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rescaling.py
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rescaling.py
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#!/usr/bin/env python
from __future__ import division
import numpy as np
import bokeh.plotting as bplt
import utils
from matplotlib import pyplot as plt
from bokeh.models import HoverTool
def scale(data_matrix):
'''returns the means and standard deviations of each column'''
num_rows, num_cols = data_matrix.shape
means = [data_matrix[:,j].mean() for j in range(num_cols)]
stdevs = [data_matrix[:,j].std() for j in range(num_cols)]
return means, stdevs
def rescale(data_matrix):
'''rescales the input data so that each column
has mean 0 and standard deviation 1
leaves alone columns with no deviation'''
means, stdevs = scale(data_matrix)
def rescaled(i, j):
if stdevs[j] > 0:
return (data_matrix[i,j] - means[j]) / stdevs[j]
else:
return data_matrix[i,j]
num_rows, num_cols = data_matrix.shape
return utils.make_matrix(num_rows, num_cols, rescaled)
def de_mean_matrix(A):
"""returns the result of subtracting from every value in A the mean
value of its column. the resulting matrix has mean 0 in every column"""
nr, nc = A.shape
column_means, _ = scale(A)
return utils.make_matrix(nr, nc, lambda i, j: A[i,j] - column_means[j])
def plot(X):
Y = de_mean_matrix(X)
plt.subplot(2, 1, 1)
plt.scatter(X[:,0], X[:,1])
plt.title('Data')
plt.subplot(2, 1, 2)
plt.scatter(Y[:,0], Y[:,1])
plt.title('De-meaned')
plt.gca().set_aspect('equal', adjustable='box')
plt.show()
def bokeh(X):
# output to static HTML file
bplt.output_file("data.html", title="Rescaling")
# create a new plot with a title and axis labels
p = bplt.figure(title="Data", x_axis_label='x', y_axis_label='y')
# add a line renderer with legend and line thickness
p.scatter(X[:,0].A1, X[:,1].A1, marker="circle",
line_color="#6666ee", fill_color="#ee6666",
fill_alpha=0.5, size=12)
# show the results
bplt.show(p)
def bokeh2(X):
Y = de_mean_matrix(X)
TOOLS="resize,crosshair,pan,wheel_zoom,box_zoom,reset,previewsave,box_select"
hover = HoverTool(
tooltips=[
("index", "$index"),
("(x,y)", "($x, $y)"),
("desc", "@desc"),
]
)
bplt.output_file("data.html", title="Rescaling")
s1 = bplt.figure(width=500, plot_height=250, title="Data", tools=[hover, TOOLS])
s1.scatter(X[:,0].A1, X[:,1].A1, marker="circle",
line_color="#6666ee", fill_color="#ee6666",
fill_alpha=0.5, size=12)
s2 = bplt.figure(width=500, plot_height=250, title="De-meaned", tools=TOOLS)
s2.scatter(Y[:,0].A1, Y[:,1].A1, marker="circle",
line_color="#6666ee", fill_color="#ee6666",
fill_alpha=0.5, size=12)
# put all the plots in a VBox
p = bplt.vplot(s1, s2)
# show the results
bplt.show(p)
if __name__ == '__main__':
X = np.matrix([
[20.9666776351559,-13.1138080189357],
[22.7719907680008,-19.8890894944696],
[25.6687103160153,-11.9956004517219],
[18.0019794950564,-18.1989191165133],
[21.3967402102156,-10.8893126308196],
[0.443696899177716,-19.7221132386308],
[29.9198322142127,-14.0958668502427],
[19.0805843080126,-13.7888747608312],
[16.4685063521314,-11.2612927034291],
[21.4597664701884,-12.4740034586705],
[3.87655283720532,-17.575162461771],
[34.5713920556787,-10.705185165378],
[13.3732115747722,-16.7270274494424],
