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util.py
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util.py
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##########################################
# File: util.py #
# Copyright Richard Stebbing 2014. #
# Distributed under the MIT License. #
# (See accompany file LICENSE or copy at #
# http://opensource.org/licenses/MIT) #
##########################################
# Imports
import re
# raise_if_not_shape
def raise_if_not_shape(name, A, shape):
"""Raise a `ValueError` if the np.ndarray `A` does not have dimensions
`shape`."""
if A.shape != shape:
raise ValueError('{}.shape != {}'.format(name, shape))
# previous_float
PARSE_FLOAT_RE = re.compile(r'([+-]*)0x1\.([\da-f]{13})p(.*)')
def previous_float(x):
"""Return the next closest float (towards zero)."""
s, f, e = PARSE_FLOAT_RE.match(float(x).hex().lower()).groups()
f, e = int(f, 16), int(e)
if f > 0:
f -= 1
else:
f = int('f' * 13, 16)
e -= 1
return float.fromhex('{}0x1.{:013x}p{:d}'.format(s, f, e))
##############################################################################
"""
Author(s): Wei Chen ([email protected])
"""
import os
import sys
import numpy as np
from matplotlib import pyplot as plt
from sklearn.decomposition import PCA
from sklearn.utils.graph import graph_shortest_path
from sklearn.neighbors import kneighbors_graph
from scipy.sparse.csgraph import connected_components
from sklearn.manifold import Isomap
from sklearn.preprocessing import scale
from sklearn.metrics import pairwise_distances
from sklearn.neighbors import NearestNeighbors
from scipy.stats import pearsonr
from sklearn.externals import joblib
import ConfigParser
def create_dir(path):
if os.path.isdir(path):
pass
else:
os.mkdir(path)
def reduce_dim(data_h, plot=False, save=False, c=None):
if plot:
# Scree plot
plt.rc("font", size=12)
pca = PCA()
pca.fit(data_h)
plt.plot(range(1,data_h.shape[1]+1), pca.explained_variance_ratio_)
plt.xlabel('Dimensionality')
plt.ylabel('Explained variance ratio')
plt.title('Scree Plot')
plt.show()
plt.close()
# Dimensionality reduction
pca = PCA(n_components=.995) # 99.5% variance attained
data_l = pca.fit_transform(data_h)
print 'Reduced dimensionality: %d' % data_l.shape[1]
if save:
save_model(pca, 'xpca', c)
return data_l, pca.inverse_transform
def sort_eigen(M):
''' Sort the eigenvalues and eigenvectors in DESCENT order '''
w, v = np.linalg.eigh(M)
idx = w.argsort()[::-1]
w = w[idx]
v = v[:,idx]
return w, v
def find_gap(metrics, threshold=.99, method='difference', multiple=False, verbose=0):
''' Find the largest gap of any NONNEGATIVE metrics (which is in DESCENT order)
The returned index is before the gap
threshold: needs to be specified only if method is 'percentage'
multiple: whether to find multiple gaps
'''
if method == 'percentage':
s = np.sum(metrics)
for i in range(len(metrics)):
if np.sum(metrics[:i+1])/s > threshold:
break
if verbose == 2:
plt.figure()
plt.plot(metrics, 'o-')
plt.title('metrics')
plt.show()
return i
else:
if method == 'difference':
m0 = np.array(metrics[:-1])
m1 = np.array(metrics[1:])
d = m0-m1
elif method == 'divide':
metrics = np.clip(metrics, np.finfo(float).eps, np.inf)
m0 = np.array(metrics[:-1])
m1 = np.array(metrics[1:])
d = m0/m1
else:
print 'No method called %s!' % method
sys.exit(0)
if multiple:
# dmin = np.min(d)
# dmax = np.max(d)
# t = dmin + (dmax-dmin)/10 # set a threshold
# n_gap = sum(d > t)
# idx = d.argsort()[::-1][:n_gap]
# arggap = idx
tol = 1e-4
arggap = []
if d[0] > tol:
arggap.append(0)
for i in range(len(d)-1):
if d[i+1] > d[i]:
