-- 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 8.2.2 -- | Tools for identifying patterns in data. module Data.Datamining.Pattern adjustNum :: (Num a, Ord a, Eq a) => a -> a -> a -> a absDifference :: Num a => a -> a -> a -- | adjustVector target amount vector adjusts each element -- of vector to move it closer to the corresponding element of -- target. The amount of adjustment is controlled by the -- learning rate amount, which is a number between 0 and 1. -- Larger values of amount permit more adjustment. If -- amount=1, the result will be identical to the -- target. If amount=0, the result will be the -- unmodified pattern. If target is shorter than -- vector, the result will be the same length as -- target. If target is longer than vector, -- the result will be the same length as vector. adjustVector :: (Num a, Ord a, Eq a) => [a] -> a -> [a] -> [a] -- | Same as adjustVector, except that the result will -- always be the same length as vector. This means that if -- target is shorter than vector, the "leftover" -- elements of vector will be copied the result, unmodified. adjustVectorPreserveLength :: (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 GHC.Show.Show a => GHC.Show.Show (Data.Datamining.Pattern.ScaledVector a) instance GHC.Show.Show a => GHC.Show.Show (Data.Datamining.Pattern.NormalisedVector a) -- | A module containing private SOS internals. Most developers -- should use SOS instead. This module is subject to change -- without notice. module Data.Datamining.Clustering.SOSInternal -- | A typical learning function for classifiers. exponential r0 -- d t returns the learning rate at time t. When t = -- 0, the learning rate is r0. Over time the learning rate -- decays exponentially; the decay rate is d. Normally the -- parameters are chosen such that: -- -- exponential :: (Floating a, Integral t) => a -> a -> t -> a -- | A Simplified Self-Organising Map (SOS). t is the type of the -- counter. x is the type of the learning rate and the -- difference metric. k is the type of the model indices. -- p is the type of the input patterns and models. data SOS t x k p SOS :: Map k (p, t) -> (t -> x) -> Int -> x -> Bool -> (p -> p -> x) -> (p -> x -> p -> p) -> k -> SOS t x k p -- | Maps patterns and match counts to nodes. [toMap] :: SOS t x k p -> Map k (p, t) -- | A function which determines the learning rate for a node. The input -- parameter indicates how many patterns (or pattern batches) have -- previously been presented to the classifier. Typically this is used to -- make the learning rate decay over time. The output is the learning -- rate for that node (the amount by which the node's model should be -- updated to match the target). The learning rate should be between zero -- and one. [learningRate] :: SOS t x k p -> t -> x -- | The maximum number of models this SOS can hold. [maxSize] :: SOS t x k p -> Int -- | The threshold that triggers creation of a new model. [diffThreshold] :: SOS t x k p -> x -- | Delete existing models to make room for new ones? The least useful -- (least frequently matched) models will be deleted first. [allowDeletion] :: SOS t x k p -> Bool -- | A function which compares two patterns and returns a -- non-negative number representing how different the patterns -- are. A result of 0 indicates that the patterns are identical. [difference] :: SOS t x k p -> p -> p -> x -- | A function which updates models. For example, if this function is -- f, then f target amount pattern returns a modified -- copy of pattern that is more similar to target than -- pattern is. The magnitude of the adjustment is controlled by -- the amount parameter, which should be a number between 0 and -- 1. Larger values for amount permit greater adjustments. If -- amount=1, the result should be identical to the -- target. If amount=0, the result should be the -- unmodified pattern. [makeSimilar] :: SOS t x k p -> p -> x -> p -> p -- | Index for the next node to add to the SOS. [nextIndex] :: SOS t x k p -> k makeSOS :: Bounded k => (t -> x) -> Int -> x -> Bool -> (p -> p -> x) -> (p -> x -> p -> p) -> SOS t x k p -- | Returns true if the SOS has no models, false