diff --git a/LICENSE b/LICENSE new file mode 100644 --- /dev/null +++ b/LICENSE @@ -0,0 +1,674 @@ + GNU GENERAL PUBLIC LICENSE + Version 3, 29 June 2007 + + Copyright (C) 2007 Free Software Foundation, Inc. + Everyone is permitted to copy and distribute verbatim copies + of this license document, but changing it is not allowed. + + Preamble + + The GNU General Public License is a free, copyleft license for +software and other kinds of works. + + The licenses for most software and other practical works are designed +to take away your freedom to share and change the works. By contrast, +the GNU General Public License is intended to guarantee your freedom to +share and change all versions of a program--to make sure it remains free +software for all its users. We, the Free Software Foundation, use the +GNU General Public License for most of our software; it applies also to +any other work released this way by its authors. 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If not, see . + +Also add information on how to contact you by electronic and paper mail. + + If the program does terminal interaction, make it output a short +notice like this when it starts in an interactive mode: + + {project} Copyright (C) {year} {fullname} + This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'. + This is free software, and you are welcome to redistribute it + under certain conditions; type `show c' for details. + +The hypothetical commands `show w' and `show c' should show the appropriate +parts of the General Public License. Of course, your program's commands +might be different; for a GUI interface, you would use an "about box". + + You should also get your employer (if you work as a programmer) or school, +if any, to sign a "copyright disclaimer" for the program, if necessary. +For more information on this, and how to apply and follow the GNU GPL, see +. + + The GNU General Public License does not permit incorporating your program +into proprietary programs. If your program is a subroutine library, you +may consider it more useful to permit linking proprietary applications with +the library. If this is what you want to do, use the GNU Lesser General +Public License instead of this License. But first, please read +. diff --git a/Setup.hs b/Setup.hs new file mode 100644 --- /dev/null +++ b/Setup.hs @@ -0,0 +1,2 @@ +import Distribution.Simple +main = defaultMain diff --git a/app/Main.hs b/app/Main.hs new file mode 100644 --- /dev/null +++ b/app/Main.hs @@ -0,0 +1,231 @@ +{- cluster-tree +Gregory W. Schwartz + +Hierarchical spectral clustering of data. +-} + +{-# LANGUAGE BangPatterns #-} +{-# LANGUAGE DataKinds #-} +{-# LANGUAGE DeriveGeneric #-} +{-# LANGUAGE OverloadedStrings #-} +{-# LANGUAGE TypeOperators #-} +{-# LANGUAGE StandaloneDeriving #-} + +module Main where + +-- Standard +import Data.Maybe (fromMaybe, catMaybes) +import GHC.Generics + +-- Cabal +import Data.Char (ord) +import Data.List (intercalate) +import Data.Monoid ((<>)) +import Options.Generic +import Safe (atMay) +import System.IO (stdin) +import Text.Read (readMaybe) +import TextShow (showt) +import qualified Control.Lens as L +import qualified Data.Aeson as A +import qualified Data.Aeson.Encode.Pretty as A +import qualified Data.ByteString.Lazy.Char8 as B +import qualified Data.Csv as CSV +import qualified Data.Map.Strict as Map +import qualified Data.Set as Set +import qualified Data.Text as T +import qualified Data.Vector as V +import qualified Numeric.LinearAlgebra as H +import qualified System.FilePath as File +import Math.Graph.Types + +-- Local +import Math.Clustering.Hierarchical.Spectral.Load +import Math.Clustering.Hierarchical.Spectral.Types +import Math.Graph.Components +import qualified Math.Clustering.Hierarchical.Spectral.Dense as HD +import qualified Math.Clustering.Hierarchical.Spectral.Eigen.AdjacencyMatrix as HS + +newtype Delimiter = Delimiter { unDelimiter :: Char } deriving (Read, Show) +newtype Row = Row { unRow :: Int } deriving (Eq, Ord, Read, Show) +newtype Column = Column { unColumn :: Int } deriving (Eq, Ord, Read, Show) +newtype OutputTree = OutputTree { unOutputTree :: String } deriving (Read, Show) +newtype MinSize = MinSize { unMinSize :: Int } deriving (Read, Show) +newtype NumEigen = NumEigen { unNumEigen :: Int } deriving (Read, Show) + +data ClusteringType = Sparse | Dense deriving (Read, Show) +data Components a = Single (ClusteringTree a) | Multiple [ClusteringTree a] + +instance A.ToJSON Q where + toEncoding = A.genericToEncoding A.defaultOptions +instance A.FromJSON Q + +instance (A.ToJSON a) => A.ToJSON (ClusteringVertex a) where + toEncoding = A.genericToEncoding A.defaultOptions +instance (A.FromJSON a) => A.FromJSON (ClusteringVertex a) + +-- | Command line arguments +data Options = Options { clusteringType :: Maybe String + "([Sparse] | Dense) Method for clustering data." + , delimiter :: Maybe Char + "([,] | CHAR) The delimiter of the CSV file. Format is row,column,value with no header." + , minSize :: Maybe Int + "([Nothing] | INT) Minimum size of a cluster." + , numEigen :: Maybe Int + "([1] | INT) Number of eigenvectors to use while clustering with kmeans. Takes from the first eigenvector. Recommended to start at 2 and work up from there if needed." + , minModularity :: Maybe Double + "([0] | DOUBLE) Minimum modularity to be over to continue recursion." + , eigenGroup :: Maybe String + "([SignGroup] | KMeansGroup) Whether to group the eigenvector using the sign or kmeans while clustering. While the default is sign, kmeans may be more accurate (but starting points are arbitrary)." + , separateComponents :: Bool + "Whether to first separate connected components of the graph first. Will output a dendrogram for each component with the name of the tree and the number of nodes within the tree, along with the base set by --output-tree." + , outputTree :: Maybe String + "([Nothing] | FILE) The name of the file to output the tree in JSON format." + } + deriving (Generic) + +modifiers :: Modifiers +modifiers = lispCaseModifiers { shortNameModifier = short } + where + short "minSize" = Just 'S' + short x = firstLetter x + +instance ParseRecord Options where + parseRecord = parseRecordWithModifiers modifiers + +main :: IO () +main = do + opts <- getRecord "cluster-tree, Gregory W. Schwartz.\ + \ Hierarchical spectral clustering of data Computes real\ + \ symmetric part of matrix, so ensure the input is real\ + \ and symmetric. Diagonal should be 0s for\ + \ adjacency matrix.\ + \ Format is row,column,value with no header.\ + \ Must end with a newline." + + let readOrErr err = fromMaybe (error err) . readMaybe + clusteringType' = + maybe Sparse (readOrErr "Cannot read --clustering-type") + . unHelpful + . clusteringType + $ opts + delim' = + Delimiter . fromMaybe ',' . unHelpful . delimiter $ opts + minSize' = fmap MinSize . unHelpful . minSize $ opts + numEigen' = fmap NumEigen . unHelpful . numEigen $ opts + minModularity' = fmap Q . unHelpful . minModularity $ opts + eigenGroup' = + maybe SignGroup (readOrErr "Cannot read --eigen-group") + . unHelpful + . eigenGroup + $ opts + separateComponents' = unHelpful . separateComponents $ opts + outputTree' = fmap OutputTree . unHelpful . outputTree $ opts + decodeOpt = CSV.defaultDecodeOptions + { CSV.decDelimiter = + fromIntegral (ord . unDelimiter $ delim') + } + encodeOpt = CSV.defaultEncodeOptions + { CSV.encDelimiter = + fromIntegral (ord . unDelimiter $ delim') + } + + clusteringTree <- + case clusteringType' of + Dense -> do + (items, mat) <- readDenseAdjMatrix decodeOpt stdin + + let cluster items = HD.hierarchicalSpectralCluster + eigenGroup' + (fmap unNumEigen numEigen') + (fmap unMinSize minSize') + minModularity' + items + + return $ + if separateComponents' + then Multiple + . fmap (uncurry cluster) + . getComponentMatsItems items + $ mat + else Single $ cluster items mat + Sparse -> do + (items, mat) <- readEigenSparseAdjMatrix decodeOpt stdin + + let cluster items = HS.hierarchicalSpectralCluster + eigenGroup' + (fmap unNumEigen numEigen') + (fmap unMinSize minSize') + minModularity' + items + + return $ + if separateComponents' + then Multiple + . fmap (uncurry cluster) + . getComponentMatsItems items + $ mat + else Single $ cluster items mat + + body <- case clusteringTree of + (Single ct) -> do + let clustering = zip ([1..] :: [Int]) . getClusterItemsTree $ ct + body :: [(T.Text, T.Text)] + body = concatMap + (\(!c, xs) -> fmap (\ !x -> (x, showt c)) . V.toList $ xs) + clustering + + case outputTree' of + Nothing -> return () + Just (OutputTree file) -> B.writeFile file + . A.encodePretty + . clusteringTreeToDendrogram + $ ct + + return body + (Multiple cts) -> do + let clustering = + fmap (L.over L._2 (zip ([1..] :: [Int]) . getClusterItemsTree)) + . zip ([1..] :: [Int]) + $ cts + body :: [(T.Text, T.Text)] + body = concatMap + (\ (!t, xs) + -> concatMap (\ (!c, ys) + -> fmap (\ x -> (x, showt t <> "/" <> showt c)) + . V.toList + $ ys + ) + xs + ) + clustering + + case outputTree' of + Nothing -> return () + Just (OutputTree file) -> do + let getSize :: ClusteringTree a -> Int + getSize = sum . fmap V.length . getClusterItemsTree + getFileName :: Int -> Int -> String + getFileName t n = + uncurry (File.) + . L.over L._2 (\x -> intercalate "_" ["tree", show t, "size", show n, x]) + . File.splitFileName + $ file + write :: (A.ToJSON a) => Int -> ClusteringTree a -> IO () + write t tree = do + B.writeFile (getFileName t (getSize tree)) + . A.encodePretty + . clusteringTreeToDendrogram + $ tree + + mapM_ (uncurry write) . zip [1..] $ cts + + return body + + -- | Print final result. + B.putStr + . (<>) "item,cluster\n" + . CSV.encodeWith encodeOpt + $ body + + return () diff --git a/hierarchical-spectral-clustering.cabal b/hierarchical-spectral-clustering.cabal new file mode 100644 --- /dev/null +++ b/hierarchical-spectral-clustering.cabal @@ -0,0 +1,76 @@ +name: hierarchical-spectral-clustering +version: 0.2.1.0 +synopsis: Hierarchical spectral clustering of a graph. +description: Generate a tree of hierarchical spectral clustering using Newman-Girvan modularity as a stopping criteria. +homepage: http://github.com/GregorySchwartz/hierarchical-spectral-clustering#readme +license: GPL-3 +license-file: LICENSE +author: Gregory W. Schwartz +maintainer: gsch@pennmedicine.upenn.edu +copyright: 2018 Gregory W. Schwartz +category: Bioinformatics +build-type: Simple +-- extra-source-files: +cabal-version: >=1.10 + +library + hs-source-dirs: src + exposed-modules: Math.Clustering.Hierarchical.Spectral.Dense + , Math.Clustering.Hierarchical.Spectral.Sparse + , Math.Clustering.Hierarchical.Spectral.Load + , Math.Clustering.Hierarchical.Spectral.Eigen.AdjacencyMatrix + , Math.Clustering.Hierarchical.Spectral.Eigen.FeatureMatrix + , Math.Clustering.Hierarchical.Spectral.Types + , Math.Clustering.Hierarchical.Spectral.Utility + , Math.Graph.Components + , Math.Graph.Types + other-modules: Math.Clustering.Hierarchical.Spectral.Test + build-depends: base >= 4.7 && < 5 + , aeson + , cassava + , clustering + , containers + , eigen == 3.3.4.1 + , hierarchical-clustering + , hmatrix + , fgl + , managed + , modularity + , mtl + , safe + , sparse-linear-algebra + , spectral-clustering + , streaming + , streaming-bytestring + , streaming-cassava + , streaming-with + , text + , tree-fun + , vector + ghc-options: -O2 + default-language: Haskell2010 + +executable cluster-tree + hs-source-dirs: app + main-is: Main.hs + ghc-options: -threaded -rtsopts -O2 + build-depends: base + , hierarchical-spectral-clustering + , aeson + , aeson-pretty + , bytestring + , cassava + , containers + , filepath + , hmatrix + , lens + , optparse-generic + , safe + , text + , text-show + , vector + default-language: Haskell2010 + +source-repository head + type: git + location: https://github.com/GregorySchwartz/hierarchical-spectral-clustering diff --git a/src/Math/Clustering/Hierarchical/Spectral/Dense.hs b/src/Math/Clustering/Hierarchical/Spectral/Dense.hs new file mode 100644 --- /dev/null +++ b/src/Math/Clustering/Hierarchical/Spectral/Dense.hs @@ -0,0 +1,94 @@ +{- Math.Clustering.Hierarchical.Spectral +Gregory W. Schwartz + +Collects the functions pertaining to hierarchical spectral clustering. +-} + +{-# LANGUAGE BangPatterns #-} + +module Math.Clustering.Hierarchical.Spectral.Dense + ( hierarchicalSpectralCluster + , AdjacencyMatrix (..) + , Items (..) + ) where + +-- Remote +import Data.Bool (bool) +import Data.Clustering.Hierarchical (Dendrogram (..)) +import Data.Maybe (fromMaybe) +import Data.Tree (Tree (..)) +import Math.Clustering.Spectral.Dense (spectralClusterNorm, spectralClusterKNorm) +import Math.Modularity.Dense (getModularity) +import Math.Modularity.Types (Q (..)) +import qualified Data.Foldable as F +import qualified Data.Set as Set +import qualified Data.Vector as V +import qualified Data.Vector.Storable as VS +import qualified Numeric.LinearAlgebra as H + +-- Local +import Math.Clustering.Hierarchical.Spectral.Types +import Math.Clustering.Hierarchical.Spectral.Utility + +type AdjacencyMatrix = H.Matrix Double +type Items a = V.Vector a + +-- | Check if there is more than one cluster. +hasMultipleClusters :: H.Vector Double -> Bool +hasMultipleClusters = (> 1) . Set.size . Set.fromList . H.toList + +-- | Generates a