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ktsne.py
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ktsne.py
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'''
@author: dan
'''
from __future__ import division
import numpy as np
from kernels import Kernels
class Ktsne:
def __init__(self, X, f_opts={}):
self._dim = f_opts["n_dims"]
self._perp = f_opts["perplexity"]
self._eta = f_opts["eta"]
self.f_opts = f_opts
self._momentum = .4
self.X = X.copy()
self.P = None
self.Q = None
self._iter = 0
(n, d) = self.X.shape
y_sz = (n, self._dim)
mw, Mw = (-np.sqrt(6. / sum(y_sz)), np.sqrt(6. / sum(y_sz)))
# self.Y = np.random.uniform(mw, Mw, y_sz)
self.Y = np.random.randn(n, self._dim)*Mw
self.dY = None # np.zeros((n, self._dim))
self.Y_t = np.array(
[np.zeros_like(self.Y), np.zeros_like(self.Y)])
np.seterr(divide='ignore', invalid='ignore')
def reduce_X(self):
XX = self.X.copy()
p_dims = self.f_opts["p_dims"]
gamma = self.f_opts["gamma"]
degree = self.f_opts["p_degree"]
kernel = self.f_opts["ker"]
kn = Kernels(XX, k_opts={
"kernel": kernel, "gamma": gamma, "degree": degree, "p_dims": p_dims})
self.X = kn.process_data()
def L1(self, X):
D = np.sum(np.abs(X[:, None] - X[None, :], -1))
return D
def L2(self, X):
D = np.sum((X[:, None] - X[None, :])**2, -1)
return D
def bin_search(self, d_row, target, tol=1e-2, niter=1000, low=1e-10, up=1e3):
for i in xrange(niter):
estimated = (low + up)/2.
# print estimated
p_row = np.exp(- (d_row) / estimated)
sumP = np.sum(p_row)
p_row = p_row/sumP
val = self.entropy(p_row)
dif = np.abs(val-target)
if dif <= tol:
break
if val > target:
up = estimated
else:
low = estimated
return p_row, estimated
def entropy(self, p_row):
H = -np.sum(p_row*np.log2(p_row))
return H
def compute_P(self):
n, d = self.X.shape
P = np.zeros((n, n))
sigmas = np.ones((n, 1))
D = self.L2(self.X)
target_entropy = np.log2(self._perp)
for i in xrange(n):
d_row = D[i, np.hstack((np.arange(0, i), np.arange(i+1, n)))]
p_row, estimated = self.bin_search(d_row, target_entropy)
P[i, np.hstack((np.arange(0, i), np.arange(i+1, n)))] = p_row
sigmas[i] = estimated
msig = np.mean(np.sqrt(1/sigmas))
print "Mean value of sigma: ", msig
# (pik + pki ) the average divide by 2n usualy.. in docs
P = (P + np.transpose(P)) / (2*n)
P = P / np.sum(P)
P = np.maximum(P, 1e-12)
return P
def compute_Q(self):
D = self.L2(self.Y)
q = 1 / (1 + D)
np.fill_diagonal(q, 0)
self.Q = q / np.sum(q)
self.Q = np.maximum(self.Q, 1e-12)
return q
def gradient(self, q):
PQ = self.P - self.Q
M = PQ * q
MD = 4 * (np.diag(np.sum(M, 1)) - M)
self.dY = np.dot(MD, self.Y)
def get_solution(self, steps=500):
self.reduce_X()
self.P = self.compute_P()
self.P = self.P * 10.
for i in xrange(steps):
cost = self.step()
if i % 500 == 0:
print "Iteration ", i, ": cost is ", cost
print "cost : ", cost
self.Y = self.Y - np.mean(self.Y, 0)
#print self.Y[:5]
return self.Y
def step(self):
q = self.compute_Q()
self.gradient(q)
if self._iter == 100:
self.P = self.P / 10.
if self._iter == 25:
self._momentum = .8
self.Y = self.Y - self._eta*self.dY
self.Y = self.Y + self._momentum * \
np.diff(self.Y_t, axis=0)[0]
self.Y_t[1] = self.Y_t[0].copy()
self.Y_t[0] = self.Y
C = np.sum(self.P * np.log(self.P / self.Q))
self._iter += 1
return C