otherwise. isEmpty :: SOS t x k p -> Bool -- | Returns the number of models the SOS currently contains. numModels :: SOS t x k p -> Int -- | Returns a map from node ID to model. modelMap :: SOS t x k p -> Map k p -- | Returns a map from node ID to counter (number of times the node's -- model has been the closest match to an input pattern). counterMap :: SOS t x k p -> Map k t -- | Returns the current models. models :: SOS t x k p -> [p] -- | Returns the current counters (number of times the node's model has -- been the closest match to an input pattern). counters :: SOS t x k p -> [t] -- | The current "time" (number of times the SOS has been trained). time :: Num t => SOS t x k p -> t -- | Adds a new node to the SOS. addNode :: (Num t, Enum k, Ord k) => p -> SOS t x k p -> SOS t x k p -- | Removes a node from the SOS. Deleted nodes are never re-used. deleteNode :: Ord k => k -> SOS t x k p -> SOS t x k p incrementCounter :: (Num t, Ord k) => k -> SOS t x k p -> SOS t x k p -- | Trains the specified node to better match a target. Most users should -- use train, which automatically determines the BMU and -- trains it. trainNode :: (Num t, Ord k) => SOS t x k p -> k -> p -> SOS t x k p leastUsefulNode :: Ord t => SOS t x k p -> k deleteLeastUsefulNode :: (Ord t, Ord k) => SOS t x k p -> SOS t x k p addModel :: (Num t, Ord t, Enum k, Ord k) => p -> SOS t x k p -> SOS t x k p -- | classify s p identifies the model s that most -- closely matches the pattern p. If necessary, it will create a -- new node and model. Returns the ID of the node with the best matching -- model, the difference between the best matching model and the pattern, -- the differences between the input and each model in the SOS, and the -- (possibly updated) SOS. classify :: (Num t, Ord t, Num x, Ord x, Enum k, Ord k) => SOS t x k p -> p -> (k, x, [(k, x)], SOS t x k p) -- | train s p identifies the model in s that most -- closely matches p, and updates it to be a somewhat better -- match. train :: (Num t, Ord t, Num x, Ord x, Enum k, Ord k) => SOS t x k p -> p -> SOS t x k p -- | For each pattern p in ps, trainBatch s -- ps identifies the model in s that most closely matches -- p, and updates it to be a somewhat better match. trainBatch :: (Num t, Ord t, Num x, Ord x, Enum k, Ord k) => SOS t x k p -> [p] -> SOS t x k p instance GHC.Generics.Selector Data.Datamining.Clustering.SOSInternal.S1_0_7SOS instance GHC.Generics.Selector Data.Datamining.Clustering.SOSInternal.S1_0_6SOS instance GHC.Generics.Selector Data.Datamining.Clustering.SOSInternal.S1_0_5SOS instance GHC.Generics.Selector Data.Datamining.Clustering.SOSInternal.S1_0_4SOS instance GHC.Generics.Selector Data.Datamining.Clustering.SOSInternal.S1_0_3SOS instance GHC.Generics.Selector Data.Datamining.Clustering.SOSInternal.S1_0_2SOS instance GHC.Generics.Selector Data.Datamining.Clustering.SOSInternal.S1_0_1SOS instance GHC.Generics.Selector Data.Datamining.Clustering.SOSInternal.S1_0_0SOS instance GHC.Generics.Constructor Data.Datamining.Clustering.SOSInternal.C1_0SOS instance GHC.Generics.Datatype Data.Datamining.Clustering.SOSInternal.D1SOS instance (Control.DeepSeq.NFData t, Control.DeepSeq.NFData x, Control.DeepSeq.NFData k, Control.DeepSeq.NFData p) => Control.DeepSeq.NFData (Data.Datamining.Clustering.SOSInternal.SOS t x k p) instance GHC.Generics.Generic (Data.Datamining.Clustering.SOSInternal.SOS t x k p) -- | A Self-organising Set (SOS). An SOS maps input patterns onto a set, -- where each element in the set is a model of the input data. An SOS is -- like a Kohonen Self-organising Map (SOM), except: -- -- -- -- This implementation supports the use of non-numeric patterns. -- -- In layman's terms, a SOS 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.SOS -- | A Simplified Self-Organising Map (SOS). t is the type of the -- counter. x is the type of the learning rate and the -- difference metric. k is the type of the model indices. -- p is the type of the input patterns and models. data SOS t x k p SOS :: Map k (p, t) -> (t -> x) -> Int -> x -> Bool -> (p -> p -> x) -> (p -> x -> p -> p) -> k -> SOS t x k p -- | Maps patterns and match counts to