SOM.hs

-----------------------------------------------------------------------------
-- |
-- Module      :  Data.Datamining.Clustering.SOM
-- Copyright   :  (c) Amy de Buitléir 2012
-- License     :  BSD-style
-- Maintainer  :  amy@nualeargais.ie
-- Stability   :  experimental
-- Portability :  portable
--
-- A Kohonen Self-organising Map (SOM). A SOM maps input patterns onto a 
-- regular grid (usually two-dimensional) where each node in the grid is a
-- model of the input data, and does so using a method which ensures that any
-- topological relationships within the input data are also represented in the
-- grid. This implementation supports the use of non-numeric patterns.
--
-- In layman's terms, a SOM can be useful when you you want to discover the
-- underlying structure of some data. A tutorial is available at
-- <https://github.com/mhwombat/som/wiki>
--
-- References:
--
-- * Kohonen, T. (1982). Self-organized formation of topologically correct
-- feature maps. Biological Cybernetics, 43 (1), 59–69.
--
-----------------------------------------------------------------------------

{-# LANGUAGE UnicodeSyntax #-}

module Data.Datamining.Clustering.SOM
  (
    -- Patterns
    Pattern(..),
    -- * Using the SOM
    train,
    trainBatch,
    classify,
    classifyAndTrain,
    differences,
    -- * Numeric vectors as patterns
    -- ** Normalised vectors
    normalise,
    NormalisedVector,
    -- ** Scaled vectors
    scale,
    ScaledVector,
    -- ** Useful functions
    -- $Vector
    adjustVector,
    euclideanDistanceSquared,
    gaussian
  ) where

import Data.Datamining.Clustering.SOMInternal (adjustVector, classify, 
  classifyAndTrain, differences, euclideanDistanceSquared, normalise, 
  NormalisedVector, scale,ScaledVector, train, trainBatch, Pattern(..))

-- | Calculates @c/e/^(-d^2/2w^2)@.
--   This form of the Gaussian function is useful as a learning rate function.
--   In @'gaussian' c w d@, @c@ specifies the highest learning rate, which
--   will be applied to the SOM node that best matches the input pattern.
--   The learning rate applied to other nodes will be applied based on their
--   distance @d@ from the best matching node. The value @w@ controls the 
--   \'width\' of the Gaussian. Higher values of @w@ cause the learning rate
--   to fall off more slowly with distance.
gaussian ∷ Double → Double → Int → Double
gaussian c w d = c * exp (-d'*d'/(2*w*w))
  where d' = fromIntegral d

{- $Vector
If you wish to use a SOM with raw numeric vectors, use @no-warn-orphans@ and
add the following to your code:

> instance (Floating a, Fractional a, Ord a, Eq a) ⇒ Pattern [a] a where
>   difference = euclideanDistanceSquared
>   makeSimilar = adjustVector
-}