/usr/share/pyshared/mlpy/_dlda.py is in python-mlpy 2.2.0~dfsg1-2.1.
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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 | ## This file is part of MLPY.
## Diagonal Linear Discriminant Analysis.
## This is an implementation of Diagonal Linear Discriminant Analysis described in:
## 'Block Diagonal Linear Discriminant Analysis With Sequential Embedded Feature Selection'
## Roger Pique'-Regi'
## This code is written by Roberto Visintainer, <visintainer@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__ = ['Dlda']
from numpy import *
from numpy.linalg import inv, LinAlgError
def wmw_auc(y, r):
"""
Compute the AUC by using the Wilcoxon-Mann-Whitney formula.
"""
if y.shape[0] != r.shape[0]:
raise ValueError("y and r have different length")
if unique(y).shape[0] > 2:
raise ValueError("wmw_auc() works only for two-classes")
idxp = where(y == 1)[0]
idxn = where(y == -1)[0]
AUC = 0.0
for p in idxp:
for n in idxn:
if (r[p] - r[n]) > 0.0:
AUC += 1.0
return AUC / float(idxp.shape[0] * idxn.shape[0])
def mcc(y, p):
"""
Compute the Matthews Correlation Coefficient (MCC).
"""
if y.shape[0] != p.shape[0]:
raise ValueError("y and p have different length")
if unique(y).shape[0] > 2 or unique(p).shape[0] > 2:
raise ValueError("mcc() works only for two-classes")
tpdiff = (y[y == 1] == p[y == 1])
tndiff = (y[y == -1] == p[y == -1])
fpdiff = (y[p == 1] == p[p == 1])
fndiff = (y[p == -1] == p[p == -1])
tp = tpdiff[tpdiff == True] .shape[0]
tn = tndiff[tndiff == True] .shape[0]
fp = fpdiff[fpdiff == False].shape[0]
fn = fndiff[fndiff == False].shape[0]
den = sqrt((tp+fn)*(tp+fp)*(tn+fn)*(tn+fp))
if den == 0.0:
return 0.0
num = ((tp*tn)-(fp*fn))
return num / den
def dot3(a1, M, a2):
"""
Compute a1 * M * a2T
"""
a1M = dot(a1, M)
res = inner(a1M, a2)
return res
class Dlda:
"""
Diagonal Linear Discriminant Analysis.
Example:
>>> from numpy import *
>>> from mlpy import *
>>> xtr = array([[1.1, 2.4, 3.1, 1.0], # first sample
... [1.2, 2.3, 3.0, 2.0], # second sample
... [1.3, 2.2, 3.5, 1.0], # third sample
... [1.4, 2.1, 3.2, 2.0]]) # fourth sample
>>> ytr = array([1, -1, 1, -1]) # classes
>>> mydlda = Dlda(nf = 2) # initialize dlda class
>>> mydlda.compute(xtr, ytr) # compute dlda
1
>>> mydlda.predict(xtr) # predict dlda model on training data
array([ 1, -1, 1, -1])
>>> xts = array([4.0, 5.0, 6.0, 7.0]) # test point
>>> mydlda.predict(xts) # predict dlda model on test point
-1
>>> mydlda.realpred # real-valued prediction
-21.999999999999954
>>> mydlda.weights(xtr, ytr) # compute weights on training data
array([ 2.13162821e-14, 0.00000000e+00, 0.00000000e+00, 4.00000000e+00])
"""
def __init__(self, nf = 0, tol = 10, overview = False, bal = False):
"""
Initialize Dlda class.
:Parameters:
nf : int (1 <= nf >= #features)
the number of the best features that you want to use in
the model. If nf = 0 the system stops at a number of features
corresponding to a peak of accuracy
tol : int
in case of nf = 0 it's the number of steps
of classification to be calculated after the peak to avoid a
local maximum
overview : bool
set True to print informations about the
accuracy of the classifier at every step of the compute
bal : bool
set True if it's reasonable to consider the
unbalancement of the test set similar to the one of the
training set
"""
if nf < 0:
raise ValueError("nf value must be >= 1 or 0")
self.__nf = nf
self.__tol = tol
self.__computed = False
self.__overview = overview
self.__bal = bal
def __compute_d(self, j):
"""Compute the distance between the centroids of the
distribution of the two classes of data.
"""
a = self.__A[:]
a.append(j)
X = self.__x[:, a]
medpos = mean(X[where (self.__y == 1)], axis = 0)
medneg = mean(X[where (self.__y == -1)], axis = 0)
d = (medpos - medneg)
return d
def __compute_sigma(self, j):
""" Compute a metric in order to choose the 'best' features
between the ones left from the previous passages.
See Eq.7 Pg.3
"""
Xa = self.__x[:, j]
Xpos = Xa[where(self.__y==1), :][0]
Xneg = Xa[where(self.__y==-1), :][0]
sigma = sqrt(var(Xpos, axis = 0)) + sqrt(var(Xneg, axis = 0))
return sigma
def __compute_b(self):
""" Compute of the parameter 'b' offset of the classification
hyperplan.