nodes. [toMap] :: SOS t x k p -> Map k (p, t) -- | A function which determines the learning rate for a node. The input -- parameter indicates how many patterns (or pattern batches) have -- previously been presented to the classifier. Typically this is used to -- make the learning rate decay over time. The output is the learning -- rate for that node (the amount by which the node's model should be -- updated to match the target). The learning rate should be between zero -- and one. [learningRate] :: SOS t x k p -> t -> x -- | The maximum number of models this SOS can hold. [maxSize] :: SOS t x k p -> Int -- | The threshold that triggers creation of a new model. [diffThreshold] :: SOS t x k p -> x -- | Delete existing models to make room for new ones? The least useful -- (least frequently matched) models will be deleted first. [allowDeletion] :: SOS t x k p -> Bool -- | A function which compares two patterns and returns a -- non-negative number representing how different the patterns -- are. A result of 0 indicates that the patterns are identical. [difference] :: SOS t x k p -> p -> p -> x -- | A function which updates models. For example, if this function is -- f, then f target amount pattern returns a modified -- copy of pattern that is more similar to target than -- pattern is. The magnitude of the adjustment is controlled by -- the amount parameter, which should be a number between 0 and -- 1. Larger values for amount permit greater adjustments. If -- amount=1, the result should be identical to the -- target. If amount=0, the result should be the -- unmodified pattern. [makeSimilar] :: SOS t x k p -> p -> x -> p -> p -- | Index for the next node to add to the SOS. [nextIndex] :: SOS t x k p -> k makeSOS :: Bounded k => (t -> x) -> Int -> x -> Bool -> (p -> p -> x) -> (p -> x -> p -> p) -> SOS t x k p -- | The current "time" (number of times the SOS has been trained). time :: Num t => SOS t x k p -> t -- | Returns true if the SOS has no models, false otherwise. isEmpty :: SOS t x k p -> Bool -- | Returns the number of models the SOS currently contains. numModels :: SOS t x k p -> Int -- | Returns a map from node ID to model. modelMap :: SOS t x k p -> Map k p -- | Returns a map from node ID to counter (number of times the node's -- model has been the closest match to an input pattern). counterMap :: SOS t x k p -> Map k t -- | A typical learning function for classifiers. exponential r0 -- d t returns the learning rate at time t. When t = -- 0, the learning rate is r0. Over time the learning rate -- decays exponentially; the decay rate is d. Normally the -- parameters are chosen such that: -- -- exponential :: (Floating a, Integral t) => a -> a -> t -> a -- | classify s p identifies the model s that most -- closely matches the pattern p. If necessary, it will create a -- new node and model. Returns the ID of the node with the best matching -- model, the difference between the best matching model and the pattern, -- the differences between the input and each model in the SOS, and the -- (possibly updated) SOS. classify :: (Num t, Ord t, Num x, Ord x, Enum k, Ord k) => SOS t x k p -> p -> (k, x, [(k, x)], SOS t x k p) -- | train s p identifies the model in s that most -- closely matches p, and updates it to be a somewhat better -- match. train :: (Num t, Ord t, Num x, Ord x, Enum k, Ord k) => SOS t x k p -> p -> SOS t x k p -- | For each pattern p in ps, trainBatch s -- ps identifies the model in s that most closely matches -- p, and updates it to be a somewhat better match. trainBatch :: (Num t, Ord t, Num x, Ord x, Enum k, Ord k) => SOS t x k p -> [p] -> SOS t x k p -- | 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 :: * -> * -> * -> *) v 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 -- | Returns a list of index/model pairs. toList :: Classifier c v k p => c v k p -> [(k, p)] -- | Returns the number of models this classifier can learn. numModels :: Classifier c v k p => c v k p -> Int -- | Returns the current models of the classifier. models :: Classifier c v k p => c v k p -> [p] -- | differences c target returns the indices of all nodes -- in c, paired with