ai/lda.py: creation

ai/lda.py

@@ -0,0 +1,56 @@
+#!/usr/bin/python
+# -*- coding: utf-8 -*-
+
+# Copyright (C) 2018  David Arroyo Menéndez
+
+# Author: David Arroyo Menéndez <[email protected]>
+# Maintainer: David Arroyo Menéndez <[email protected]>
+
+# This file is free software; you can redistribute it and/or modify
+# it under the terms of the GNU General Public License as published by
+# the Free Software Foundation; either version 3, or (at your option)
+# any later version.
+
+# This file is distributed in the hope that it will be useful,
+# but WITHOUT ANY WARRANTY; without even the implied warranty of
+# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+# GNU General Public License for more details.
+
+# You should have received a copy of the GNU General Public License
+# along with GNU Emacs; see the file COPYING.  If not, write to
+# the Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+# Boston, MA 02110-1301 USA,
+
+import numpy as np
+import matplotlib.pyplot as plt
+from matplotlib import style
+style.use('fivethirtyeight')
+np.random.seed(seed=42)
+# Create data
+rectangles = np.array([[1,1.5,1.7,1.45,1.1,1.6,1.8],[1.8,1.55,1.45,1.6,1.65,1.7,1.75]])
+triangles = np.array([[0.1,0.5,0.25,0.4,0.3,0.6,0.35,0.15,0.4,0.5,0.48],[1.1,1.5,1.3,1.2,1.15,1.0,1.4,1.2,1.3,1.5,1.0]])
+circles = np.array([[1.5,1.55,1.52,1.4,1.3,1.6,1.35,1.45,1.4,1.5,1.48,1.51,1.52,1.49,1.41,1.39,1.6,1.35,1.55,1.47,1.57,1.48,
+                    1.55,1.555,1.525,1.45,1.35,1.65,1.355,1.455,1.45,1.55,1.485,1.515,1.525,1.495,1.415,1.395,1.65,1.355,1.555,1.475,1.575,1.485]
+                    ,[1.3,1.35,1.33,1.32,1.315,1.30,1.34,1.32,1.33,1.35,1.30,1.31,1.35,1.33,1.32,1.315,1.38,1.34,1.28,1.23,1.25,1.29,
+                     1.35,1.355,1.335,1.325,1.3155,1.305,1.345,1.325,1.335,1.355,1.305,1.315,1.355,1.335,1.325,1.3155,1.385,1.345,1.285,1.235,1.255,1.295]])
+#Plot the data
+fig = plt.figure(figsize=(10,10))
+ax0 = fig.add_subplot(111)
+ax0.scatter(rectangles[0],rectangles[1],marker='s',c='grey',edgecolor='black')
+ax0.scatter(triangles[0],triangles[1],marker='^',c='yellow',edgecolor='black')
+ax0.scatter(circles[0],circles[1],marker='o',c='blue',edgecolor='black')
+# Calculate the mean vectors per class
+mean_rectangles = np.mean(rectangles,axis=1).reshape(2,1) # Creates a 2x1 vector consisting of the means of the dimensions
+mean_triangles = np.mean(triangles,axis=1).reshape(2,1)
+mean_circles = np.mean(circles,axis=1).reshape(2,1)
+# Calculate the scatter matrices for the SW (Scatter within) and sum the elements up
+scatter_rectangles = np.dot((rectangles-mean_rectangles),(rectangles-mean_rectangles).T)
+# Mind that we do not calculate the covariance matrix here because then we have to divide by n or n-1 as shown below
+#print((1/7)*np.dot((rectangles-mean_rectangles),(rectangles-mean_rectangles).T))
+#print(np.var(rectangles[0],ddof=0))
+scatter_triangles = np.dot((triangles-mean_triangles),(triangles-mean_triangles).T)
+scatter_circles = np.dot((circles-mean_circles),(circles-mean_circles).T)
+# Calculate the SW by adding the scatters within classes
+SW = scatter_triangles+scatter_circles+scatter_rectangles
+print(SW)
+plt.show()