-- 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 7.3.0 -- | 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 adjustNum :: (Num a, Ord a, Eq a) => a -> a -> a -> a absDifference :: Num a => a -> a -> 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 -- | 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] 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 = f $ differences c p where f [] = error "classifier has no models" f xs = fst $ minimumBy (comparing snd) xs 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 DSOM internals. Most developers -- should use DSOM instead. This module is subject to change -- without notice. module Data.Datamining.Clustering.DSOMInternal -- | A Self-Organising Map (DSOM). -- -- Although DSOM implements GridMap, most users will -- only need the interface provided by -- Data.Datamining.Clustering.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 DSOM and the output -- DSOM would have to have the same Metric type.
    3. --
data DSOM gm k p DSOM :: gm p -> (Metric p -> Metric p -> Metric p -> Metric p) -> DSOM gm k p sGridMap :: DSOM gm k p -> gm p sLearningFunction :: DSOM gm k p -> (Metric p -> Metric p -> Metric p -> Metric p) -- | Extracts the grid and current models from the DSOM. toGridMap :: GridMap gm p => DSOM gm k p -> gm p adjustNode :: (Pattern p, FiniteGrid (gm p), GridMap gm p, k ~ Index (gm p), Ord k, k ~ Index (BaseGrid gm p), Num (Metric p), Fractional (Metric p)) => gm p -> (Metric p -> Metric p -> Metric p) -> p -> k -> k -> p -> p scaleDistance :: (Num a, Fractional a) => Int -> Int -> a -- | 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, FiniteGrid (gm p), GridMap gm p, Num (Metric p), Ord k, k ~ Index (gm p), k ~ Index (BaseGrid gm p), Fractional (Metric p)) => DSOM gm t p -> k -> p -> DSOM gm k p justTrain :: (Pattern p, FiniteGrid (gm p), GridMap gm p, Num (Metric p), Ord (Metric p), Ord (Index (gm p)), GridMap gm (Metric p), Fractional (Metric p), Index (BaseGrid gm (Metric p)) ~ Index (gm p), Index (BaseGrid gm p) ~ Index (gm p)) => DSOM gm t p -> p -> DSOM gm (Index (gm p)) p -- | Creates a classifier with a default (bell-shaped) learning function. -- Usage is defaultDSOM gm r w t, where: -- -- defaultDSOM :: (Eq (Metric p), Ord (Metric p), Floating (Metric p)) => gm p -> Metric p -> Metric p -> DSOM gm k p -- | Creates a classifier with a custom learning function. Usage is -- customDSOM gm g, where: -- -- customDSOM :: gm p -> (Metric p -> Metric p -> Metric p -> Metric p) -> DSOM gm k p -- | Configures a learning function that depends not on the time, but on -- how good a model we already have for the target. If the BMU is an -- exact match for the target, no learning occurs. Usage is -- rougierLearningFunction r p, where r is the -- maximal learning rate (0 <= r <= 1), and p is the -- elasticity. -- -- NOTE: When using this learning function, ensure that abs . -- difference is always between 0 and 1, inclusive. Otherwise you -- may get invalid learning rates. rougierLearningFunction :: (Eq a, Ord a, Floating a) => a -> a -> (a -> a -> a -> a) instance (GridMap gm p, k ~ Index (BaseGrid gm p), Pattern p, FiniteGrid (gm p), GridMap gm (Metric p), k ~ Index (gm p), k ~ Index (BaseGrid gm (Metric p)), Ord k, Ord (Metric p), Num (Metric p), Fractional (Metric p)) => Classifier (DSOM gm) k p instance (Foldable gm, GridMap gm p, FiniteGrid (BaseGrid gm p)) => GridMap (DSOM gm k) p instance Grid (gm p) => Grid (DSOM gm k p) instance Foldable gm => Foldable (DSOM gm k) -- | A modified Kohonen Self-organising Map (SOM) which supports a -- time-independent learning function. (See SOM for a -- description of a SOM.) -- -- References: -- -- module Data.Datamining.Clustering.DSOM -- | A Self-Organising Map (DSOM). -- -- Although DSOM implements GridMap, most users will -- only need the interface provided by -- Data.Datamining.Clustering.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 DSOM and the output -- DSOM would have to have the same Metric type.