the difference between target and -- the node's model. differences :: Classifier c v k p => c v k p -> p -> [(k, v)] -- | classify c target returns the index of the node in c -- whose model best matches the target. classify :: (Classifier c v k p, Ord v) => c v k p -> p -> k -- | train c target returns a modified copy of the -- classifier c that has partially learned the target. train :: Classifier c v k p => c v k p -> p -> c v k p -- | trainBatch c targets returns a modified copy of the -- classifier c that has partially learned the targets. trainBatch :: Classifier c v k p => c v k p -> [p] -> c v k p -- | classifyAndTrain c target returns a tuple containing -- the index of the node in c whose model best matches the input -- target, and a modified copy of the classifier c that -- has partially learned the target. Invoking -- classifyAndTrain c p may be faster than invoking (p -- classify c, train c p), but they should give identical -- results. classifyAndTrain :: Classifier c v k p => c v k p -> p -> (k, c v k p) -- | diffAndTrain c target returns a tuple containing: 1. -- The indices of all nodes in c, paired with the difference -- between target and the node's model 2. A modified copy of the -- classifier c that has partially learned the target. -- Invoking diffAndTrain c p may be faster than invoking (p -- diff c, train c p), but they should give identical -- results. diffAndTrain :: Classifier c v k p => c v k p -> p -> ([(k, v)], c v k p) -- | reportAndTrain c f target returns a tuple containing: -- 1. The index of the node in c whose model best matches the -- input target 2. The indices of all nodes in c, -- paired with the difference between target and the node's -- model 3. A modified copy of the classifier c that has -- partially learned the target Invoking diffAndTrain c -- p may be faster than invoking (p diff c, train c -- p), but they should give identical results. reportAndTrain :: Classifier c v k p => c v k p -> p -> (k, [(k, v)], c v 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 x k p DSOM :: gm p -> (x -> x -> x -> x) -> (p -> p -> x) -> (p -> x -> p -> p) -> DSOM gm x k p -- | Maps patterns to tiles in a regular grid. In the context of a SOM, the -- tiles are called "nodes" [gridMap] :: DSOM gm x k p -> gm p -- | A function which determines the how quickly the SOM learns. [learningRate] :: DSOM gm x k p -> (x -> x -> x -> x) -- | A function which compares two patterns and returns a -- non-negative number representing how different the patterns -- are. A result of 0 indicates that the patterns are identical. [difference] :: DSOM gm x k p -> p -> p -> x -- | A function which updates models. If this function is f, then -- f target amount pattern returns a modified copy of -- pattern that is more similar to target than -- pattern is. The magnitude of the adjustment is controlled by -- the amount parameter, which should be a number between 0 and -- 1. Larger values for amount permit greater adjustments. If -- amount=1, the result should be identical to the -- target. If amount=0, the result should be the -- unmodified pattern. [makeSimilar] :: DSOM gm x k p -> p -> x -> p -> p withGridMap :: (gm p -> gm p) -> DSOM gm x k p -> DSOM gm x k p -- | Extracts the grid and current models from the DSOM. toGridMap :: GridMap gm p => DSOM gm x k p -> gm p adjustNode :: (FiniteGrid (gm p), GridMap gm p, k ~ Index (gm p), k ~ Index (BaseGrid gm p), Ord k, Num x, Fractional x) => gm p -> (p -> x -> p -> p) -> (p -> p -> x) -> (x -> x -> x) -> 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 :: (FiniteGrid (gm p), GridMap gm p, k ~ Index (gm p), k ~ Index (BaseGrid gm p), Ord k, Num x, Fractional x) => DSOM gm x t p -> k -> p -> DSOM gm x k p justTrain :: (FiniteGrid (gm p), GridMap gm p, GridMap gm x, k ~ Index (gm p), k ~ Index (gm x), k ~ Index (BaseGrid gm p), k ~ Index (BaseGrid gm x), Ord k, Ord x, Num x, Fractional x) => DSOM gm x t p -> p -> DSOM gm x 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 GHC.Generics.Selector Data.Datamining.Clustering.DSOMInternal.S1_0_3DSOM instance GHC.Generics.Selector Data.Datamining.Clustering.DSOMInternal.S1_0_2DSOM