: 300.0; index = 81", "a: 1.7105263157894737; b: 0.20526315789473684, L: 300.0; index = 82", "a: 1.7105263157894737; b: 0.20526315789473684, L: 300.0; index = 83", "a: 1.7105263157894737; b: 0.20526315789473684, L: 300.0; index = 84", "a: 1.7105263157894737; b: 0.20526315789473684, L: 300.0; index = 85", "a: 1.7105263157894737; b: 0.20526315789473684, L: 300.0; index = 86", "a: 1.7105263157894737; b: 0.20526315789473684, L: 300.0; index = 87", "a: 1.7105263157894737; b: 0.20526315789473684, L: 300.0; index = 88", "a: 1.7105263157894737; b: 0.20526315789473684, L: 300.0; index = 89", "a: 1.7105263157894737; b: 0.20526315789473684, L: 300.0; index = 90", "a: 1.7105263157894737; b: 0.20526315789473684, L: 300.0; index = 91", "a: 1.7105263157894737; b: 0.20526315789473684, L: 300.0; index = 92", "a: 1.7105263157894737; b: 0.20526315789473684, L: 300.0; index = 93", "a: 1.7105263157894737; b: 0.20526315789473684, L: 300.0; index = 94", "a: 1.7105263157894737; b: 0.20526315789473684, L: 300.0; index = 95", "a: 1.7105263157894737; b: 0.20526315789473684, L: 300.0; index = 96", "a: 1.7105263157894737; b: 0.20526315789473684, L: 300.0; index = 97", "a: 1.7105263157894737; b: 0.20526315789473684, L: 300.0; index = 98", "a: 1.7105263157894737; b: 0.20526315789473684, L: 300.0; index = 99", "a: 1.763157894736842; b: 0.23157894736842105, L: 300.0; index = 100", "a: 1.763157894736842; b: 0.23157894736842105, L: 300.0; index = 101", "a: 1.763157894736842; b: 0.23157894736842105, L: 300.0; index = 102", "a: 1.763157894736842; b: 0.23157894736842105, L: 300.0; index = 103", "a: 1.763157894736842; b: 0.23157894736842105, L: 300.0; index = 104", "a: 1.763157894736842; b: 0.23157894736842105, L: 300.0; index = 105", "a: 1.763157894736842; b: 0.23157894736842105, L: 300.0; index = 106", "a: 1.763157894736842; b: 0.23157894736842105, L: 300.0; index = 107", "a: 1.763157894736842; b: 0.23157894736842105, L: 300.0; index = 108", "a: 1.763157894736842; b: 0.23157894736842105, L: 300.0; index = 109", "a: 1.763157894736842; b: 0.23157894736842105, L: 300.0; index = 110", "a: 1.763157894736842; b: 0.23157894736842105, L: 300.0; index = 111", "a: 1.763157894736842; b: 0.23157894736842105, L: 300.0; index = 112", "a: 1.763157894736842; b: 0.23157894736842105, L: 300.0; index = 113", "a: 1.763157894736842; b: 0.23157894736842105, L: 300.0; index = 114", "a: 1.763157894736842; b: 0.23157894736842105, L: 300.0; index = 115", "a: 1.763157894736842; b: 0.23157894736842105, L: 300.0; index = 116", "a: 1.763157894736842; b: 0.23157894736842105, L: 300.0; index = 117", "a: 1.763157894736842; b: 0.23157894736842105, L: 300.0; index = 118", "a: 1.763157894736842; b: 0.23157894736842105, L: 300.0; index = 119", "a: 1.8157894736842106; b: 0.2578947368421053, L: 300.0; index = 120", "a: 1.8157894736842106; b: 0.2578947368421053, L: 300.0; index = 121", "a: 1.8157894736842106; b: 0.2578947368421053, L: 300.0; index = 122", "a: 1.8157894736842106; b: 0.2578947368421053, L: 300.0; index = 123", "a: 1.8157894736842106; b: 0.2578947368421053, L: 300.0; index = 124", "a: 1.8157894736842106; b: 0.2578947368421053, L: 300.0; index = 125", "a: 1.8157894736842106; b: 0.2578947368421053, L: 300.0; index = 126", "a: 1.8157894736842106; b: 0.2578947368421053, L: 300.0; index = 127", "a: 1.8157894736842106; b: 0.2578947368421053, L: 300.0; index = 128", "a: 1.8157894736842106; b: 0.2578947368421053, L: 300.0; index = 129", "a: 1.8157894736842106; b: 0.2578947368421053, L: 300.0; index = 130", "a: 1.8157894736842106; b: 0.2578947368421053, L: 300.0; index = 131", "a: 1.8157894736842106; b: 0.2578947368421053, L: 300.0; index = 132", "a: 1.8157894736842106; b: 0.2578947368421053, L: 300.0; index = 133", "a: 1.8157894736842106; b: 0.2578947368421053, L: 300.0; index = 134", "a: 1.8157894736842106; b: 0.2578947368421053, L: 300.0; index = 135", "a: 1.8157894736842106; b: 0.2578947368421053, L: 300.0; index = 136", "a: 1.8157894736842106; b: 0.2578947368421053, L: 300.0; index = 137", "a: 1.8157894736842106; b: 0.2578947368421053, L: 300.0; index = 138", "a: 1.8157894736842106; b: 0.2578947368421053, L: 300.0; index = 139", "a: 1.868421052631579; b: 0.28421052631578947, L: 300.0; index = 140", "a: 1.868421052631579; b: 0.28421052631578947, L: 300.0; index = 141", "a: 1.868421052631579; b: 0.28421052631578947, L: 