Adaptive offset (b) based on MCC value of the prediction is computed.
"""
MAXMCC = -1
BestB = 0
RP = self.realpred = dot(self.__x[:, self.__A], self.__WA)
L = zeros_like(RP)
SRP = sort(RP)
for i in range(len(SRP)-1):
B = 0.5 * (SRP[i] + SRP[i+1])
L[where(RP < B)] = -1
L[where(RP >= B)] = 1
MCC = mcc(self.__y,L)
if MCC > MAXMCC:
MAXMCC = MCC
BestB = B
self.__b = BestB
def __choose_model(self):
"""With a l.o.o. classification verify which model gives the
best accuracy.
"""
tmp = ones((self.__K.shape[0], self.__K.shape[1]), dtype = int8)
tmp[:-1, :-1] = self.__Kmask
tmp[-1, : - (len(self.__A) - self.__m_code)] = tmp[:-(len(self.__A) - self.__m_code), -1] = 0
mask_sameblock = tmp.copy()
tmp[-1, :-1] = tmp[:-1, -1] = 0
mask_otherblock = tmp.copy()
try:
acc_ob, mcc_ob, auc_ob = self.__check_model(mask_otherblock)
acc_sb, mcc_sb, auc_sb = self.__check_model(mask_sameblock)
except:
return 0
if mcc_ob > mcc_sb:
self.__Kmask = mask_otherblock
self.__checkstop(mcc_ob)
self.__m_code = len(self.__A) - 1
if self.__overview == True:
print 'With', len(self.__A), 'features the accuracy on training data is:', \
acc_ob * 100, '%, the MCC value is', mcc_ob, "and auc =",auc_ob
else:
self.__Kmask = mask_sameblock
self.__checkstop(mcc_sb)
if self.__overview == True:
print 'With', len(self.__A), 'features the accuracy on training data is:', \
acc_sb * 100, '%, the MCC value is', mcc_sb, "and auc =",auc_sb
def __check_model(self, mask):
"""Given the next best feature calculates which covariance
matrix model is the best.
See Table1 Pg.2
"""
p_mcc = zeros(self.__x.shape[0])
rp_auc = zeros(self.__x.shape[0])
n_right = 0
pred = 0
xf = self.__x[:, self.__A]
for i in range(self.__x.shape[0]):
s = range(self.__x.shape[0])
s.remove(i)
xsf = xf[s,:]
ys = self.__y[s]
ytest = self.__y[i]
try:
K = cov(xsf.transpose(), bias = 1) * mask
except:
return 0
medpos = mean(xsf[where(ys == 1), :][0], axis = 0)
medneg = mean(xsf[where(ys == -1), :][0], axis = 0)
d = medpos - medneg
try:
w = dot(inv(K), d)
except LinAlgError:
w = dot(pinv(K), d)
pred = dot(self.__x[i,self.__A], w) - self.__b
rp_auc[i] = pred
if pred >= 0.0:
p_mcc[i] = 1
elif pred < 0.0:
p_mcc[i] = -1
if (pred >= 0 and ytest == 1) or (pred < 0 and ytest == -1):
n_right += 1
acc = n_right*1.0 / self.__x.shape[0]*1.0
mcc_res = mcc(self.__y, p_mcc)
auc_res = wmw_auc(self.__y, rp_auc)
return acc, mcc_res, auc_res
def __addfeat(self, BF):
"""Adds the chosen feature to the final list of features 'A'
and deletes it from 'AC'. Update correlation matrix 'K',
distance 'd' and weights 'WA'.
"""
if self.__K == None:
self.__K = array([[cov(self.__x[:,BF], bias = 1)]])
self.__d = self.__compute_d(BF)
try:
self.__WA = dot(inv(self.__K), self.__d)
except:
self.__WA = dot(pinv(self.__K), self.__d)
else:
res = self.__compute_WA(BF)
self.__WA = res[0]
self.__K = res[2]
self.__d = res[1]
self.__A.append(BF)
self.__AC.remove(BF)
self.__compute_b()
def __update_K(self, j):
"""Updates the correlation matrix starting from the one
result of the previous step.
"""
a = self.__A[:]
a.append(j)
X = self.__x[:, a]
return cov(X.transpose(), bias = 1)
def __compute_WA(self, j):
"""Compute the vector of weights at every step of the cycle
(the number of weights increases with the number of features
considered).
See Eq.6 Pg.3
"""
d = self.__compute_d(j)
K = self.__update_K(j)
### NB: adding a new feature we don't have info about the mask so we use the whole cov matrik K
try:
WA = dot(inv(K),d)
except:
WA = dot(pinv(K),d)
return [WA,d,K]
def __compute_j(self, j):
"""
Compute a metric in order to choose the 'best' features between
the ones left from the previous passages
See Eq.7 Pg.3
"""
res_WA = self.__compute_WA(j)
WA = res_WA[0]
d_t = res_WA[1].transpose()
K = res_WA[2]
num = inner(d_t,WA)**2.0
den = dot3(WA, K, WA)
return (num / den)
def __checkstop(self, M):
"""In case of 'auto stop mode' (nf = 0). Counts the number
of steps in which the model doesn't exceeds the peak value,
resets the peak value and count otherwise.