arggap.append(i+1)
arggap = np.array(arggap)
else:
arggap = np.argmax(d)
if verbose == 2:
plt.figure()
plt.subplot(211)
plt.plot(metrics, 'o')
plt.title('metrics')
plt.subplot(212)
plt.plot(d, 'o')
# plt.plot([0, len(d)], [t, t], 'g--')
plt.title('gaps')
plt.show()
gap = d[arggap]
return arggap, gap
def create_graph(X, n_neighbors, include_self=False, verbose=0):
kng = kneighbors_graph(X, n_neighbors, mode='distance', include_self=include_self)
nb_graph = graph_shortest_path(kng, directed=False)
if verbose:
# Visualize nearest neighbor graph
neigh = NearestNeighbors().fit(X)
nbrs = neigh.kneighbors(n_neighbors=n_neighbors, return_distance=False)
visualize_graph(X, nbrs)
return nb_graph
def get_geo_dist(X, K='auto', verbose=0):
m = X.shape[0]
if K == 'auto':
# Choose the smallest k that gives a fully connected graph
for k in range(2, m):
G = create_graph(X, k, verbose=verbose)
if connected_components(G, directed=False, return_labels=False) == 1:
break;
return G, k
else:
return create_graph(X, K, verbose=verbose)
def get_k_range(X, verbose=0):
N = X.shape[0]
# Select k_min
for k in range(1, N):
G = create_graph(X, k, include_self=False, verbose=verbose)
if connected_components(G,directed=False,return_labels=False) == 1:
break;
k_min = k
# Select k_max
for k in range(k_min, N):
kng = kneighbors_graph(X, k, include_self=False).toarray()
A = np.logical_or(kng, kng.T) # convert to undirrected graph
P = np.sum(A)/2
if 2*P/float(N) > k+2:
break;
k_max = k-1#min(k_min+10, N)
if verbose == 2:
print 'k_range: [%d, %d]' % (k_min, k_max)
if k_max < k_min:
print 'No suitable neighborhood size!'
return k_min, k_max
def get_candidate(X, dim, k_min, k_max, verbose=0):
errs = []
k_candidates = []
for k in range(k_min, k_max+1):
isomap = Isomap(n_neighbors=k, n_components=dim).fit(X)
rec_err = isomap.reconstruction_error()
errs.append(rec_err)
i = k - k_min
if i > 1 and errs[i-1] < errs[i-2] and errs[i-1] < errs[i]:
k_candidates.append(k-1)
if len(k_candidates) == 0:
k_candidates.append(k)
if verbose == 2:
print 'k_candidates: ', k_candidates
plt.figure()
plt.rc("font", size=12)
plt.plot(range(k_min, k_max+1), errs, '-o')
plt.xlabel('Neighborhood size')
plt.ylabel('Reconstruction error')
plt.title('Select candidates of neighborhood size')
plt.show()
return k_candidates
def pick_k(X, dim, k_min=None, k_max=None, verbose=0):
''' Pick optimal neighborhood size for isomap algothm
Reference:
Samko, O., Marshall, A. D., & Rosin, P. L. (2006). Selection of the optimal parameter
value for the Isomap algorithm. Pattern Recognition Letters, 27(9), 968-979.
'''
if k_min is None or k_max is None:
k_min, k_max = get_k_range(X, verbose=verbose)
ccs = []
k_candidates = range(k_min, k_max+1)#get_candidate(X, dim, k_min, k_max, verbose=verbose)
for k in k_candidates:
isomap = Isomap(n_neighbors=k, n_components=dim).fit(X)
F = isomap.fit_transform(X)
distF = pairwise_distances(F)
distX = create_graph(X, k, verbose=verbose)
cc = 1-pearsonr(distX.flatten(), distF.flatten())[0]**2
ccs.append(cc)
k_opt = k_candidates[np.argmin(ccs)]
if verbose == 2:
print 'k_opt: ', k_opt
plt.figure()
plt.rc("font", size=12)
plt.plot(k_candidates, ccs, '-o')
plt.xlabel('Neighborhood size')
plt.ylabel('Residual variance')
plt.title('Select optimal neighborhood size')
plt.show()
return k_opt
def estimate_dim(data, verbose=0):
''' Estimate intrinsic dimensionality of data
data: input data
Reference:
"Samko, O., Marshall, A. D., & Rosin, P. L. (2006). Selection of the optimal parameter
value for the Isomap algorithm. Pattern Recognition Letters, 27(9), 968-979."