instance GHC.Generics.Selector Data.Datamining.Clustering.DSOMInternal.S1_0_1DSOM instance GHC.Generics.Selector Data.Datamining.Clustering.DSOMInternal.S1_0_0DSOM instance GHC.Generics.Constructor Data.Datamining.Clustering.DSOMInternal.C1_0DSOM instance GHC.Generics.Datatype Data.Datamining.Clustering.DSOMInternal.D1DSOM instance Control.DeepSeq.NFData (gm p) => Control.DeepSeq.NFData (Data.Datamining.Clustering.DSOMInternal.DSOM gm x k p) instance GHC.Generics.Generic (Data.Datamining.Clustering.DSOMInternal.DSOM gm x k p) instance Data.Foldable.Foldable gm => Data.Foldable.Foldable (Data.Datamining.Clustering.DSOMInternal.DSOM gm x k) instance Math.Geometry.GridInternal.Grid (gm p) => Math.Geometry.GridInternal.Grid (Data.Datamining.Clustering.DSOMInternal.DSOM gm x k p) instance (Data.Foldable.Foldable gm, Math.Geometry.GridMap.GridMap gm p, Math.Geometry.GridInternal.FiniteGrid (Math.Geometry.GridMap.BaseGrid gm p)) => Math.Geometry.GridMap.GridMap (Data.Datamining.Clustering.DSOMInternal.DSOM gm x k) p instance (Math.Geometry.GridMap.GridMap gm p, k ~ Math.Geometry.GridInternal.Index (Math.Geometry.GridMap.BaseGrid gm p), Math.Geometry.GridInternal.FiniteGrid (gm p), Math.Geometry.GridMap.GridMap gm x, k ~ Math.Geometry.GridInternal.Index (gm p), k ~ Math.Geometry.GridInternal.Index (gm x), k ~ Math.Geometry.GridInternal.Index (Math.Geometry.GridMap.BaseGrid gm x), GHC.Classes.Ord k, GHC.Classes.Ord x, GHC.Num.Num x, GHC.Real.Fractional x) => Data.Datamining.Clustering.Classifier.Classifier (Data.Datamining.Clustering.DSOMInternal.DSOM gm) x k p -- | 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 x k p DSOM :: gm p -> (x -> x -> x -> x) -> (p -> p -> x) -> (p -> x -> p -> p) -> DSOM gm x k p -- | Maps patterns to tiles in a regular grid. In the context of a SOM, the -- tiles are called "nodes" [gridMap] :: DSOM gm x k p -> gm p -- | A function which determines the how quickly the SOM learns. [learningRate] :: DSOM gm x k p -> (x -> x -> x -> x) -- | A function which compares two patterns and returns a -- non-negative number representing how different the patterns -- are. A result of 0 indicates that the patterns are identical. [difference] :: DSOM gm x k p -> p -> p -> x -- | A function which updates models. If this function is f, then -- f target amount pattern returns a modified copy of -- pattern that is more similar to target than -- pattern is. The magnitude of the adjustment is controlled by -- the amount parameter, which should be a number between 0 and -- 1. Larger values for amount permit greater adjustments. If -- amount=1, the result should be identical to the -- target. If amount=0, the result should be the -- unmodified pattern. [makeSimilar] :: DSOM gm x k p -> p -> x -> p -> p -- | Extracts the grid and current models from the DSOM. toGridMap :: GridMap gm p => DSOM gm x k p -> gm 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) -- | 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 :: (FiniteGrid (gm p), GridMap gm p, k ~ Index (gm p), k ~ Index (BaseGrid gm p), Ord k, Num x, Fractional x) => DSOM gm x t p -> k -> p -> DSOM gm x 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 typical learning function for classifiers. exponential r0 -- d t returns the learning rate at time t. When t = -- 0, the learning rate is r0. Over time the learning rate -- decays exponentially; the decay rate is d. Normally the -- parameters are chosen such that: -- -- exponential :: Floating a => a -> a -> a -> a -- | A Simplified Self-Organising Map (SSOM). x is the type of the -- learning rate and the difference metric. t is the type of the -- counter. k is the type of the model indices. p is -- the type of the input patterns and models. data SSOM t x k p SSOM :: Map k p -> (t -> x) -> (p -> p -> x) -> (p -> x -> p -> p) -> t -> SSOM t x k p -- | Maps patterns to nodes. [sMap] :: SSOM t x k p -> Map k p -- | A function which determines the learning rate for a node. The input -- parameter indicates how many patterns (or pattern batches) have -- previously been presented to the classifier. Typically this is used to -- make the learning rate decay over