/usr/share/pyshared/mlpy/_fda.py is in python-mlpy 2.2.0~dfsg1-2.1.
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## 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
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