'''
# Standardize by center to the mean and component wise scale to unit variance
data = scale(data)
# The reconstruction error will decrease as n_components is increased until n_components == intr_dim
errs = []
found = False
k_min, k_max = get_k_range(data, verbose=verbose)
for dim in range(1, data.shape[1]+1):
k_opt = pick_k(data, dim, k_min, k_max, verbose=verbose)
isomap = Isomap(n_neighbors=k_opt, n_components=dim).fit(data)
err = isomap.reconstruction_error()
#print(err)
errs.append(err)
if dim > 2 and errs[dim-2]-errs[dim-1] < .5 * (errs[dim-3]-errs[dim-2]):
intr_dim = dim-1
found = True
break
if not found:
intr_dim = 1
# intr_dim = find_gap(errs, method='difference', verbose=verbose)[0] + 1
# intr_dim = find_gap(errs, method='percentage', threshold=.9, verbose=verbose) + 1
if verbose == 2:
plt.figure()
plt.rc("font", size=12)
plt.plot(range(1,dim+1), errs, '-o')
plt.xlabel('Dimensionality')
plt.ylabel('Reconstruction error')
plt.title('Select intrinsic dimension')
plt.show()
return intr_dim
def get_singular_ratio(X_nbr, d):
x_mean = np.mean(X_nbr, axis=1).reshape(-1,1)
s = np.linalg.svd(X_nbr-x_mean, compute_uv=0)
r = (np.sum(s[d:]**2.)/np.sum(s[:d]**2.))**.5
return r
def select_neighborhood(X, dims, k_range=None, get_full_ind=False, verbose=0):
''' Inspired by the Neighborhood Contraction and Neighborhood Expansion algorithms
The selected neighbors for each sample point should reflect the local geometric structure of the manifold
Reference:
"Zhang, Z., Wang, J., & Zha, H. (2012). Adaptive manifold learning. IEEE Transactions
on Pattern Analysis and Machine Intelligence, 34(2), 253-265."
'''
print 'Selecting neighborhood ... '
m = X.shape[0]
if type(dims) == int:
dims = [dims] * m
if k_range is None:
k_min, k_max = get_k_range(X)
else:
k_min, k_max = k_range
# G = get_geo_dist(X, verbose=verbose)[0] # geodesic distances
# ind = np.argsort(G)[:,:k_max+1]
neigh = NearestNeighbors().fit(X)
ind = neigh.kneighbors(n_neighbors=k_max, return_distance=False)
ind = np.concatenate((np.arange(m).reshape(-1,1), ind), axis=1)
nbrs = []
# Choose eta
k0 = k_max
r0s =[]
for j in range(m):
X_nbr0 = X[ind[j,:k0]].T
r0 = get_singular_ratio(X_nbr0, dims[j])
r0s.append(r0)
r0s.sort(reverse=True)
j0 = find_gap(r0s, method='divide')[0]
eta = (r0s[j0]+r0s[j0+1])/2
# eta = 0.02
if verbose:
print 'eta = %f' % eta
for i in range(m):
''' Neighborhood Contraction '''
rs = []
for k in range(k_max, k_min-1, -1):
X_nbr = X[ind[i,:k]].T
r = get_singular_ratio(X_nbr, dims[i])
rs.append(r)
if r < eta:
ki = k
break
if k == k_min:
ki = k_max-np.argmin(rs)
nbrs.append(ind[i,:ki])
''' Neighborhood Expansion '''
pca = PCA(n_components=dims[i]).fit(X[nbrs[i]])
nbr_out = ind[i, ki:] # neighbors of x_i outside the neighborhood set by Neighborhood Contraction
for j in nbr_out:
theta = pca.transform(X[j].reshape(1,-1))
err = np.linalg.norm(pca.inverse_transform(theta) - X[j]) # reconstruction error
if err < eta * np.linalg.norm(theta):
nbrs[i] = np.append(nbrs[i], [j])
# print ki, len(nbrs[i])
# print max([len(nbrs[i]) for i in range(m)])
if verbose:
# Visualize nearest neighbor graph
visualize_graph(X, nbrs)
# Visualize neighborhood selection
if X.shape[1] > 3:
pca = PCA(n_components=3)
F = pca.fit_transform(X)
else:
F = np.zeros((X.shape[0], 3))
F[:,:X.shape[1]] = X
fig3d = plt.figure()
ax3d = fig3d.add_subplot(111, projection = '3d')
# Create cubic bounding box to simulate equal aspect ratio
max_range = np.array([F[:,0].max()-F[:,0].min(), F[:,1].max()-F[:,1].min(), F[:,2].max()-F[:,2].min()]).max()
