/usr/share/pyshared/mlpy/_kmedoids.py is in python-mlpy 2.2.0~dfsg1-2.1.
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k-medoids algorithm.
"""
## This code is written by Davide Albanese, <albanese@fbk.eu>
## (C) 2009 Fondazione Bruno Kessler - Via Santa Croce 77, 38100 Trento, ITALY.
## This program is free software: you can redistribute it and/or modify
## it under the terms of the GNU General Public License as published by
## the Free Software Foundation, either version 3 of the License, or
## (at your option) any later version.
## This program is distributed in the hope that it will be useful,
## but WITHOUT ANY WARRANTY; without even the implied warranty of
## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
## GNU General Public License for more details.
## You should have received a copy of the GNU General Public License
## along with this program. If not, see <http://www.gnu.org/licenses/>.
__all__= ['Kmedoids', 'Minkowski']
import numpy as np
import mlpy
def kmedoids_core(x, med, oth, clust, cost, dist):
"""
* for each mediod m
* for each non-mediod data point n
Swap m and n and compute the total cost of the configuration
Select the configuration with the lowest cost
"""
d = np.empty((oth.shape[0], med.shape[0]), dtype=float)
med_n = np.empty_like(med)
oth_n = np.empty_like(oth)
idx = np.arange(oth.shape[0])
med_cur = med.copy()
oth_cur = oth.copy()
clust_cur = clust.copy()
cost_cur = cost
for i, m in enumerate(med):
for j, n in enumerate(oth[clust == i]):
med_n, oth_n = med.copy(), oth.copy()
med_n[i] = n
tmp = oth_n[clust == i]
tmp[j] = m
oth_n[clust == i] = tmp
for ii, nn in enumerate(oth_n):
for jj, mm in enumerate(med_n):
d[ii, jj] = dist.compute(x[mm], x[nn])
clust_n = np.argmin(d, axis=1) # clusters
cost_n = np.sum(d[idx, clust_n]) # total cost of configuration
if cost_n <= cost_cur:
med_cur = med_n.copy()
oth_cur = oth_n.copy()
clust_cur = clust_n.copy()
cost_cur = cost_n
return med_cur, oth_cur, clust_cur, cost_cur
class Kmedoids:
"""k-medoids algorithm.
"""
def __init__(self, k, dist, maxloops=100, rs=0):
"""Initialize Kmedoids.
:Parameters:
k : int
Number of clusters/medoids
dist : class
class with a .compute(x, y) method which
returns a distance
maxloops : int
maximum number of loops
rs : int
random seed
Example:
>>> import numpy as np
>>> import mlpy
>>> x = np.array([[ 1. , 1.5],
... [ 1.1, 1.8],
... [ 2. , 2.8],
... [ 3.2, 3.1],
... [ 3.4, 3.2]])
>>> dtw = mlpy.Dtw(onlydist=True)
>>> km = mlpy.Kmedoids(k=3, dist=dtw)
>>> km.compute(x)
(array([4, 0, 2]), array([3, 1]), array([0, 1]), 0.072499999999999981)
Samples 4, 0, 2 are medoids and represent cluster 0, 1, 2 respectively.
* cluster 0: samples 4 (medoid) and 3
* cluster 1: samples 0 (medoid) and 1
* cluster 2: sample 2 (medoid)
"""
self.__k = k
self.__maxloops = maxloops
self.__rs = rs
self.__dist = dist
np.random.seed(self.__rs)
def compute(self, x):
"""Compute Kmedoids.
:Parameters:
x : ndarray
An 2-dimensional vector (sample x features).
:Returns:
m : ndarray (1-dimensional vector)
medoids indexes
n : ndarray (1-dimensional vector)
non-medoids indexes
cl : ndarray 1-dimensional vector)
cluster membership for non-medoids.
Groups are in 0, ..., k-1
co : double
total cost of configuration
"""
# randomly select k of the n data points as the mediods
idx = np.arange(x.shape[0])
np.random.shuffle(idx)
med = idx[0:self.__k]
oth = idx[self.__k::]
# compute distances
d = np.empty((oth.shape[0], med.shape[0]), dtype=float)
for i, n in enumerate(oth):
for j, m in enumerate(med):
d[i, j] = self.__dist.compute(x[m], x[n])
# associate each data point to the closest medoid
clust = np.argmin(d, axis=1)
# total cost of configuration
cost = np.sum(d[np.arange(d.shape[0]), clust])
# repeat kmedoids_core until there is no change in the medoid
for l in range(self.__maxloops):
med_n, oth_n, clust_n, cost_n = kmedoids_core(x, med, oth, clust, cost, self.__dist)
if (cost_n < cost):
med, oth, clust, cost = med_n, oth_n, clust_n, cost_n
else:
break
return med, oth, clust, cost
class Minkowski:
"""
Computes the Minkowski distance between two vectors ``x`` and ``y``.
.. math::
{||x-y||}_p = (\sum{|x_i - y_i|^p})^{1/p}.
"""
def __init__(self, p):
"""
Initialize Minkowski class.
:Parameters:
p : float
The norm of the difference :math:`{||x-y||}_p`
"""
self.__p = p
def compute(self, x, y):
"""
Compute Minkowski distance
:Parameters:
x : ndarray
An 1-dimensional vector.
y : ndarray
An 1-dimensional vector.
:Returns:
d : float
The Minkowski distance between vectors ``x`` and ``y``
"""
return (abs(x - y)**self.__p).sum() ** (1.0 / self.__p)
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