[20.7281704141919,-8.81165591556553],
[24.839851437942,-12.1240962157419],
[20.3019544741252,-12.8725060780898],
[21.9021426929599,-17.3225432396452],
[23.2285885715486,-12.2676568419045],
[28.5749111681851,-13.2616470619453],
[29.2957424128701,-14.6299928678996],
[15.2495527798625,-18.4649714274207],
[26.5567257400476,-9.19794350561966],
[30.1934232346361,-12.6272709845971],
[36.8267446011057,-7.25409849336718],
[32.157416823084,-10.4729534347553],
[5.85964365291694,-22.6573731626132],
[25.7426190674693,-14.8055803854566],
[16.237602636139,-16.5920595763719],
[14.7408608850568,-20.0537715298403],
[6.85907008242544,-18.3965586884781],
[26.5918329233128,-8.92664811750842],
[-11.2216019958228,-27.0519081982856],
[8.93593745011035,-20.8261235122575],
[24.4481258671796,-18.0324012215159],
[2.82048515404903,-22.4208457598703],
[30.8803004755948,-11.455358009593],
[15.4586738236098,-11.1242825084309],
[28.5332537090494,-14.7898744423126],
[40.4830293441052,-2.41946428697183],
[15.7563759125684,-13.5771266003795],
[19.3635588851727,-20.6224770470434],
[13.4212840786467,-19.0238227375766],
[7.77570680426702,-16.6385739839089],
[21.4865983854408,-15.290799330002],
[12.6392705930724,-23.6433305964301],
[12.4746151388128,-17.9720169566614],
[23.4572410437998,-14.602080545086],
[13.6878189833565,-18.9687408182414],
[15.4077465943441,-14.5352487124086],
[20.3356581548895,-10.0883159703702],
[20.7093833689359,-12.6939091236766],
[11.1032293684441,-14.1383848928755],
[17.5048321498308,-9.2338593361801],
[16.3303688220188,-15.1054735529158],
[26.6929062710726,-13.306030567991],
[34.4985678099711,-9.86199941278607],
[39.1374291499406,-10.5621430853401],
[21.9088956482146,-9.95198845621849],
[22.2367457578087,-17.2200123442707],
[10.0032784145577,-19.3557700653426],
[14.045833906665,-15.871937521131],
[15.5640911917607,-18.3396956121887],
[24.4771926581586,-14.8715313479137],
[26.533415556629,-14.693883922494],
[12.8722580202544,-21.2750596021509],
[24.4768291376862,-15.9592080959207],
[18.2230748567433,-14.6541444069985],
[4.1902148367447,-20.6144032528762],
[12.4332594022086,-16.6079789231489],
[20.5483758651873,-18.8512560786321],
[17.8180560451358,-12.5451990696752],
[11.0071081078049,-20.3938092335862],
[8.30560561422449,-22.9503944138682],
[33.9857852657284,-4.8371294974382],
[17.4376502239652,-14.5095976075022],
[29.0379635148943,-14.8461553663227],
[29.1344666599319,-7.70862921632672],
[32.9730697624544,-15.5839178785654],
[13.4211493998212,-20.150199857584],
[11.380538260355,-12.8619410359766],
[28.672631499186,-8.51866271785711],
[16.4296061111902,-23.3326051279759],
[25.7168371582585,-13.8899296143829],
[13.3185154732595,-17.8959160024249],
[3.60832478605376,-25.4023343597712],
[39.5445949652652,-11.466377647931],
[25.1693484426101,-12.2752652925707],
[25.2884257196471,-7.06710309184533],
[6.77665715793125,-22.3947299635571],
[20.1844223778907,-16.0427471125407],
[25.5506805272535,-9.33856532270204],
[25.1495682602477,-7.17350567090738],
[15.6978431006492,-17.5979197162642],
[37.42780451491,-10.843637288504],
[22.974620174842,-10.6171162611686],
[34.6327117468934,-9.26182440487384],
[34.7042513789061,-6.9630753351114],
[15.6563953929008,-17.2196961218915],
[25.2049825789225,-14.1592086208169]
])
#plot(X)
bokeh2(X)