Xb = 0.5*max_range*np.mgrid[-1:2:2,-1:2:2,-1:2:2][0].flatten() + 0.5*(F[:,0].max()+F[:,0].min())
Yb = 0.5*max_range*np.mgrid[-1:2:2,-1:2:2,-1:2:2][1].flatten() + 0.5*(F[:,1].max()+F[:,1].min())
Zb = 0.5*max_range*np.mgrid[-1:2:2,-1:2:2,-1:2:2][2].flatten() + 0.5*(F[:,2].max()+F[:,2].min())
ax3d.scatter(Xb, Yb, Zb, c='white', alpha=0)
# Plot point sets in 3D
plot_samples = [0, 1]
nbr_indices = []
for i in plot_samples:
nbr_indices = list(set(nbr_indices) | set(nbrs[i]))
F_ = np.delete(F, nbr_indices, axis=0)
ax3d.scatter(F_[:,0], F_[:,1], F_[:,2], c='white')
colors = ['b', 'g', 'y', 'r', 'c', 'm', 'y', 'k']
from itertools import cycle
colorcycler = cycle(colors)
for i in plot_samples:
color = next(colorcycler)
ax3d.scatter(F[nbrs[i][1:],0], F[nbrs[i][1:],1], F[nbrs[i][1:],2], marker='*', c=color, s=100)
ax3d.scatter(F[i,0], F[i,1], F[i,2], marker='x', c=color, s=100)
plt.show()
if get_full_ind:
return nbrs, ind
else:
return nbrs
def visualize_graph(X, nbrs):
# Reduce dimensionality
if X.shape[1] > 3:
pca = PCA(n_components=3)
F = pca.fit_transform(X)
else:
F = np.zeros((X.shape[0], 3))
F[:,:X.shape[1]] = X
m = F.shape[0]
fig3d = plt.figure()
ax3d = fig3d.add_subplot(111, projection = '3d')
# Create cubic bounding box to simulate equal aspect ratio
max_range = np.array([F[:,0].max()-F[:,0].min(), F[:,1].max()-F[:,1].min(), F[:,2].max()-F[:,2].min()]).max()
Xb = 0.5*max_range*np.mgrid[-1:2:2,-1:2:2,-1:2:2][0].flatten() + 0.5*(F[:,0].max()+F[:,0].min())
Yb = 0.5*max_range*np.mgrid[-1:2:2,-1:2:2,-1:2:2][1].flatten() + 0.5*(F[:,1].max()+F[:,1].min())
Zb = 0.5*max_range*np.mgrid[-1:2:2,-1:2:2,-1:2:2][2].flatten() + 0.5*(F[:,2].max()+F[:,2].min())
ax3d.scatter(Xb, Yb, Zb, c='white', alpha=0)
# Plot point sets in 3D
ax3d.scatter(F[:,0], F[:,1], F[:,2], c='blue')
# Plot edges
# for i in range(m-1):
# for j in range(i+1, m):
# if j in nbrs[i]:
# line = np.vstack((F[i], F[j]))
# ax3d.plot(line[:,0], line[:,1], line[:,2], c='green')
for i in [3]:
for j in range(i+1, m):
if j in nbrs[i]:
line = np.vstack((F[i], F[j]))
ax3d.plot(line[:,0], line[:,1], line[:,2], c='green')
plt.show()
def get_fname(mname, c, directory='./trained_models/', extension='pkl'):
config = ConfigParser.ConfigParser()
config.read('config.ini')
source = config.get('Global', 'source')
noise_scale = config.getfloat('Global', 'noise_scale')
if source == 'sf':
alpha = config.getfloat('Superformula', 'nonlinearity')
beta = config.getint('Superformula', 'n_clusters')
sname = source + '-' + str(beta) + '-' + str(alpha)
elif source == 'glass' or source[:3] == 'sf-':
sname = source
if c is None:
fname = '%s/%s_%.4f_%s.%s' % (directory, sname, noise_scale, mname, extension)
else:
fname = '%s/%s_%.4f_%s_%d.%s' % (directory, sname, noise_scale, mname, c, extension)
return fname
def save_model(model, mname, c=None):
# Get the file name
fname = get_fname(mname, c)
# Save the model
joblib.dump(model, fname, compress=9)
print 'Model ' + mname + ' saved!'
def load_model(mname, c=None):
# Get the file name
fname = get_fname(mname, c)
# Load the model
model = joblib.load(fname)
return model
def save_array(array, dname, c=None):
# Get the file name
fname = get_fname(dname, c, extension='npy')
# Save the model
np.save(fname, array)
print 'Model ' + dname + ' saved!'
def load_array(dname, c=None):
# Get the file name
fname = get_fname(dname, c, extension='npy')
# Load the model
array = np.load(fname)
return array