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diversity.py
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diversity.py
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# -*- coding: utf-8 -*-
"""
.. invisible:
_ _ _____ _ _____ _____
| | | | ___| | | ___/ ___|
| | | | |__ | | | |__ \ `--.
| | | | __|| | | __| `--. \
\ \_/ / |___| |___| |___/\__/ /
\___/\____/\_____|____/\____/
Created on Jul 8, 2014
Defines the class which calculates similarity/difference between neural network
layers.
███████████████████████████████████████████████████████████████████████████████
Licensed to the Apache Software Foundation (ASF) under one
or more contributor license agreements. See the NOTICE file
distributed with this work for additional information
regarding copyright ownership. The ASF licenses this file
to you under the Apache License, Version 2.0 (the
"License"); you may not use this file except in compliance
with the License. You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing,
software distributed under the License is distributed on an
"AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
KIND, either express or implied. See the License for the
specific language governing permissions and limitations
under the License.
███████████████████████████████████████████████████████████████████████████████
"""
from collections import namedtuple
import numpy
from numpy.linalg import norm
try:
import scipy.signal
import scipy.stats
except ImportError:
pass
from veles.znicz.nn_plotting_units import Weights2D
SimilarityCalculationParameters = namedtuple(
'SimilarityCalculationParameters', ['form_threshold', 'peak_threshold',
'magnitude_threshold'])
def get_similar_kernels(weights, channels=3,
params=SimilarityCalculationParameters(1.1, .5, .65)):
# number of neurons
N = weights.shape[0]
# number of weights in each channel
S = int(numpy.sqrt(weights.shape[1] / channels))
# size of the x-correlation matrix between two SxS matrices
corr_S = S * 2 - 1
peak_C = corr_S // 2
maxdist = numpy.sqrt(2) * peak_C
parts = [weights[:, c::channels] for c in range(channels)]
# the following matrices will be filled in for-s
corr_matrix = numpy.empty((N, N))
sub_matrix = numpy.empty((N, N))
kurt_matrix = numpy.empty((N, N))
# compare each with each
for x in range(N):
for y in range(N):
if x == y:
corr_matrix[x, y] = sub_matrix[x, y] = 0
kurt_matrix[x, y] = numpy.NAN
continue
corr = numpy.zeros((corr_S, corr_S))
for ch in parts:
corr += scipy.signal.correlate2d(ch[x].reshape(S, S),
ch[y].reshape(S, S),
boundary='symm')
amx, amy = numpy.unravel_index(numpy.argmax(corr), corr.shape)
dist = numpy.sqrt((amx - peak_C) ** 2 + (amy - peak_C) ** 2)
corr_matrix[x, y] = 1 - dist / maxdist
kurt_matrix[x, y] = scipy.stats.kurtosis(corr.ravel(), bias=False)
diff = 0
for ch in parts:
delta = ch[x] - ch[y]
delta = norm(delta)
diff += delta * delta
diff = numpy.sqrt(diff)
sub_matrix[x, y] = 1 - diff
# the indices of similar kernels
mask = numpy.ones((N, N))
# Filter by normalized difference
vals = sub_matrix[sub_matrix > 0]
mean = numpy.mean(vals)
stddev = numpy.std(vals)
threshold = numpy.max([
numpy.min([0.95, mean + stddev * params.magnitude_threshold]), 0.75])
mask *= sub_matrix > threshold
# Filter by peak sharpness
vals = kurt_matrix[numpy.logical_not(numpy.isnan(kurt_matrix))]
mean = numpy.mean(vals)
stddev = numpy.std(vals)
kurt_matrix[numpy.isnan(kurt_matrix)] = numpy.min(vals)
mask *= kurt_matrix > mean + stddev * params.peak_threshold
# Filter by x-correlation argmax distance from the center
vals = corr_matrix[corr_matrix > 0]
mean = numpy.mean(vals)
stddev = numpy.std(vals)
threshold = numpy.max([
numpy.min([0.95, mean + stddev * params.form_threshold]), 0.8])
mask *= corr_matrix > threshold
# Fix boundary='symm' symmetry violation
for x in range(N):
for y in range(N):
if x == y:
continue
if mask[x, y] > 0 and mask[y, x] == 0:
mask[x, y] = 0
del corr_matrix
del sub_matrix
del kurt_matrix
# Find cliques in the similarity graph.
# We use Bron-Kerbosch algorithm.
# http://en.wikipedia.org/wiki/Bron%E2%80%93Kerbosch_algorithm.
similar_sets = []
visited = set()
for x in range(N):
if x in visited:
continue
stack = [x]
clique = {x}
wrong = set()
while len(stack):
cx = stack.pop()
for y in range(N):
if mask[cx, y] == 0 or y in wrong:
continue
good = True
for z in clique:
if mask[y, z] == 0:
good = False
wrong.add(y)
break
if good:
clique.add(y)
stack.append(y)
if len(clique) > 1:
similar_sets.append(clique)
visited.update(clique)
return similar_sets
class SimilarWeights2D(Weights2D):
"""
Class for plotters, which show similar kernels
"""
def __init__(self, workflow, **kwargs):
kwargs['split_channels'] = False
super(SimilarWeights2D, self).__init__(workflow, **kwargs)
self.form_threshold = kwargs.get('form_threshold', 1.1)
self.peak_threshold = kwargs.get('peak_threshold', 0.5)
self.magnitude_threshold = kwargs.get('magnitude_threshold', 0.65)
def prepare_pics(self, inp, transposed):
if self.transposed:
inp = inp.transpose()
n_channels, _, _ = self.get_number_of_channels(inp)
if n_channels is None:
return None
sims = get_similar_kernels(
inp, n_channels,
SimilarityCalculationParameters(
self.form_threshold, self.peak_threshold,
self.magnitude_threshold))
self.info("Founf similar kernels: %s", str(sims))
siminp = numpy.empty((sum([len(s) for s in sims]), inp.shape[1]),
dtype=inp.dtype)
counter = 0
for simset in sims:
for s in simset:
siminp[counter] = inp[s]
counter += 1
if counter == 0:
return []
return super(SimilarWeights2D, self).prepare_pics(siminp, False)