/usr/share/pyshared/mlpy/_fda.py is in python-mlpy 2.2.0~dfsg1-2.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 | ## This file is part of MLPY.
## Fisher Discriminant Analysis.
## This is an implementation of Fisher Discriminant Analysis described in:
## 'An Improved Training Algorithm for Kernel Fisher Discriminants' S. Mika,
## A. Smola, B Scholkopf. 2001.
## This code is written by Roberto Visintainer, <visintainer@fbk.eu> and
## Davide Albanese <albanese@fbk.eu>.
## (C) 2008 Fondazione Bruno Kessler - Via Santa Croce 77, 38100 Trento, ITALY.
## This program 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 of the License, or
## (at your option) any later version.
## This program 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 this program. If not, see <http://www.gnu.org/licenses/>.
__all__ = ['Fda']
from numpy import *
from numpy.linalg import inv
import random as rnd
def dot3(a1, M, a2):
"""Compute a1 * M * a2T
"""
a1M = dot(a1, M)
res = inner(a1M, a2)
return res
class Fda:
"""Fisher Discriminant Analysis.
Example:
>>> import numpy as np
>>> import mlpy
>>> xtr = np.array([[1.0, 2.0, 3.1, 1.0], # first sample
... [1.0, 2.0, 3.0, 2.0], # second sample
... [1.0, 2.0, 3.1, 1.0]]) # third sample
>>> ytr = np.array([1, -1, 1]) # classes
>>> myfda = mlpy.Fda() # initialize fda class
>>> myfda.compute(xtr, ytr) # compute fda
1
>>> myfda.predict(xtr) # predict fda model on training data
array([ 1, -1, 1])
>>> xts = np.array([4.0, 5.0, 6.0, 7.0]) # test point
>>> myfda.predict(xts) # predict fda model on test point
-1
>>> myfda.realpred # real-valued prediction
-42.51475717037367
>>> myfda.weights(xtr, ytr) # compute weights on training data
array([ 9.60629896, 9.77148463, 9.82027615, 11.58765243])
"""
def __init__(self, C = 1):
"""
Initialize Fda class.
:Parameters:
C : float
regularization parameter
"""
self.__C = C
self.__w = 'cr'
self.__x = None
self.__y = None
self.__xpred = None
self.__a = None
self.__b = None
self.__K = None
def __stdinvH(self, x, C):
"""Build matrix H and invert it.
See eq. 4 at page 2.
Matrix H:
|-------------------------|
|l(Val) | oneK(Vet) |
|-------------------------|
|oneKT(Vet) | M(Mat) |
|-------------------------|
"""
# Compute kernel matrix
xT = x.transpose()
K = dot(x, xT)
KT = K # (symmetric matrix)
# Alloc H
H = empty((K.shape[0] + 1, K.shape[0] + 1), dtype = float)
# Compute oneK = 1T * K
oneK = K.sum(axis = 0)
# Build H
# Compute M = (KT * K) + (C * P)
H[1:, 1:] = dot(KT, K) + identity(K.shape[1]) * C
H[0, 1:] = oneK
H[1:, 0] = oneK
H[0, 0] = x.shape[0]
invH = inv(H)
return (K, KT, invH)
def __compute_a(self, x, y, KT, invH):
"""Compute a
See eq. 8, 9 at page 3.
"""
lp = y[y == 1].shape[0]
ln = y[y == -1].shape[0]
# Compute c, A+ and A-.
# See eq. 4 at page 2.
c = append((lp - ln), dot(KT, y))
onep = zeros_like(y)
onen = zeros_like(y)
onep[y == 1 ] = 1
onen[y == -1] = 1
Ap = append(lp, dot(KT, onep))
An = append(ln, dot(KT, onen))
# Compute lambda
# See eq. 9 at page 3.
A = dot3(Ap, invH, Ap)
B = dot3(Ap, invH, An)
C = dot3(An, invH, Ap)
D = dot3(An, invH, An)
E = -(lp) + dot3(c, invH, Ap)
F = ln + dot3(c, invH, An)
G = -0.5 * dot3(c, invH, c)
lambdan = ( -F + ((C + B) * E / (2 * A)) ) / \
( -D + ((C + B)**2 / (4 * A)) )
lambdap = ( -E + (0.5 * (C + B) * lambdan) ) / -A
# Compute a
# See eq. 8 at page 3.
lambdaAp = dot(lambdap, Ap)
lambdaAn = dot(lambdan, An)
a = dot(invH, (c - (lambdaAp + lambdaAn)))
return a
def __standard(self):
self.__K, KT, invH = self.__stdinvH(self.__x, self.__C)
a = self.__compute_a(self.__x, self.__y, KT, invH)
self.__xpred = self.__x
# Return b, a
return a[0], a[1:]
def compute(self, x, y):
"""Compute fda model.
:Parameters:
x : 2d numpy array float (sample x feature)
training data
y : 1d numpy array integer (two classes, 1 or -1)
classes
:Returns:
1
"""
self.__x = x
self.__y = y
self.__b, self.__a = self.__standard()
return 1
def predict(self, p):
"""Predict fda model on test point(s).
:Parameters:
p : 1d or 2d ndarray float (sample(s) x feats)
test sample(s)
:Returns:
cl : integer or 1d numpy array integer
class(es) predicted
:Attributes:
self.realpred : float or 1d numpy array float
real valued prediction
"""
if p.ndim == 2:
# Real prediction
pT = p.transpose()
K = dot(self.__xpred, pT)
self.realpred = dot(self.__a, K) + self.__b
# Prediction
pred = zeros(p.shape[0], dtype = int)
pred[self.realpred > 0.0] = 1
pred[self.realpred < 0.0] = -1
elif p.ndim == 1:
# Real prediction
pT = p.reshape(-1, 1)
K = dot(self.__xpred, pT)
self.realpred = (dot(self.__a, K) + self.__b)[0]
# Prediction
pred = 0.0
if self.realpred > 0.0:
pred = 1
elif self.realpred < 0.0:
pred = -1
return pred
def weights (self, x, y):
"""
Return feature weights.
:Parameters:
x : 2d ndarray float (samples x feats)
training data
y : 1d ndarray integer (-1 or 1)
classes
:Returns:
fw : 1d ndarray float
feature weights
"""
self.compute(x,y)
if self.__w == 'cr':
n1idx = where(y == 1)[0]
n2idx = where(y == -1)[0]
idx = append(n1idx, n2idx)
y = self.__y[idx]
K = self.__K[idx][:, idx]
target = ones((y.shape[0], y.shape[0]), dtype = int)
target[:n1idx.shape[0], n1idx.shape[0]:] = -1
target[n1idx.shape[0]:, :n1idx.shape[0]] = -1
yy = trace(dot(target, target))
w = empty(x.shape[1], dtype = float)
for i in range(x.shape[1]):
mask = dot(x[:, i].reshape(-1, 1), x[:, i].reshape(1, -1))
newK = K - mask
w[i] = sqrt( trace(dot(newK, newK)) * yy) / trace(dot(newK, target))
return w
|