"""
if M > (self.__peak + 1e-3): # Don't update under 1e-3 over the peak
try:
self.__WA_stored = dot(inv(self.__K*self.__Kmask),self.__d)
except:
self.__SingularMatrix = True
return 0
self.__b_stored = self.__b
self.__A_stored = self.__A[:]
self.__cont = 0
self.__peak = M
else:
self.__cont += 1
def __select_features(self):
"""In a cycle selects the best features and the best model to use.
See Algorithm 1 Pg.3
"""
if len(self.__A) == 0: # Check it's really the first step (for landscape)
self.__b = 0
Bestval = 0
for j in self.__AC:
dist = sum(abs(self.__compute_d(j))) ## Distance L2
val = dist / self.__compute_sigma(j) * 1.0
if val > Bestval:
Bestval = val
Bestfeat = j
self.__addfeat(Bestfeat)
# IF N OF FEATURES IS DEFINED
if self.__nf > 0:
while (len(self.__A) < self.__nf):
bestval = None
bestfeat = None
for j in self.__AC:
res_j = self.__compute_j(j)
val_j = res_j
if val_j >= bestval:
bestval = val_j
bestfeat = j
if bestfeat == None: # If all the features generate a singular matrix the compute returns 0
return 0
else:
self.__addfeat(bestfeat)
self.__choose_model()
try:
self.__WA = dot(inv(self.__K*self.__Kmask),self.__d)
except:
self.__WA = dot(pinv(self.__K*self.__Kmask),self.__d)
if self.__overview == True:
print "Weights for ", self.__nf, "features: " ,self.__WA
print 'This model is going to use', len(self.__A), 'features'
# IF USE AUTOSTOP
if self.__nf == 0:
while ((len(self.__AC) > 0) and (self.__cont < self.__tol)):
bestval = None
bestfeat = None
for j in self.__AC:
res_j = self.__compute_j(j)
val_j = res_j
if val_j >= bestval:
bestval = val_j
bestfeat = j
print bestfeat
if bestfeat == None: # If all the features generate a singular matrix the compute returns 0
return 0
else:
self.__addfeat(bestfeat)
self.__choose_model()
self.__WA = self.__WA_stored
self.__b = self.__b_stored
self.__A = self.__A_stored
if self.__overview == True:
print "Weights for ",len(self.__A),"features: ", self.__WA
print 'This model is going to use', len(self.__A), 'features'
def compute (self, x, y, mf = 0):
"""
Compute Dlda model.
:Parameters:
x : 2d ndarray float (samples x feats)
training data
y : 1d ndarray integer (-1 or 1)
classes
mf : int
number of classification steps to be calculated
more on a model already computed
:Returns:
1
:Raises:
LinAlgError
if x is singular matrix
"""
if (self.__nf == 0) or (self.__computed == False):
mf = 0
if mf == 0:
self.__classes = unique(y)
if self.__classes.shape[0] != 2:
raise ValueError("DLDA works only for two-classes problems")
if x.shape[1] < self.__nf:
raise ValueError("nf value must be <= total number of features")
cl0 = where(y == self.__classes[0])[0]
cl1 = where(y == self.__classes[1])[0]
self.__ncl0 = cl0.shape[0]
self.__ncl1 = cl1.shape[0]
self.__piN = self.__ncl0 * 1.0 / x.shape[0] * 1.0
self.__piP = self.__ncl1 * 1.0 / x.shape[0] * 1.0
self.__AC = range(x.shape[1])
self.__x = x
self.__y = y
self.__b = None
self.__d = None
self.__K = None
self.__Kmask = ones((1,1))
self.__A = []
self.__m_code = 0
self.__WA = None
self.__peak = 0
self.__cont = 0
self.__WA_stored= None
self.__b_stored = None
self.__A_stored = None
else:
self.__nf += mf
self.__select_features()
self.__computed = True
return 1
def predict (self, p):
"""
Predict Dlda 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 self.__computed == False:
raise StandardError("Dlda model not computed yet")
if p.ndim == 2:
self.realpred = dot(p[:, self.__A], self.__WA) - self.__b
pred = zeros(self.realpred.shape[0], dtype=int)
pred[where(self.realpred > 0.0)] = 1
pred[where(self.realpred < 0.0)] = -1
elif p.ndim == 1:
pred = 0.0
self.realpred = dot(p[:, self.__A], self.__WA) - self.__b
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, they are going to be
> 0 for the features chosen for the classification and = 0 for
all the others
"""
self.compute(x, y, 0)
weights = zeros(x.shape[1])
for i in range(len(self.__A)):
weights[self.__A[i]] = self.__WA[i]
if self.__overview:
print "The positions of the best features are:", self.__A
return abs(weights)
|