-- Hoogle documentation, generated by Haddock -- See Hoogle, http://www.haskell.org/hoogle/ -- | Self-Organising Maps -- -- A Kohonen Self-organising Map (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. -- -- The userguide is available at -- https://github.com/mhwombat/som/wiki. @package som @version 4.1 -- | Tools for identifying patterns in data. module Data.Datamining.Pattern -- | A pattern to be learned or classified. class Pattern p where type family Metric p difference :: Pattern p => p -> p -> Metric p makeSimilar :: Pattern p => p -> Metric p -> p -> p -- | A vector that has been normalised, i.e., the magnitude of the vector = -- 1. data NormalisedVector a -- | Normalises a vector normalise :: Floating a => [a] -> NormalisedVector a -- | A vector that has been scaled so that all elements in the vector are -- between zero and one. To scale a set of vectors, use -- scaleAll. Alternatively, if you can identify a maximum -- and minimum value for each element in a vector, you can scale -- individual vectors using scale. data ScaledVector a -- | Given a vector qs of pairs of numbers, where each pair -- represents the maximum and minimum value to be expected at each index -- in xs, scale qs xs scales the vector -- xs element by element, mapping the maximum value expected at -- that index to one, and the minimum value to zero. scale :: Fractional a => [(a, a)] -> [a] -> ScaledVector a -- | Scales a set of vectors by determining the maximum and minimum values -- at each index in the vector, and mapping the maximum value to one, and -- the minimum value to zero. scaleAll :: (Fractional a, Ord a) => [[a]] -> [ScaledVector a] -- | adjustVector target amount vector adjusts -- vector to move it closer to target. The amount of -- adjustment is controlled by the learning rate r, which is a -- number between 0 and 1. Larger values of r permit more -- adjustment. If r=1, the result will be identical to the -- target. If amount=0, the result will be the -- unmodified pattern. adjustVector :: (Num a, Ord a, Eq a) => [a] -> a -> [a] -> [a] -- | Calculates the square of the Euclidean distance between two vectors. euclideanDistanceSquared :: Num a => [a] -> [a] -> a magnitudeSquared :: Num a => [a] -> a instance Show a => Show (NormalisedVector a) instance Show a => Show (ScaledVector a) instance (Fractional a, Ord a, Eq a) => Pattern (ScaledVector a) instance (Floating a, Fractional a, Ord a, Eq a) => Pattern (NormalisedVector a) -- | Tools for identifying patterns in data. module Data.Datamining.Clustering.Classifier -- | A machine which learns to classify input patterns. Minimal complete -- definition: trainBatch, reportAndTrain. class Classifier (c :: * -> * -> *) k p where classify c p = fst . minimumBy (comparing snd) $ differences c p train c p = c' where (_, _, c') = reportAndTrain c p classifyAndTrain c p = (bmu, c') where (bmu, _, c') = reportAndTrain c p diffAndTrain c p = (ds, c') where (_, ds, c') = reportAndTrain c p toList :: Classifier c k p => c k p -> [(k, p)] numModels :: Classifier c k p => c k p -> Int models :: Classifier c k p => c k p -> [p] differences :: (Classifier c k p, Pattern p, v ~ Metric p) => c k p -> p -> [(k, v)] classify :: (Classifier c k p, Pattern p, Ord v, v ~ Metric p) => c k p -> p -> k train :: (Classifier c k p, Ord v, v ~ Metric p) => c k p -> p -> c k p trainBatch :: Classifier c k p => c k p -> [p] -> c k p classifyAndTrain :: (Classifier c k p, Ord v, v ~ Metric p) => c k p -> p -> (k, c k p) diffAndTrain :: (Classifier c k p, Ord v, v ~ Metric p) => c k p -> p -> ([(k, v)], c k p) reportAndTrain :: (Classifier c k p, Ord v, v ~ Metric p) => c k p -> p -> (k, [(k, v)], c k p) -- | A module containing private SOM internals. Most developers -- should use SOM instead. This module is subject to change -- without notice. module Data.Datamining.Clustering.SOMInternal -- | A Self-Organising Map (SOM). -- -- Although SOM implements GridMap, most users will -- only need the interface provided by Classifier. If you chose -- to use the GridMap functions, please note: -- --
    --
  1. The functions adjust, and adjustWithKey do not -- increment the counter. You can do so manually with -- incrementCounter.
    2. --
  2. The functions map and mapWithKey are not -- implemented (they just return an error). It would be -- problematic to implement them because the input SOM and the output SOM -- would have to have the same Metric type.