time. The output is the learning -- rate for that node (the amount by which the node's model should be -- updated to match the target). The learning rate should be between zero -- and one. [learningRate] :: SSOM t x k p -> t -> x -- | A function which compares two patterns and returns a -- non-negative number representing how different the patterns -- are. A result of 0 indicates that the patterns are identical. [difference] :: SSOM t x k p -> p -> p -> x -- | A function which updates models. For example, if this function is -- f, then f target amount pattern returns a modified -- copy of pattern that is more similar to target than -- pattern is. The magnitude of the adjustment is controlled by -- the amount parameter, which should be a number between 0 and -- 1. Larger values for amount permit greater adjustments. If -- amount=1, the result should be identical to the -- target. If amount=0, the result should be the -- unmodified pattern. [makeSimilar] :: SSOM t x k p -> p -> x -> p -> p -- | 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 t x k p -> t -- | Extracts the current models from the SSOM. A synonym for -- sMap. toMap :: SSOM t x k p -> Map k p -- | Trains the specified node to better match a target. Most users should -- use train, which automatically determines the BMU and -- trains it. trainNode :: (Num t, Ord k) => SSOM t x k p -> k -> p -> SSOM t x k p incrementCounter :: Num t => SSOM t x k p -> SSOM t x k p justTrain :: (Num t, Ord k, Ord x) => SSOM t x k p -> p -> SSOM t x k p instance GHC.Generics.Selector Data.Datamining.Clustering.SSOMInternal.S1_0_4SSOM instance GHC.Generics.Selector Data.Datamining.Clustering.SSOMInternal.S1_0_3SSOM instance GHC.Generics.Selector Data.Datamining.Clustering.SSOMInternal.S1_0_2SSOM instance GHC.Generics.Selector Data.Datamining.Clustering.SSOMInternal.S1_0_1SSOM instance GHC.Generics.Selector Data.Datamining.Clustering.SSOMInternal.S1_0_0SSOM instance GHC.Generics.Constructor Data.Datamining.Clustering.SSOMInternal.C1_0SSOM instance GHC.Generics.Datatype Data.Datamining.Clustering.SSOMInternal.D1SSOM instance (Control.DeepSeq.NFData t, Control.DeepSeq.NFData k, Control.DeepSeq.NFData p) => Control.DeepSeq.NFData (Data.Datamining.Clustering.SSOMInternal.SSOM t x k p) instance GHC.Generics.Generic (Data.Datamining.Clustering.SSOMInternal.SSOM t x k p) instance (GHC.Num.Num t, GHC.Classes.Ord x, GHC.Num.Num x, GHC.Classes.Ord k) => Data.Datamining.Clustering.Classifier.Classifier (Data.Datamining.Clustering.SSOMInternal.SSOM t) x k p -- | 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). x is the type of the -- learning rate and the difference metric. t is the type of the -- counter. k is the type of the model indices. p is -- the type of the input patterns and models. data SSOM t x k p SSOM :: Map k p -> (t -> x) -> (p -> p -> x) -> (p -> x -> p -> p) -> t -> SSOM t x k p -- | Maps patterns to nodes. [sMap] :: SSOM t x k p -> Map k p -- | A function which determines the learning rate for a node. The input -- parameter indicates how many patterns (or pattern batches) have -- previously been presented to the classifier. Typically this is used to -- make the learning rate decay over time. The output is the learning -- rate for that node (the amount by which the node's model should be -- updated to match the target). The learning rate should be between zero -- and one. [learningRate] :: SSOM t x k p -> t -> x -- | A function which compares two patterns and returns a -- non-negative number representing how different the patterns -- are. A result of 0 indicates that the patterns are identical. [difference] :: SSOM t x k p -> p -> p -> x -- | A function which updates models. For example, if this function is -- f, then f target amount pattern returns a modified -- copy of pattern that is more similar to target than -- pattern is. The magnitude of the adjustment is controlled by -- the amount parameter, which should be a number between 0 and -- 1. Larger values for amount permit greater adjustments. If -- amount=1, the result should be identical to the -- target. If amount=0, the result should be the -- unmodified