    3. --
data DSOM gm k p -- | Creates a classifier with a default (bell-shaped) learning function. -- Usage is defaultDSOM gm r w t, where: -- -- defaultDSOM :: (Eq (Metric p), Ord (Metric p), Floating (Metric p)) => gm p -> Metric p -> Metric p -> DSOM gm k p -- | Creates a classifier with a custom learning function. Usage is -- customDSOM gm g, where: -- -- customDSOM :: gm p -> (Metric p -> Metric p -> Metric p -> Metric p) -> DSOM gm k p -- | Configures a learning function that depends not on the time, but on -- how good a model we already have for the target. If the BMU is an -- exact match for the target, no learning occurs. Usage is -- rougierLearningFunction r p, where r is the -- maximal learning rate (0 <= r <= 1), and p is the -- elasticity. -- -- NOTE: When using this learning function, ensure that abs . -- difference is always between 0 and 1, inclusive. Otherwise you -- may get invalid learning rates. rougierLearningFunction :: (Eq a, Ord a, Floating a) => a -> a -> (a -> a -> a -> a) -- | Extracts the grid and current models from the DSOM. toGridMap :: GridMap gm p => DSOM 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, FiniteGrid (gm p), GridMap gm p, Num (Metric p), Ord k, k ~ Index (gm p), k ~ Index (BaseGrid gm p), Fractional (Metric p)) => DSOM gm t p -> k -> p -> DSOM gm k p -- | A module containing private SSOM internals. Most developers -- should use SSOM instead. This module is subject to change -- without notice. module Data.Datamining.Clustering.SSOMInternal -- | A function used to adjust the models in a classifier. class LearningFunction f where type family LearningRate f rate :: LearningFunction f => f -> LearningRate f -> LearningRate f -- | A typical learning function for classifiers. Gaussian r0 rf -- tf returns a gaussian function. At time zero, the learning rate -- is r0. Over time the learning rate tapers off, until at time -- tf, the learning rate is rf. Normally the parameters -- should be chosen such that: -- -- -- -- where << means "is much smaller than" (not the Haskell -- << operator!) data Gaussian a Gaussian :: a -> a -> a -> Gaussian a -- | A Simplified Self-Organising Map (SSOM). data SSOM f t k p SSOM :: Map k p -> f -> t -> SSOM f t k p -- | Maps patterns to nodes. sMap :: SSOM f t k p -> Map k p -- | The function used to update the nodes. learningFunction :: SSOM f t k p -> f -- | A counter used as a "time" parameter. If you create the SSOM with a -- counter value 0, and don't directly modify it, then the -- counter will represent the number of patterns that this SSOM has -- classified. counter :: SSOM f t k p -> t -- | Extracts the current models from the SSOM. A synonym for -- sMap. toMap :: SSOM f t k p -> Map k 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. trainNode :: (Pattern p, LearningFunction f, Metric p ~ LearningRate f, Num (LearningRate f), Ord k, Integral t) => SSOM f t k p -> k -> p -> SSOM f t k p incrementCounter :: Num t => SSOM f t k p -> SSOM f t k p justTrain :: (Ord (Metric p), Pattern p, LearningFunction f, Metric p ~ LearningRate f, Num (LearningRate f), Ord k, Integral t) => SSOM f t k p -> p -> SSOM f t k p instance Eq a => Eq (Gaussian a) instance Show a => Show (Gaussian a) instance Generic (Gaussian a) instance (Eq f, Eq t, Eq k, Eq p) => Eq (SSOM f t k p) instance (Show f, Show t, Show k, Show p) => Show (SSOM f t k p) instance Generic (SSOM f t k p) instance Datatype D1Gaussian instance Constructor C1_0Gaussian instance Datatype D1SSOM instance Constructor C1_0SSOM instance Selector S1_0_0SSOM instance Selector S1_0_1SSOM instance Selector S1_0_2SSOM instance (Pattern p, Ord (Metric p), LearningFunction f, Metric p ~ LearningRate f, Num (LearningRate f), Ord k, Integral t) => Classifier (SSOM f t) k p instance (Floating a, Fractional a, Num a) => LearningFunction (Gaussian a) -- | A Simplified Self-organising Map (SSOM). An SSOM maps input patterns -- onto a set, where each element in the set is a model of the input -- data. An SSOM is like