    3. --
data SOM gm k p SOM :: gm p -> (Int -> Int -> Metric p) -> Int -> SOM gm k p sGridMap :: SOM gm k p -> gm p sLearningFunction :: SOM gm k p -> Int -> Int -> Metric p sCounter :: SOM gm k p -> Int -- | Creates a classifier with a default (bell-shaped) learning function. -- Usage is defaultSOM gm r w t, where: -- -- defaultSOM :: Floating (Metric p) => gm p -> Metric p -> Metric p -> Int -> SOM gm k p -- | Creates a classifier with a custom learning function. Usage is -- customSOM gm g, where: -- -- customSOM :: gm p -> (Int -> Int -> Metric p) -> SOM gm k p -- | Calculates re^(-d^2/2w^2). This form of the Gaussian -- function is useful as a learning rate function. In gaussian -- r w d, r 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 -- d. gaussian :: Floating a => a -> a -> Int -> a -- | Configures a typical learning function for classifiers. -- decayingGaussian r w0 tMax returns a bell curve-shaped -- function. At time zero, the maximum learning rate (applied to the BMU) -- is r, and the neighbourhood width is w. Over time -- the bell curve shrinks and the learning rate tapers off, until at time -- tMax, the learning rate is negligible. decayingGaussian :: Floating a => a -> a -> Int -> (Int -> Int -> a) -- | Extracts the grid and current models from the SOM. toGridMap :: GridMap gm p => SOM gm k p -> gm p -- | Trains the specified node and the neighbourood around it to better -- match a target. Most users should use train, which -- automatically determines the BMU and trains it and its neighbourhood. trainNeighbourhood :: (Pattern p, Grid (gm p), GridMap gm p, Index (BaseGrid gm p) ~ Index (gm p)) => SOM gm k p -> Index (gm p) -> p -> SOM gm k p incrementCounter :: SOM gm k p -> SOM gm k p instance (GridMap gm p, k ~ Index (BaseGrid gm p), Pattern p, Grid (gm p), GridMap gm (Metric p), k ~ Index (gm p), k ~ Index (BaseGrid gm (Metric p)), Ord (Metric p)) => Classifier (SOM gm) k p instance (Foldable gm, GridMap gm p, Grid (BaseGrid gm p)) => GridMap (SOM gm k) p instance Grid (gm p) => Grid (SOM gm k p) instance Foldable gm => Foldable (SOM gm k) -- | 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: -- -- module Data.Datamining.Clustering.SOM -- | A Self-Organising Map (SOM). -- -- Although SOM implements GridMap, most users will -- only need the interface provided by Classifier. If you chose -- to use the GridMap functions, please note: -- --
    --
  1. The functions adjust, and adjustWithKey do not -- increment the counter. You can do so manually with -- incrementCounter.
    2. --
  2. The functions map and mapWithKey are not -- implemented (they just return an error). It would be -- problematic to implement them because the input SOM and the output SOM -- would have to have the same Metric type.
    3. --
data SOM gm k p -- | Creates a classifier with a default (bell-shaped) learning function. -- Usage is defaultSOM gm r w t, where: -- -- defaultSOM :: Floating (Metric p) => gm p -> Metric p -> Metric p -> Int -> SOM gm k p -- | Creates a classifier with a custom learning function. Usage is -- customSOM gm g, where: -- -- customSOM :: gm p -> (Int -> Int -> Metric p) -> SOM gm k p -- | Calculates re^(-d^2/2w^2). This form of the Gaussian -- function is useful as a learning rate function. In gaussian -- r w d, r 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 -- d. gaussian :: Floating a => a -> a -> Int -> a -- | Configures a typical learning function for classifiers. -- decayingGaussian r w0 tMax returns a bell curve-shaped -- function. At time zero, the maximum learning rate (applied to the BMU) -- is r, and the neighbourhood width is w. Over time -- the bell curve shrinks and the learning rate tapers off, until at time -- tMax, the learning rate is negligible. decayingGaussian :: Floating a => a -> a -> Int -> (Int -> Int -> a) -- | Extracts the grid and current models from the SOM. toGridMap :: GridMap gm p => SOM gm k p -> gm p -- | Trains the specified node and the neighbourood around it to better -- match a target. Most users should use train, which -- automatically determines the BMU and trains it and its neighbourhood. trainNeighbourhood :: (Pattern p, Grid (gm p), GridMap gm p, Index (BaseGrid gm p) ~ Index (gm p)) => SOM gm k p -> Index (gm p) -> p -> SOM gm k p incrementCounter :: SOM gm k p -> SOM gm k p