pattern. [makeSimilar] :: SSOM t x k p -> p -> x -> p -> p -- | 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 t x k p -> t -- | Extracts the current models from the SSOM. A synonym for -- sMap. toMap :: SSOM t x k p -> Map k p -- | A typical learning function for classifiers. exponential r0 -- d t returns the learning rate at time t. When t = -- 0, the learning rate is r0. Over time the learning rate -- decays exponentially; the decay rate is d. Normally the -- parameters are chosen such that: -- -- exponential :: Floating a => a -> a -> a -> a -- | Trains the specified node to better match a target. Most users should -- use train, which automatically determines the BMU and -- trains it. trainNode :: (Num t, Ord k) => SSOM t x k p -> k -> p -> SSOM t x 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 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!) decayingGaussian :: Floating x => x -> x -> x -> x -> x -> x -> x -> x -- | A learning function that only updates the BMU and has a constant -- learning rate. stepFunction :: (Num d, Fractional x, Eq d) => x -> t -> d -> x -- | A learning function that updates all nodes with the same, constant -- learning rate. This can be useful for testing. constantFunction :: x -> t -> d -> x -- | 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 t d gm x k p SOM :: gm p -> (t -> d -> x) -> (p -> p -> x) -> (p -> x -> p -> p) -> t -> SOM t d gm x k p -- | Maps patterns to tiles in a regular grid. In the context of a SOM, the -- tiles are called "nodes" [gridMap] :: SOM t d gm x k p -> gm p -- | A function which determines the how quickly the SOM learns. For -- example, if the function is f, then f t d returns -- the learning rate for a node. The parameter t indicates how -- many patterns (or pattern batches) have previously been presented to -- the classifier. Typically this is used to make the learning rate decay -- over time. The parameter d is the grid distance from the node -- being updated to the BMU (Best Matching Unit). The output is the -- learning rate for that node (the amount by which the node's model -- should be updated to match the target). The learning rate should be -- between zero and one. [learningRate] :: SOM t d gm x k p -> t -> d -> x -- | A function which compares two patterns and returns a -- non-negative number representing how different the patterns -- are. A result of 0 indicates that the patterns are identical. [difference] :: SOM t d gm x k p -> p -> p -> x -- | A function which updates models. If this function is f, then -- f target amount pattern returns a modified copy of -- pattern that is more similar to target than -- pattern is. The magnitude of the adjustment is controlled by -- the amount parameter, which should be a number between 0 and -- 1. Larger values for amount permit greater adjustments. If -- amount=1, the result should be identical to the -- target. If amount=0, the result should be the -- unmodified pattern. [makeSimilar] :: SOM t d gm x k p -> p -> x -> p -> p -- | 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 t d gm x k p -> t withGridMap :: (gm p -> gm p) -> SOM t d gm x k p -> SOM t d gm x k p currentLearningFunction :: (Num t) => SOM t d gm x k p -> (d -> x) -- | Extracts the grid and current models from the SOM. A synonym for -- gridMap. toGridMap :: GridMap gm p => SOM t d gm x k p -> gm p adjustNode :: (Grid g, k ~ Index g, Num t) => g -> (t -> x) -> (p -> x -> p -> 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 :: (Grid (gm p), GridMap gm p, Index (BaseGrid gm p) ~ Index (gm p), Num t, Num x, Num d) => SOM t d gm x k p -> Index (gm p) -> p -> SOM t d gm x k p incrementCounter :: Num t => SOM t d gm x k p -> SOM t d gm x k p justTrain :: (Ord x, Grid (gm p), GridMap gm x, GridMap gm p, Index (BaseGrid gm x) ~ Index (gm p), Index (BaseGrid gm p) ~ Index (gm p), Num t, Num x, Num d) => SOM t d gm x k p -> p -> SOM t d gm x k p instance GHC.Generics.Selector Data.Datamining.Clustering.SOMInternal.S1_0_4SOM instance GHC.Generics.Selector Data.Datamining.Clustering.SOMInternal.S1_0_3SOM instance GHC.Generics.Selector Data.Datamining.Clustering.SOMInternal.S1_0_2SOM instance