#!/usr/bin/env python
# coding: utf-8
#########################################################################
#########################################################################
"""
File Name: distance.py
Author: Wan Ji
E-mail: wanji@live.com
Created on: Mon Jun 30 13:23:40 2014 CST
"""
DESCRIPTION = """
Computing distances
Common parameters:
is_sparse:
is the feature sparse
is_trans:
is `feat` transfered
"""
import logging
import numpy as np
import scipy as sp
def fast_euclidean(feat, query, featl2norm):
""" Euclidean distance.
Args:
feat: N x D feature matrix
query: 1 x D feature vector
featl2norm: 1 x N vector
Returns:
dist: 1 x N vector
"""
return ((query ** 2).sum() + featl2norm) - 2 * query.dot(feat.T)
def euclidean(feat, query, featl2norm=None, qryl2norm=None):
""" Euclidean distance.
Args:
feat: N x D feature matrix
query: Q x D feature vector
featl2norm: 1 x N vector
qryl2norm: Q x 1 vector
Returns:
dist: 1 x N vector
"""
dotprod = query.dot(feat.T)
# return dotprod
if qryl2norm is None:
qryl2norm = (query ** 2).sum(1).reshape(-1, 1)
if featl2norm is None:
featl2norm = (feat ** 2).sum(1).reshape(1, -1)
return - 2 * dotprod + qryl2norm + featl2norm
def Euclidean(feat, query=None,
is_sparse=False, is_trans=False):
""" Euclidean distance.
"""
if query is None:
(N, D) = feat.shape
dotprod = feat.dot(feat.T)
featl2norm = sp.repeat(dotprod.diagonal().reshape(1, -1), N, 0)
qryl2norm = featl2norm.T
else:
(nQ, D) = query.shape
(N, D) = feat.shape
dotprod = query.dot(feat.T)
qryl2norm = \
sp.repeat(np.multiply(query, query).sum(1).reshape(-1, 1), N, 1)
featl2norm = \
sp.repeat(np.multiply(feat, feat).sum(1).reshape(1, -1), nQ, 0)
return qryl2norm + featl2norm - 2 * dotprod
def Euclidean_DML(feat, M, query=None,
is_sparse=False, is_trans=False):
""" Euclidean distance with DML.
"""
(N, D) = feat.shape
dotprod = feat.dot(M).dot(feat.T)
l2norm = sp.repeat(dotprod.diagonal().reshape(1, -1), N, 0)
return l2norm + l2norm.T - 2 * dotprod
def Cosine(feat, query=None,
is_sparse=False, is_trans=False):
""" Cosine distance.
"""
logging.info("Cosine")
try:
feat = feat / np.sqrt(np.sum(np.multiply(feat, feat), axis=1))\
.reshape((feat.shape[0], 1))
except ValueError as e:
logging.debug("%s (take feature as sparse matrix)" % e.message)
feat2 = feat.copy()
feat2.data **= 2
rows_sums = np.array(feat2.sum(axis=1))[:, 0]
feat.data /= rows_sums[feat2.nonzero()[0]]
if query is None:
query = feat
else:
try:
query = query/np.sqrt(np.sum(np.multiply(query, query), axis=1))\
.reshape((query.shape[0], 1))
except ValueError as e:
logging.debug("%s (take query as sparse matrix)" % e.message)
query2 = query.copy()
query2.data **= 2
rows_sums = np.array(query2.sum(axis=1))[:, 0]
query.data /= rows_sums[query2.nonzero()[0]]
return DotProduct(feat, query)
def Cosine_DML(feat, M, query=None,
is_sparse=False, is_trans=False):
""" Cosine distance with DML.
"""
try:
feat = feat/np.sqrt(np.sum(np.multiply(feat, feat), axis=1))\
.reshape((feat.shape[0], 1))
except ValueError as e:
logging.debug("%s (take feature as sparse matrix)" % e.message)
feat2 = feat.copy()
feat2.data **= 2
rows_sums = np.array(feat2.sum(axis=1))[:, 0]
feat.data /= rows_sums[feat2.nonzero()[0]]
if query is None:
query = feat
else:
try:
query = query/np.sqrt(np.sum(np.multiply(query, query), axis=1))\
.reshape((query.shape[0], 1))
except ValueError as e:
logging.debug("%s(take query as sparse matrix)" % e.message)
query2 = query.copy()
query2.data **= 2
rows_sums = np.array(query2.sum(axis=1))[:, 0]
query.data /= rows_sums[query2.nonzero()[0]]
return DotProduct_DML(feat, M, query)
def DotProduct(feat, query=None,
is_sparse=False, is_trans=False):
""" DotProduct distance.
"""
logging.debug("DotProduct")
if query is None:
query = feat
return -query.dot(feat.T)
def DotProduct_DML(feat, M, query=None,
is_sparse=False, is_trans=False):
""" DotProduct distance with DML.
"""
if query is None:
query = feat
return -query.dot(M).dot(feat.T)
def DotProduct_DML_Diagonal(feat, M, query=None,
is_sparse=False, is_trans=False):
""" DotProduct distance with DML.
"""
if query is None:
query = feat
query.data = query.data * M[query.nonzero()[1]]
return -query.dot(feat.T)
def Intersection(feat, query=None,
is_sparse=False, is_trans=False):
""" Intersection distance.
"""
raise Exception("Untested function")
if query is None:
query = feat
qnum = query.shape[0]
fnum = feat.shape[0]
dist = np.zeros((qnum, fnum))
for i in range(qnum):
for j in range(fnum):
dist[i, j] = sp.vstack((query[i, :], feat[j, :])).min(0).sum()
return dist
def Intersection_DML(feat, M, query=None,
is_sparse=False, is_trans=False):
""" Intersection distance with DML.
"""
raise Exception("Untested function")
if query is None:
query = feat
qnum = query.shape[0]
fnum = feat.shape[0]
dist = np.zeros((qnum, fnum))
for i in range(qnum):
query = query[i, :].dot(M)
for j in range(fnum):
dist[i, j] = sp.vstack((query, feat[j, :])).min(0).sum()
return -query.dot(M).dot(feat.T)
distFunc = {
"euclidean": Euclidean,
"dotproduct": DotProduct,
"intersection": Intersection,
"cosine": Cosine}
distFunc_DML = {
"euclidean": Euclidean_DML,
"dotproduct": DotProduct_DML,
"intersection": Intersection_DML,
"cosine": Cosine_DML}
