# ulfaslak/py_pcha

Python package that implements the PCHA algorithm for Archetypal Analysis by Mørup et. al.
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# py_pcha

Fast Python implementation of Archetypal Analysis using Principle Convex Hull Analysis (PCHA).

From the source article [1]:

"Archetypal analysis (AA) proposed by Cutler and Breiman (1994) [2] estimates the principal convex hull (PCH) of a data set. As such AA favors features that constitute representative ‘corners’ of the data, i.e., distinct aspects or archetypes."

All code contained in this package was originally written in Matlab. The Matlab package is available here. Matlab package also handles sparse- and kernel matrices.

Matlab implementation by: Morten Mørup Python implementation by: Ulf Aslak

## Install:

Install with pip or easy_install

``````\$ pip install py_pcha
# or
\$ easy_install py_pcha
``````

## Example use:

```import numpy as np
from py_pcha import PCHA

dimensions = 15
examples = 100
X = np.random.random((dimensions, examples))

XC, S, C, SSE, varexpl = PCHA(X, noc=3, delta=0.1)

print "   # Arc 1     # Arc 2     # Arc 3\n", XC
# Arc 1     # Arc 2     # Arc 3
[[ 0.32588061  0.3940908   0.71705364]
[ 0.69790165  0.50729565  0.34076419]
[ 0.79184963  0.43616783  0.22377323]
[ 0.36865992  0.51199461  0.68595464]
[ 0.55887694  0.46533484  0.54946409]
[ 0.29774011  0.90728239  0.26895903]
[ 0.33116078  0.87118458  0.26744578]
[ 0.65678325  0.3104401   0.56770064]
[ 0.37132093  0.32720999  0.76015795]
[ 0.31707091  0.44002078  0.81080826]
[ 0.87002607  0.24002814  0.40317367]
[ 0.33147574  0.48692694  0.72084014]
[ 0.2591176   0.81004636  0.34852488]
[ 0.79427686  0.49692525  0.28712657]
[ 0.39198509  0.50703908  0.67609915]]```

Notice: PCHA takes a 2D-array of shape (dimensions, examples). The same shape applies to any output from the function. Therefore, the archetypes contained in returned matrix `XC` will be the column vectors.

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