GHC.Generics.Selector Data.Datamining.Clustering.SOMInternal.S1_0_1SOM instance GHC.Generics.Selector Data.Datamining.Clustering.SOMInternal.S1_0_0SOM instance GHC.Generics.Constructor Data.Datamining.Clustering.SOMInternal.C1_0SOM instance GHC.Generics.Datatype Data.Datamining.Clustering.SOMInternal.D1SOM instance (Control.DeepSeq.NFData t, Control.DeepSeq.NFData (gm p)) => Control.DeepSeq.NFData (Data.Datamining.Clustering.SOMInternal.SOM t d gm x k p) instance GHC.Generics.Generic (Data.Datamining.Clustering.SOMInternal.SOM t d gm x k p) instance Data.Foldable.Foldable gm => Data.Foldable.Foldable (Data.Datamining.Clustering.SOMInternal.SOM t d gm x k) instance Math.Geometry.GridInternal.Grid (gm p) => Math.Geometry.GridInternal.Grid (Data.Datamining.Clustering.SOMInternal.SOM t d gm x k p) instance (Data.Foldable.Foldable gm, Math.Geometry.GridMap.GridMap gm p, Math.Geometry.GridInternal.Grid (Math.Geometry.GridMap.BaseGrid gm p)) => Math.Geometry.GridMap.GridMap (Data.Datamining.Clustering.SOMInternal.SOM t d gm x k) p instance (Math.Geometry.GridMap.GridMap gm p, k ~ Math.Geometry.GridInternal.Index (Math.Geometry.GridMap.BaseGrid gm p), Math.Geometry.GridInternal.Grid (gm p), Math.Geometry.GridMap.GridMap gm x, k ~ Math.Geometry.GridInternal.Index (gm p), k ~ Math.Geometry.GridInternal.Index (Math.Geometry.GridMap.BaseGrid gm x), GHC.Num.Num t, GHC.Classes.Ord x, GHC.Num.Num x, GHC.Num.Num d) => Data.Datamining.Clustering.Classifier.Classifier (Data.Datamining.Clustering.SOMInternal.SOM t d gm) x k p -- | 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 t d gm x k p SOM :: gm p -> (t -> d -> x) -> (p -> p -> x) -> (p -> x -> p -> p) -> t -> SOM t d gm x k p -- | Maps patterns to tiles in a regular grid. In the context of a SOM, the -- tiles are called "nodes" [gridMap] :: SOM t d gm x k p -> gm p -- | A function which determines the how quickly the SOM learns. For -- example, if the function is f, then f t d returns -- the learning rate for a node. The parameter t indicates how -- many patterns (or pattern batches) have previously been presented to -- the classifier. Typically this is used to make the learning rate decay -- over time. The parameter d is the grid distance from the node -- being updated to the BMU (Best Matching Unit). The output is the -- learning rate for that node (the amount by which the node's model -- should be updated to match the target). The learning rate should be -- between zero and one. [learningRate] :: SOM t d gm x k p -> t -> d -> x -- | A function which compares two patterns and returns a -- non-negative number representing how different the patterns -- are. A result of 0 indicates that the patterns are identical. [difference] :: SOM t d gm x k p -> p -> p -> x -- | A function which updates models. If this function is f, then -- f target amount pattern returns a modified copy of -- pattern that is more similar to target than -- pattern is. The magnitude of the adjustment is controlled by -- the amount parameter, which should be a number between 0 and -- 1. Larger values for amount permit greater adjustments. If -- amount=1, the result should be identical to the -- target. If amount=0, the result should be the -- unmodified pattern. [makeSimilar] :: SOM t d gm x k p -> p -> x -> p -> p -- | 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 t d gm x k p -> t -- | Extracts the grid and current models from the SOM. A synonym for -- gridMap. toGridMap :: GridMap gm p => SOM t d gm x k p -> gm p -- | 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!) decayingGaussian :: Floating x => x -> x -> x -> x -> x -> x -> x -> x -- | A learning function that only updates the BMU and has a constant -- learning rate. stepFunction :: (Num d, Fractional x, Eq d) => x -> t -> d -> x -- | A learning function that updates all nodes with the same, constant -- learning rate. This can be useful for testing. constantFunction :: x -> t -> d -> x -- | 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 :: (Grid (gm p), GridMap gm p, Index (BaseGrid gm p) ~ Index (gm p), Num t, Num x, Num d) => SOM t d gm x k p -> Index (gm p) -> p -> SOM t d gm x k p