a Kohonen Self-organising Map (SOM), except that -- instead of a grid, it uses a simple set of unconnected models. Since -- the models are unconnected, only the model that best matches the input -- is ever updated. This makes it faster, however, topological -- relationships within the input data are not preserved. This -- implementation supports the use of non-numeric patterns. -- -- In layman's terms, a SSOM can be useful when you you want to build a -- set of models on some data. A tutorial is available at -- https://github.com/mhwombat/som/wiki. -- -- References: -- -- module Data.Datamining.Clustering.SSOM -- | A Simplified Self-Organising Map (SSOM). data SSOM f t k p SSOM :: Map k p -> f -> t -> SSOM f t k p -- | Maps patterns to nodes. sMap :: SSOM f t k p -> Map k p -- | The function used to update the nodes. learningFunction :: SSOM f t k p -> f -- | A counter used as a "time" parameter. If you create the SSOM with a -- counter value 0, and don't directly modify it, then the -- counter will represent the number of patterns that this SSOM has -- classified. counter :: SSOM f t k p -> t -- | A typical learning function for classifiers. Gaussian r0 rf -- tf returns a gaussian function. At time zero, the learning rate -- is r0. Over time the learning rate tapers off, until at time -- tf, the learning rate is rf. Normally the parameters -- should be chosen such that: -- -- -- -- where << means "is much smaller than" (not the Haskell -- << operator!) data Gaussian a Gaussian :: a -> a -> a -> Gaussian a -- | Extracts the current models from the SSOM. A synonym for -- sMap. toMap :: SSOM f t k p -> Map k 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. trainNode :: (Pattern p, LearningFunction f, Metric p ~ LearningRate f, Num (LearningRate f), Ord k, Integral t) => SSOM f t k p -> k -> p -> SSOM f t 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 function used to adjust the models in a classifier. class LearningFunction f where type family LearningRate f rate :: LearningFunction f => f -> LearningRate f -> LearningRate f -> LearningRate f -- | A typical learning function for classifiers. -- DecayingGaussian r0 rf w0 wf tf returns a bell -- curve-shaped function. At time zero, the maximum learning rate -- (applied to the BMU) is r0, and the neighbourhood width is -- w0. Over time the bell curve shrinks and the learning rate -- tapers off, until at time tf, the maximum learning rate -- (applied to the BMU) is rf, and the neighbourhood width is -- wf. Normally the parameters should be chosen such that: -- -- -- -- where << means "is much smaller than" (not the Haskell -- << operator!) data DecayingGaussian a DecayingGaussian :: a -> a -> a -> a -> a -> DecayingGaussian a -- | A learning function that only updates the BMU and has a constant -- learning rate. data StepFunction a StepFunction :: a -> StepFunction a -- | A learning function that updates all nodes with the same, constant -- learning rate. This can be useful for testing. data ConstantFunction a ConstantFunction :: a -> ConstantFunction a -- | A Self-Organising Map (SOM). -- -- Although SOM implements GridMap, most users will -- only need the interface provided by -- Data.Datamining.Clustering.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 f t gm k p SOM :: gm p -> f -> t -> SOM f t gm k p -- | Maps patterns to tiles in a regular grid. In the context of a SOM, the -- tiles are called "nodes" gridMap :: SOM f t gm k p -> gm p -- | The function used to update the nodes. learningFunction :: SOM f t gm k p -> f -- | A counter used as a "time" parameter. If you create the SOM with a -- counter value 0, and don't directly modify it, then the -- counter will represent the number of patterns that this SOM has -- classified. counter :: SOM f t gm k p -> t currentLearningFunction :: (LearningFunction f, Metric p ~ LearningRate f, Num (LearningRate f), Integral t) => SOM f t gm k p -> (LearningRate f -> Metric p) -- | Extracts the grid and current models from the