R = np.mat(model.R)
model.RT = R.T
# both should be roughly the same (maybe even exactly the same for r0-R0)
assert common.norm(R.T.dot(R)-K) < 1e-10
assert common.norm(model.RT[0, :] - r0) < 1e-20
# 7/7/2013 TL: implementation seems to be working correctly.
elif nargs == 2:
N = 1000
D = 1000
X = common.randn((N, D))
U = X.dot(X.T)
import cProfile
cProfile.runctx('model = ICD.fast_ichol(U, 0.00001)', globals(), locals())
elif nargs == 3:
filename1 = sys.argv[1]
filename2 = sys.argv[2]
W1 = IO.readPickledWords(filename1)
W1.setupFeatures()
eta = 0.001
model1 = W1.ICD_representation(0, eta, 0)
W2 = IO.readPickledWords(filename2)
W2.setupFeatures()
eta = 0.001
model2 = W2.ICD_representation(0, eta, 1)
tau = 0.001
cca_model = CU.learn0(W1.features, W2.features, tau)
def find_matching(options, wordsX, wordsY):
# finds a permutation pi that best matches Y to X
# The optimization procedure works as follows:
# suppose there are 2000 words to be matched, 100 seed words and step size is 100
# The seed is stored at the end (so, X[i, :] matches Y[i, :] for i > 2000] in all iterations
# at each iteration t (starting at t=0):
# 1. compute the CCA on the last 100 + 100*t entries
# 2. compute the CCA representation of all words
# 3. perform a matching on the first N=2000 words to get pi_t
# 4. sort the first 2000 matches in descending order.
# initially, assume that pi is ID
N = len(wordsX.words)
M = N - options.seed_length # The first M entries can be permuted. The rest are fixed
GX = None
GY = None
options.cca_weights = None
sorted_edge_cost = None
fixed_point = False
for t in range(0, options.T):
options.t = t
Nt = M - options.step_size * t
# STEP 0: when the feature dimension is high, ICD the seed and project the rest
if wordsX.isPickled():
wordsX.ICD_representation(Nt, options.eta)
wordsY.ICD_representation(Nt, options.eta)
# STEP 1: compute CCA model on the well matched portion of the matching (which includes the fixed seed)
fixedX = wordsX.features[Nt:, :]
fixedY = wordsY.features[Nt:, :]
if options.useCCAWeights == 1 and sorted_edge_cost is not None:
q = np.square(sorted_edge_cost[Nt:])
bandwidth = np.median(q)
options.cca_weights = np.exp(-q / (2 * bandwidth)) # exp is useful when dist is used
# if options.noise_level > 0:
# fixedX += options.noise_level*common.randn(fixedX.shape)
# fixedY += options.noise_level*common.randn(fixedY.shape)
print >> sys.stderr, colored("CCA dimensions =", "green"), len(fixedX)
cca_model = CU.learn(fixedX, fixedY, options)
print >> sys.stderr, len(cca_model.p), "Top 10 correlation coefficients:", cca_model.p[:10]
# STEP 2: compute CCA representation of all samples
print >> sys.stderr, "norms", norm(wordsX.features), norm(wordsY.features)
Z = CU.project(options, cca_model, wordsX.features, wordsY.features)
print >> sys.stderr, "Z", norm(Z.X), norm(Z.Y)
# STEP 3: compute weight matrix and run matching (approximate) algorithm
if options.alpha > 0:
GX = wordsX.materializeGraph()
GY = wordsY.materializeGraph()
print >> sys.stderr, colored("Computing matching weight matrix.", "green")
W, U0, Z0 = MU.makeWeights(options, Z.X, Z.Y, GX, GY)
print >> sys.stderr, "Matching."
(cost, pi_t, edge_cost) = MU.exactMatch(W[:M, :M])
# STEP 4: sort the words, such that the best matches are at the end.
# note that pi_t is of length M < N and that
(sorted_edge_cost, I) = perm.sort(edge_cost, reverse=True)
sorted_edge_cost = np.concatenate((sorted_edge_cost, np.zeros(N - M)))
if perm.isID(pi_t): # the best permutation is the identity
fixed_point = True
else:
wordsX.permuteFirstWords(I)
wordsY.permuteFirstWords(pi_t[I])
# END OF ITERATION: output Matching
print >> sys.stderr, "cost =", cost, "latent inner product = ", np.sum(Z.X.A * Z.Y.A)
# MU.printMatching(wordsX.words[:M], wordsY.words[:M], sorted_edge_cost[:M], options.gold_lex)
if options.gold_lex is not None:
scores = BU.getScores(options.gold_lex, wordsX.words[:M], wordsY.words[:M], sorted_edge_cost[:M])
BU.outputScores(scores, options.title)
print "---------- ", "iteration = ", (t + 1), "/", options.T, "----------"
sys.stdout.flush()
if fixed_point:
break
# either we reached the maximum number of iterations, or a fixed point
log(100, "Stopped after, ", (t + 1), "iterations. Fixed point =", fixed_point)
IO.writeString(
options.matchingFilename,
MU.toString(wordsX.words[:M], wordsY.words[:M], sorted_edge_cost[:M], options.gold_lex),
)
if options.is_mock:
log("Hamming distance:", perm.hamming(wordsX.words, wordsY.words))
return wordsX, wordsY, sorted_edge_cost, cost