300.0; index = 142", "a: 1.868421052631579; b: 0.28421052631578947, L: 300.0; index = 143", "a: 1.868421052631579; b: 0.28421052631578947, L: 300.0; index = 144", "a: 1.868421052631579; b: 0.28421052631578947, L: 300.0; index = 145", "a: 1.868421052631579; b: 0.28421052631578947, L: 300.0; index = 146", "a: 1.868421052631579; b: 0.28421052631578947, L: 300.0; index = 147", "a: 1.868421052631579; b: 0.28421052631578947, L: 300.0; index = 148", "a: 1.868421052631579; b: 0.28421052631578947, L: 300.0; index = 149", "a: 1.868421052631579; b: 0.28421052631578947, L: 300.0; index = 150", "a: 1.868421052631579; b: 0.28421052631578947, L: 300.0; index = 151", "a: 1.868421052631579; b: 0.28421052631578947, L: 300.0; index = 152", "a: 1.868421052631579; b: 0.28421052631578947, L: 300.0; index = 153", "a: 1.868421052631579; b: 0.28421052631578947, L: 300.0; index = 154", "a: 1.868421052631579; b: 0.28421052631578947, L: 300.0; index = 155", "a: 1.868421052631579; b: 0.28421052631578947, L: 300.0; index = 156", "a: 1.868421052631579; b: 0.28421052631578947, L: 300.0; index = 157", "a: 1.868421052631579; b: 0.28421052631578947, L: 300.0; index = 158", "a: 1.868421052631579; b: 0.28421052631578947, L: 300.0; index = 159", "a: 1.9210526315789473; b: 0.31052631578947365, L: 300.0; index = 160", "a: 1.9210526315789473; b: 0.31052631578947365, L: 300.0; index = 161", "a: 1.9210526315789473; b: 0.31052631578947365, L: 300.0; index = 162", "a: 1.9210526315789473; b: 0.31052631578947365, L: 300.0; index = 163", "a: 1.9210526315789473; b: 0.31052631578947365, L: 300.0; index = 164", "a: 1.9210526315789473; b: 0.31052631578947365, L: 300.0; index = 165", "a: 1.9210526315789473; b: 0.31052631578947365, L: 300.0; index = 166", "a: 1.9210526315789473; b: 0.31052631578947365, L: 300.0; index = 167", "a: 1.9210526315789473; b: 0.31052631578947365, L: 300.0; index = 168", "a: 1.9210526315789473; b: 0.31052631578947365, L: 300.0; index = 169", "a: 1.9210526315789473; b: 0.31052631578947365, L: 300.0; index = 170", 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310", "a: 2.2894736842105265; b: 0.49473684210526314, L: 300.0; index = 311", "a: 2.2894736842105265; b: 0.49473684210526314, L: 300.0; index = 312", "a: 2.2894736842105265; b: 0.49473684210526314, L: 300.0; index = 313", "a: 2.2894736842105265; b: 0.49473684210526314, L: 300.0; index = 314", "a: 2.2894736842105265; b: 0.49473684210526314, L: 300.0; index = 315", "a: 2.2894736842105265; b: 0.49473684210526314, L: 300.0; index = 316", "a: 2.2894736842105265; b: 0.49473684210526314, L: 300.0; index = 317", "a: 2.2894736842105265; b: 0.49473684210526314, L: 300.0; index = 318", "a: 2.2894736842105265; b: 0.49473684210526314, L: 300.0; index = 319", "a: 2.3421052631578947; b: 0.5210526315789473, L: 300.0; index = 320", "a: 2.3421052631578947; b: 0.5210526315789473, L: 300.0; index = 321", "a: 2.3421052631578947; b: 0.5210526315789473, L: 300.0; index = 322", "a: 2.3421052631578947; b: 0.5210526315789473, L: 300.0; index = 323", "a: 2.3421052631578947; b: 0.5210526315789473, L: 300.0; index 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" ], "text/vnd.plotly.v1+html": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#### Let's plot the first 3 coordinates nonetheless.\n", "####\n", "fig_data= [go.Scatter3d(\n", " x = features[:,0],\n", " y = features[:,1],\n", " z = features[:,2],\n", " type='scatter3d',\n", " mode= \"markers\",\n", " text= ['a: {}; b: {}, L: {}; index = {}'.format(background[k,0],background[k,1],background[k,2], k) for k in range(background.shape[0])],\n", " marker= {\n", " 'line': {'width': 0},\n", " 'size': 4,\n", " 'symbol': 'circle',\n", " \"opacity\": .8\n", " }\n", " )]\n", "\n", "\n", "layout = go.Layout(\n", " margin=dict(\n", " l=0,\n", " r=0,\n", " b=0,\n", " t=0\n", " ),\n", " scene= Scene(\n", " yaxis=dict(\n", " title='PC2: {}'.format(round(var_comps[1],3))),\n", " xaxis=dict(\n", " title= 'PC1: {}'.format(round(var_comps[0],3))),\n", " zaxis=dict(\n", " title= 'PC3: {}'.format(round(var_comps[2],3))))\n", ")\n", "\n", "fig = go.Figure(data=fig_data, layout=layout)\n", "iplot(fig)\n" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "global fst: 0.1513\n" ] }, { "data": { "text/html": [ "\n", " | pops | \n", "fst | \n", "
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