SOM. A synonym for -- gridMap. toGridMap :: GridMap gm p => SOM f t gm k p -> gm p adjustNode :: (Pattern p, Grid g, k ~ Index g, Num t) => g -> (t -> Metric p) -> p -> k -> k -> p -> 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), LearningFunction f, Metric p ~ LearningRate f, Num (LearningRate f), Integral t) => SOM f t gm k p -> Index (gm p) -> p -> SOM f t gm k p incrementCounter :: Num t => SOM f t gm k p -> SOM f t gm k p justTrain :: (Ord (Metric p), Pattern p, Grid (gm p), GridMap gm (Metric p), GridMap gm p, Index (BaseGrid gm (Metric p)) ~ Index (gm p), Index (BaseGrid gm p) ~ Index (gm p), LearningFunction f, Metric p ~ LearningRate f, Num (LearningRate f), Integral t) => SOM f t gm k p -> p -> SOM f t gm k p instance Eq a => Eq (DecayingGaussian a) instance Show a => Show (DecayingGaussian a) instance Generic (DecayingGaussian a) instance Eq a => Eq (StepFunction a) instance Show a => Show (StepFunction a) instance Generic (StepFunction a) instance Eq a => Eq (ConstantFunction a) instance Show a => Show (ConstantFunction a) instance Generic (ConstantFunction a) instance (Eq f, Eq t, Eq (gm p)) => Eq (SOM f t gm k p) instance (Show f, Show t, Show (gm p)) => Show (SOM f t gm k p) instance Generic (SOM f t gm k p) instance Datatype D1DecayingGaussian instance Constructor C1_0DecayingGaussian instance Datatype D1StepFunction instance Constructor C1_0StepFunction instance Datatype D1ConstantFunction instance Constructor C1_0ConstantFunction instance Datatype D1SOM instance Constructor C1_0SOM instance Selector S1_0_0SOM instance Selector S1_0_1SOM instance Selector S1_0_2SOM 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), LearningFunction f, Metric p ~ LearningRate f, Num (LearningRate f), Integral t) => Classifier (SOM f t gm) k p instance (Foldable gm, GridMap gm p, Grid (BaseGrid gm p)) => GridMap (SOM f t gm k) p instance Grid (gm p) => Grid (SOM f t gm k p) instance Foldable gm => Foldable (SOM f t gm k) instance Fractional a => LearningFunction (ConstantFunction a) instance (Fractional a, Eq a) => LearningFunction (StepFunction a) instance (Floating a, Fractional a, Num a) => LearningFunction (DecayingGaussian a) -- | 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. -- -- NOTES: -- -- -- -- References: -- -- module Data.Datamining.Clustering.SOM -- | A Self-Organising Map (SOM). -- -- Although SOM implements GridMap, most users will -- only need the interface provided by -- Data.Datamining.Clustering.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 f t gm k p SOM :: gm p -> f -> t -> SOM f t gm k p -- | Maps patterns to tiles in a regular grid. In the context of a SOM, the -- tiles are called "nodes" gridMap :: SOM f t gm k p -> gm p -- | The function used to update the nodes. learningFunction :: SOM f t gm k p -> f -- | A counter used as a "time" parameter. If you create the SOM with a -- counter value 0, and don't directly modify it, then the -- counter will represent the number of patterns that this SOM has -- classified. counter :: SOM f t gm k p -> t -- | A typical learning function for classifiers. -- DecayingGaussian r0 rf w0 wf tf returns a bell -- curve-shaped function. At time zero, the maximum learning rate -- (applied to the BMU) is r0, and the neighbourhood width is -- w0. Over time the bell curve shrinks and the learning rate -- tapers off, until at time tf, the maximum learning rate -- (applied to the BMU) is rf, and the neighbourhood width is -- wf. Normally the parameters should be chosen such that: -- -- -- -- where << means "is much smaller than" (not the Haskell -- << operator!) data DecayingGaussian a DecayingGaussian :: a -> a -> a -> a -> a -> DecayingGaussian a -- | Extracts the grid and current models from the SOM. A synonym for -- gridMap. toGridMap :: GridMap gm p => SOM f t 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), LearningFunction f, Metric p ~ LearningRate f, Num (LearningRate f), Integral t) => SOM f t gm k p -> Index (gm p) -> p -> SOM f t gm k p