### Contents

# kmeans 1.0.0

## Synopsis

```
SELECT kmeans(ARRAY[x, y, z], 10) OVER (), * FROM samples;
SELECT kmeans(ARRAY[x, y, z], 2, ARRAY[0.5, 0.5, 1.0, 1.0]) OVER (), * FROM samples;
SELECT kmeans(ARRAY[x, y, z], 2, ARRAY[ARRAY[0.5, 0.5], ARRAY[1.0, 1.0]]) OVER (PARTITION BY group_key), * FROM samples
```

## Description

This module implements K-means clustering algorithm as a user-defined window function in PostgreSQL. K-means clustering is a simple way to classify data set by N-dimension vector.

It is known that the algorithm depends on how to define initial mean vectors. So the module provides two singature, one for auto-initialization and the other for user-given initial vectors.

The `kmeans`

function calculates and returns class number which starts from
0, by using input vectors. The first argument is the vector, represented
by array of float8. You must give the same-length 1-dimension array across
all the input rows. The second argument is an integer K in "K-means", the
number of class you want to partition. The third argument is optional,
an array of vector which represents initial mean vectors. Since the
algorithm is sensitive with initial mean vectors, and although the function
calculates them by input vectors in the first form, you may sometimes want
to give fixed mean vectors. The vectors can be passed as 1-d array or 2-d
array of float8. In case of 1-d, the length of it must match k * lengthof(vector).

If the third argument, initial centroids, is not given, it scans all the input vectors and stores min/max for each element of vector. Then decide initial hypothetical vector elements by the next formula:

```
init = (max - min) * (i + 1) / (k + 1) + min
```

where `i`

varies from 0 to k-1. This means that the vector elements
are decided as the liner interpolation from min to max divided by k.
Then one of the input vectors nearest to this hypothetical vector
is picked up as the centroid. Note that input vector is not picked
more than twice as far as possible, to gain good result.

See input/kmeans.source as an example to call the function.

## History

### v1.1.0 (2011-07-22)

- Fix NULL input case, thanks to the report from Mike Toews
- Improve initialization of centroids

### v1.0.0 (2011-05-20)

- Initial version

## Support

This library is stored in an open GitHub repository. Feel free to fork and contribute! Please file bug reports via GitHub Issues.

## Author

## Copyright and License

Copyright (c) Hitoshi Harada

This module is free software; you can redistribute it and/or modify it under the PostgreSQL License.

Permission to use, copy, modify, and distribute this software and its documentation for any purpose, without fee, and without a written agreement is hereby granted, provided that the above copyright notice and this paragraph and the following two paragraphs appear in all copies.

In no event shall Hitoshi Harada be liable to any party for direct, indirect, special, incidental, or consequential damages, including lost profits, arising out of the use of this software and its documentation, even if Hitoshi Harada has been advised of the possibility of such damage.

Hitoshi Harada specifically disclaim any warranties, including, but not limited to, the implied warranties of merchantability and fitness for a particular purpose. The software provided hereunder is on an "as is" basis, and Hitoshi Harada has no obligations to provide maintenance, support, updates, enhancements, or modifications.