tree through divisive hierarchical clustering using +-- Newman-Girvan modularity as a stopping criteria. Can also use minimum number +-- of observations in a cluster as the stopping criteria. +hierarchicalSpectralCluster :: (Show a) => EigenGroup + -> Maybe NumEigen + -> Maybe Int + -> Maybe Q + -> Items a + -> AdjacencyMatrix + -> ClusteringTree a +hierarchicalSpectralCluster !eigenGroup !numEigenMay !minSizeMay !minModMay !items !adjMat = + if H.rows adjMat > 1 + && hasMultipleClusters clusters + && ngMod > minMod + && H.rows left >= minSize + && H.rows right >= minSize + then + Node { rootLabel = vertex + , subForest = + [ hierarchicalSpectralCluster + eigenGroup + numEigenMay + minSizeMay + minModMay + (subsetVector items leftIdxs) + left + , hierarchicalSpectralCluster + eigenGroup + numEigenMay + minSizeMay + minModMay + (subsetVector items rightIdxs) + right + ] + } + else + Node {rootLabel = vertex, subForest = []} + where + minMod = fromMaybe (Q 0) minModMay + minSize = fromMaybe 1 minSizeMay + numEigen = fromMaybe 1 numEigenMay + vertex = ClusteringVertex { _clusteringItems = items + , _ngMod = ngMod + } + clusters = spectralClustering eigenGroup adjMat + spectralClustering :: EigenGroup -> AdjacencyMatrix -> H.Vector Double + spectralClustering SignGroup = spectralClusterNorm + spectralClustering KMeansGroup = spectralClusterKNorm numEigen 2 + ngMod = getModularity clusters $ adjMat + getIdxs val = VS.ifoldr' (\ !i !v !acc -> bool acc (i:acc) $ v == val) [] + leftIdxs = getIdxs 0 $ clusters + rightIdxs = getIdxs 1 $ clusters + left = adjMat H.?? (H.Pos (H.idxs leftIdxs), H.Pos (H.idxs leftIdxs)) + right = + adjMat H.?? (H.Pos (H.idxs rightIdxs), H.Pos (H.idxs rightIdxs)) diff --git a/src/Math/Clustering/Hierarchical/Spectral/Eigen/AdjacencyMatrix.hs b/src/Math/Clustering/Hierarchical/Spectral/Eigen/AdjacencyMatrix.hs new file mode 100644 --- /dev/null +++ b/src/Math/Clustering/Hierarchical/Spectral/Eigen/AdjacencyMatrix.hs @@ -0,0 +1,100 @@ +{- Math.Clustering.Hierarchical.Spectral.Eigen.AdjacencyMatrix +Gregory W. Schwartz + +Collects the functions pertaining to hierarchical spectral clustering. +-} + +{-# LANGUAGE BangPatterns #-} + +module Math.Clustering.Hierarchical.Spectral.Eigen.AdjacencyMatrix + ( hierarchicalSpectralCluster + , AdjacencyMatrix (..) + , Items (..) + ) where + +-- Remote +import Data.Bool (bool) +import Data.Clustering.Hierarchical (Dendrogram (..)) +import Data.Maybe (fromMaybe) +import Data.Tree (Tree (..)) +import Math.Clustering.Spectral.Eigen.AdjacencyMatrix (spectralClusterNorm, spectralClusterKNorm) +import Math.Modularity.Eigen.Sparse (getModularity) +import Math.Modularity.Types (Q (..)) +import Safe (headMay) +import qualified Data.Foldable as F +import qualified Data.Set as Set +import qualified Data.Eigen.SparseMatrix as S +import qualified Data.Vector as V +import qualified Data.Vector.Storable as VS + +-- Local +import Math.Clustering.Hierarchical.Spectral.Types +import Math.Clustering.Hierarchical.Spectral.Utility + +type AdjacencyMatrix = S.SparseMatrixXd +type Items a = V.Vector a + +-- | Check if there is more than one cluster. +hasMultipleClusters :: S.SparseMatrixXd -> Bool +hasMultipleClusters = (> 1) + . Set.size + . Set.fromList + . concat + . S.toDenseList + +-- | Generates a tree through divisive hierarchical clustering using +-- Newman-Girvan modularity as a stopping criteria. Can also use minimum number +-- of observations in a cluster as the stopping criteria. +hierarchicalSpectralCluster :: EigenGroup + -> Maybe NumEigen + -> Maybe Int + -> Maybe Q + -> Items a + -> AdjacencyMatrix + -> ClusteringTree a +hierarchicalSpectralCluster !eigenGroup !numEigenMay !minSizeMay !minModMay !items !adjMat = + + if S.rows adjMat > 1 + && hasMultipleClusters clusters + && ngMod > minMod + && S.rows left >= minSize + && S.rows right >= minSize + then do + Node { rootLabel = vertex + , subForest = [ hierarchicalSpectralCluster + eigenGroup + numEigenMay + minSizeMay + minModMay + (subsetVector items leftIdxs) + left + , hierarchicalSpectralCluster + eigenGroup + numEigenMay + minSizeMay + minModMay (subsetVector items rightIdxs) + right + ] + } + else + Node {rootLabel = vertex, subForest = []} + where + clusters = spectralClustering eigenGroup adjMat + spectralClustering :: EigenGroup -> AdjacencyMatrix -> S.SparseMatrixXd + spectralClustering SignGroup = spectralClusterNorm + spectralClustering KMeansGroup = spectralClusterKNorm numEigen 2 + minMod = fromMaybe (Q 0) minModMay + minSize = fromMaybe 1 minSizeMay + numEigen = fromMaybe 1 numEigenMay + vertex = ClusteringVertex { _clusteringItems = items + , _ngMod = ngMod + } + ngMod = getModularity clusters adjMat + getIdxs val = VS.ifoldr' (\ !i !v !acc -> bool acc (i:acc) $ v == val) [] + . VS.fromList + . concat + . S.toDenseList + leftIdxs = getIdxs 0 clusters + rightIdxs = getIdxs 1 clusters + left = S.squareSubset leftIdxs adjMat + right = S.squareSubset rightIdxs adjMat diff --git a/src/Math/Clustering/Hierarchical/Spectral/Eigen/FeatureMatrix.hs b/src/Math/Clustering/Hierarchical/Spectral/Eigen/FeatureMatrix.hs new file mode 100644 --- /dev/null +++ b/src/Math/Clustering/Hierarchical/Spectral/Eigen/FeatureMatrix.hs @@ -0,0 +1,113 @@ +{- Math.Clustering.Hierarchical.Spectral.Eigen.FeatureMatrix +Gregory W. Schwartz + +Collects the functions pertaining to hierarchical spectral clustering for +feature matrices. +-} + +{-# LANGUAGE BangPatterns #-} + +module Math.Clustering.Hierarchical.Spectral.Eigen.FeatureMatrix + ( hierarchicalSpectralCluster + , FeatureMatrix (..) + , B (..) + , Items (..) + , ShowB (..) + ) where + +-- Remote +import Data.Bool (bool) +import Data.Clustering.Hierarchical (Dendrogram (..)) +import Data.Maybe (fromMaybe) +import Data.Tree (Tree (..)) +import Math.Clustering.Spectral.Eigen.FeatureMatrix (B (..), getB, spectralCluster, spectralClusterK) +import Math.Modularity.Eigen.Sparse (getBModularity) +import Math.Modularity.Types (Q (..)) +import qualified Data.Foldable as F +import qualified Data.Set as Set +import qualified Data.Eigen.SparseMatrix as S +import qualified Data.Vector as V +import qualified Data.Vector.Storable as VS + +-- Local +import Math.Clustering.Hierarchical.Spectral.Types +import Math.Clustering.Hierarchical.Spectral.Utility + +type FeatureMatrix = S.SparseMatrixXd +type Items a = V.Vector a +type ShowB = ((Int, Int), [(Int, Int, Double)]) +type NormalizeFlag = Bool + +-- | Check if there is more than one cluster. +hasMultipleClusters :: S.SparseMatrixXd -> Bool +hasMultipleClusters = (> 1) + . Set.size + . Set.fromList + . concat + . S.toDenseList + +-- | Generates a tree through divisive hierarchical clustering using +-- Newman-Girvan modularity as a stopping criteria. Can use minimum number of +-- observations in a cluster as a stopping criteria. Assumes the feature matrix +-- has column features and row observations. Items correspond to rows. Can +-- use FeatureMatrix or a pre-generated B matrix. See Shu et al., "Efficient +-- Spectral Neighborhood Blocking for Entity Resolution", 2011. +hierarchicalSpectralCluster :: EigenGroup + -> NormalizeFlag + -> Maybe NumEigen + -> Maybe Int + -> Maybe Q + -> Items a + -> Either FeatureMatrix B + -> ClusteringTree a +hierarchicalSpectralCluster eigenGroup normFlag numEigenMay minSizeMay minModMay initItems initMat = + go initItems initB + where + initB = either (getB normFlag) id $ initMat + minMod = fromMaybe (Q 0) minModMay + minSize = fromMaybe 1 minSizeMay + numEigen = fromMaybe 1 numEigenMay + go :: Items a -> B -> ClusteringTree a + go !items !b = + if (S.rows $ unB b) > 1 + && hasMultipleClusters clusters + && ngMod > minMod + && S.rows (unB left) >= minSize + && S.rows (unB right) >= minSize + then + Node { rootLabel = vertex + , subForest = [ go (subsetVector items leftIdxs) left + , go (subsetVector items rightIdxs) right + ] + } + + else + Node {rootLabel = vertex, subForest = []} + where + vertex = ClusteringVertex + { _clusteringItems = items + , _ngMod = ngMod + } + clusters :: S.SparseMatrixXd + clusters = spectralClustering eigenGroup b + spectralClustering :: EigenGroup -> B -> S.SparseMatrixXd + spectralClustering SignGroup = spectralCluster + spectralClustering KMeansGroup = spectralClusterK numEigen 2 + ngMod :: Q + ngMod = getBModularity clusters b + getSortedIdxs :: Double -> S.SparseMatrixXd -> [Int] + getSortedIdxs val = VS.ifoldr' (\ !i !v !acc -> bool acc (i:acc) $ v == val) [] + . VS.fromList + . concat + . S.toDenseList + leftIdxs :: [Int] + leftIdxs = getSortedIdxs 0 clusters + rightIdxs :: [Int] + rightIdxs = getSortedIdxs 1 clusters + left :: B + left = B $ extractRows (unB b) leftIdxs + right :: B + right = B $ extractRows (unB b) rightIdxs + extractRows :: S.SparseMatrixXd -> [Int] -> S.SparseMatrixXd + extractRows mat [] = S.fromList 0 0 [] + extractRows mat xs = S.fromRows . fmap (flip S.getRow mat) $ xs diff --git a/src/Math/Clustering/Hierarchical/Spectral/Load.hs b/src/Math/Clustering/Hierarchical/Spectral/Load.hs new file mode 100644 --- /dev/null +++ b/src/Math/Clustering/Hierarchical/Spectral/Load.hs @@ -0,0 +1,167 @@ +{- Math.Clustering.Hierarchical.Spectral.Load +Gregory W. Schwartz + +Collects the functions pertaining to loading a matrix. +-} + +{-# LANGUAGE BangPatterns #-} +{-# LANGUAGE OverloadedStrings #-} + +module Math.Clustering.Hierarchical.Spectral.Load + ( readDenseAdjMatrix + , readSparseAdjMatrix + , readEigenSparseAdjMatrix + ) where + +-- Remote +import Control.Monad.Except (runExceptT, ExceptT (..)) +import Control.Monad.Managed (with, liftIO, Managed (..)) +import Data.Maybe (fromMaybe, catMaybes) +import System.IO (Handle (..)) +import qualified Data.ByteString.Streaming.Char8 as BS +import qualified Data.Csv as CSV +import qualified Data.Eigen.SparseMatrix as E +import qualified Data.Map.Strict as Map +import qualified Data.Set as Set +import qualified Data.Sparse.Common as SH +import qualified Data.Text as T +import qualified Data.Vector as V +import qualified Numeric.LinearAlgebra as H +import qualified Streaming as S +import qualified Streaming.Cassava as S +import qualified Streaming.Prelude as S +import qualified Streaming.With.Lifted as SW + +-- Local +import Math.Clustering.Hierarchical.Spectral.Types + +-- | Generic error message. +errorMsg = error "Not correct format (requires row,column,value)" + +-- | Parse a row of a label index file. +parseRow :: (T.Text, T.Text, Double) -> ((T.Text, T.Text), Double) +parseRow (i, j, v) = ((i, j), v) + +-- | Ignore the disconnected vertices, not used (rather use very small weight). +ignoreDisconnected :: V.Vector T.Text + -> H.Matrix Double + -> (V.Vector T.Text, H.Matrix Double) +ignoreDisconnected items mat = (newItems, newMat) + where + newItems = V.fromList $ fmap ((V.!) items) valid + newMat = mat H.?? (H.Pos $ H.idxs valid, H.Pos $ H.idxs valid) + valid = catMaybes + . zipWith (\x xs -> if sum xs > 0 then Just x else Nothing) [0..] + . H.toLists + $ mat + +-- | Ensure symmetry. +symmetric :: [((Int, Int), Double)] -> [((Int, Int), Double)] +symmetric = concatMap (\((!i, !j), v) -> [((i, j), v), ((j, i), v)]) + +-- | Ensure zeros on diagonal. +zeroDiag :: [((Int, Int), Double)] -> [((Int, Int), Double)] +zeroDiag = filter (\((!i, !j), _) -> i /= j) + +-- | Get the translated matrix indices. +getNewIndices + -- :: (Eq a, Ord a) + -- => [((a, a), Double)] -> [((Int, Int), Double)] + :: [((T.Text, T.Text), Double)] -> [((Int, Int), Double)] +getNewIndices xs = + fmap + (\((!i,!j),!v) -> + ( ( Map.findWithDefault eMsg i idxMap + , Map.findWithDefault eMsg j idxMap + ) + , v + ) + ) + xs + where + eMsg = error "Index not found during index conversion." + indices = getAllIndices xs + idxMap = Map.fromList $ zip indices [0 ..] + +-- | Get the list of all indices. +getAllIndices :: (Eq a, Ord a) => [((a, a), Double)] -> [a] +getAllIndices xs = Set.toAscList . Set.union (getSet fst) $ getSet snd + where + getSet f = Set.fromList . fmap (f . fst) $ xs + +-- | Get a dense adjacency matrix from a handle. +readDenseAdjMatrix :: CSV.DecodeOptions + -> Handle + -> IO (V.Vector T.Text, H.Matrix Double) +readDenseAdjMatrix decodeOpt handle = flip with return $ do + let getAssocList = S.toList_ . S.map parseRow + + assocList <- + fmap (either (error . show) id) + . runExceptT + . getAssocList + . S.decodeWith decodeOpt S.NoHeader + $ (BS.hGetContents handle :: BS.ByteString (ExceptT S.CsvParseException Managed) ()) + + let items = V.fromList $ getAllIndices assocList + mat = H.assoc (V.length items, V.length items) 0 + . Set.toList + . Set.fromList -- Ensure no duplicates. + . symmetric -- Ensure symmetry. + . zeroDiag -- Ensure zeros on diagonal. + . getNewIndices -- Only look at present rows by converting indices. + $ assocList + + return (items, mat) + +-- | Get a sparse adjacency matrix from a handle. +readSparseAdjMatrix :: CSV.DecodeOptions + -> Handle + -> IO (V.Vector T.Text, SH.SpMatrix Double) +readSparseAdjMatrix decodeOpt handle = flip with return $ do + let getAssocList = S.toList_ . S.map parseRow + + assocList <- + fmap (either (error . show) id) + . runExceptT + . getAssocList + . S.decodeWith decodeOpt S.NoHeader + $ (BS.hGetContents handle :: BS.ByteString (ExceptT S.CsvParseException Managed) ()) + + let items = V.fromList $ getAllIndices assocList + mat = SH.fromListSM (V.length items, V.length items) + . Set.toList + . Set.fromList -- Ensure no duplicates. + . fmap (\((i, j), v) -> (i, j, v)) + . symmetric -- Ensure symmetry. + . zeroDiag -- Ensure zeros on diagonal. + . getNewIndices -- Only look at present rows by converting indices. + $ assocList + + return (items, mat) + +-- | Get a sparse adjacency matrix from a handle. +readEigenSparseAdjMatrix :: CSV.DecodeOptions + -> Handle + -> IO (V.Vector T.Text, E.SparseMatrixXd) +readEigenSparseAdjMatrix decodeOpt handle = flip with return $ do + let getAssocList = S.toList_ . S.map parseRow + + assocList <- + fmap (either (error . show) id) + . runExceptT + . getAssocList + . S.decodeWith decodeOpt S.NoHeader + $ (BS.hGetContents handle :: BS.ByteString (ExceptT S.CsvParseException Managed) ()) + + let items = V.fromList $ getAllIndices assocList + mat = E.fromList (V.length items) (V.length items) + . Set.toList + . Set.fromList -- Ensure no duplicates. + . fmap (\((i, j), v) -> (i, j, v)) + . symmetric -- Ensure symmetry. + . zeroDiag -- Ensure zeros on diagonal. + . getNewIndices -- Only look at present rows by converting indices. + $ assocList + + return (items, mat) diff --git a/src/Math/Clustering/Hierarchical/Spectral/Sparse.hs b/src/Math/Clustering/Hierarchical/Spectral/Sparse.hs new file mode 100644 --- /dev/null +++ b/src/Math/Clustering/Hierarchical/Spectral/Sparse.hs @@ -0,0 +1,177 @@ +{- Math.Clustering.Hierarchical.Spectral.Sparse +Gregory W. Schwartz + +Collects the functions pertaining to hierarchical spectral clustering for sparse +data. +-} + +{-# LANGUAGE BangPatterns #-} + +module Math.Clustering.Hierarchical.Spectral.Sparse + ( hierarchicalSpectralCluster + , hierarchicalSpectralClusterAdj + , FeatureMatrix (..) + , B (..) + , Items (..) + , ShowB (..) + ) where + +-- Remote +import Data.Bool (bool) +import Data.Clustering.Hierarchical (Dendrogram (..)) +import Data.Maybe (fromMaybe) +import Data.Tree (Tree (..)) +import Math.Clustering.Spectral.Sparse (B (..), AdjacencyMatrix (..), getB, spectralCluster, spectralClusterK, spectralClusterNorm, spectralClusterKNorm) +import Math.Modularity.Sparse (getBModularity, getModularity) +import Math.Modularity.Types (Q (..)) +import qualified Data.Foldable as F +import qualified Data.Set as Set +import qualified Data.Sparse.Common as S +import qualified Data.Vector as V +import qualified Data.Vector.Storable as VS +import qualified Numeric.LinearAlgebra.Sparse as S + +-- Local +import Math.Clustering.Hierarchical.Spectral.Types +import Math.Clustering.Hierarchical.Spectral.Utility + +type FeatureMatrix = S.SpMatrix Double +type Items a = V.Vector a +type ShowB = ((Int, Int), [(Int, Int, Double)]) +type NormalizeFlag = Bool + +-- | Check if there is more than one cluster. +hasMultipleClusters :: S.SpVector Double -> Bool +hasMultipleClusters = (> 1) . Set.size . Set.fromList . S.toDenseListSV + +-- | Generates a tree through divisive hierarchical clustering using +-- Newman-Girvan modularity as a stopping criteria. Can use minimum number of +-- observations in a cluster as a stopping criteria. Assumes the feature matrix +-- has column features and row observations. Items correspond to rows. Can +-- use FeatureMatrix or a pre-generated B matrix. See Shu et al., "Efficient +-- Spectral Neighborhood Blocking for Entity Resolution", 2011. +hierarchicalSpectralCluster :: EigenGroup + -> NormalizeFlag + -> Maybe NumEigen + -> Maybe Int + -> Maybe Q + -> Items a + -> Either FeatureMatrix B + -> ClusteringTree a +hierarchicalSpectralCluster eigenGroup normFlag numEigenMay minSizeMay minModMay initItems initMat = + go initItems initB + where + initB = either (getB normFlag) id $ initMat + minMod = fromMaybe (Q 0) minModMay + minSize = fromMaybe 1 minSizeMay + numEigen = fromMaybe 1 numEigenMay + go :: Items a -> B -> ClusteringTree a + go !items !b = + if (S.nrows $ unB b) > 1 + && hasMultipleClusters clusters + && ngMod > minMod + && S.nrows (unB left) >= minSize + && S.nrows (unB right) >= minSize + then + Node { rootLabel = vertex + , subForest = [ go (subsetVector items leftIdxs) left + , go (subsetVector items rightIdxs) right + ] + } + + else + Node {rootLabel = vertex, subForest = []} + where + vertex = ClusteringVertex + { _clusteringItems = items + , _ngMod = ngMod + } + clusters :: S.SpVector Double + clusters = spectralClustering eigenGroup b + spectralClustering :: EigenGroup -> B -> S.SpVector Double + spectralClustering SignGroup = spectralCluster + spectralClustering KMeansGroup = spectralClusterK numEigen 2 + ngMod :: Q + ngMod = getBModularity clusters $ b + getSortedIdxs :: Double -> S.SpVector Double -> [Int] + getSortedIdxs val = VS.ifoldr' (\ !i !v !acc -> bool acc (i:acc) $ v == val) [] + . VS.fromList + . S.toDenseListSV + leftIdxs :: [Int] + leftIdxs = getSortedIdxs 0 $ clusters + rightIdxs :: [Int] + rightIdxs = getSortedIdxs 1 $ clusters + left :: B + left = B $ extractRows (unB b) leftIdxs + right :: B + right = B $ extractRows (unB b) rightIdxs + extractRows :: S.SpMatrix Double -> [Int] -> S.SpMatrix Double + extractRows mat [] = S.zeroSM 0 0 + extractRows mat xs = + S.transposeSM . S.fromColsL . fmap (S.extractRow mat) $ xs + +-- | Generates a tree through divisive hierarchical clustering using +-- Newman-Girvan modularity as a stopping criteria. Can use minimum number of +-- observations in a cluster as a stopping criteria. Uses an adjacency matrix. +-- Items correspond to rows. +hierarchicalSpectralClusterAdj :: EigenGroup + -> Maybe NumEigen + -> Maybe Int + -> Maybe Q + -> Items a + -> AdjacencyMatrix + -> ClusteringTree a +hierarchicalSpectralClusterAdj eigenGroup numEigenMay minSizeMay minModMay initItems initMat = + go initItems initMat + where + minMod = fromMaybe (Q 0) minModMay + minSize = fromMaybe 1 minSizeMay + numEigen = fromMaybe 1 numEigenMay + go :: Items a -> AdjacencyMatrix -> ClusteringTree a + go !items !mat = + if S.nrows mat > 1 + && hasMultipleClusters clusters + && ngMod > minMod + && S.nrows left >= minSize + && S.nrows right >= minSize + then + Node { rootLabel = vertex + , subForest = [ go (subsetVector items leftIdxs) left + , go (subsetVector items rightIdxs) right + ] + } + + else + Node {rootLabel = vertex, subForest = []} + where + vertex = ClusteringVertex + { _clusteringItems = items + , _ngMod = ngMod + } + clusters :: S.SpVector Double + clusters = spectralClustering eigenGroup mat + spectralClustering :: EigenGroup -> AdjacencyMatrix -> S.SpVector Double + spectralClustering SignGroup = spectralClusterNorm + spectralClustering KMeansGroup = spectralClusterKNorm numEigen 2 + ngMod :: Q + ngMod = getModularity clusters mat + getSortedIdxs :: Double -> S.SpVector Double -> [Int] + getSortedIdxs val = VS.ifoldr' (\ !i !v !acc -> bool acc (i:acc) $ v == val) [] + . VS.fromList + . S.toDenseListSV + leftIdxs :: [Int] + leftIdxs = getSortedIdxs 0 clusters + rightIdxs :: [Int] + rightIdxs = getSortedIdxs 1 clusters + left :: AdjacencyMatrix + left = getSubMat mat leftIdxs + right :: AdjacencyMatrix + right = getSubMat mat rightIdxs + getSubMat :: S.SpMatrix Double -> [Int] -> S.SpMatrix Double + getSubMat mat [] = S.zeroSM 0 0 + getSubMat mat is = S.fromColsL + . (\x -> fmap (S.extractCol x) is) + . S.transposeSM + . S.fromColsL + . fmap (S.extractRow mat) + $ is diff --git a/src/Math/Clustering/Hierarchical/Spectral/Test.hs b/src/Math/Clustering/Hierarchical/Spectral/Test.hs new file mode 100644 --- /dev/null +++ b/src/Math/Clustering/Hierarchical/Spectral/Test.hs @@ -0,0 +1,188 @@ +{- Math.Clustering.Hierarchical.Spectral.Test +Gregory W. Schwartz + +Collects the functions pertaining to testing hierarchical spectral clustering. +-} + +{-# LANGUAGE BangPatterns #-} + +module Math.Clustering.Hierarchical.Spectral.Test where + +-- Remote +import Data.List (tails) +import Data.Maybe (fromMaybe) +import Data.Monoid ((<>)) +import Math.Clustering.Spectral.Sparse (getB, B (..)) +import qualified Data.Map.Strict as Map +import qualified Data.Set as Set +import qualified Data.Sparse.Common as S +import qualified Data.Eigen.SparseMatrix as E +import qualified Data.Vector as V +import qualified Math.Clustering.Spectral.Eigen.FeatureMatrix as EF +import qualified Numeric.LinearAlgebra as H + +-- Local +import Math.Clustering.Hierarchical.Spectral.Types +import Math.Clustering.Hierarchical.Spectral.Sparse +import qualified Math.Clustering.Hierarchical.Spectral.Dense as Dense +import qualified Math.Clustering.Hierarchical.Spectral.Eigen.FeatureMatrix as EF +import qualified Math.Clustering.Hierarchical.Spectral.Eigen.AdjacencyMatrix as EA + +newtype QGram = QGram { unQGram :: String } deriving (Eq, Ord, Read, Show) +newtype QGramMap = QGramMap + { unQGramMap :: Map.Map QGram Int + } deriving (Eq,Ord,Read,Show) + +exampleData :: [String] +exampleData = [ "600 MOUNTAIN AVENUE" + , "700 MOUNTAIN AVE" + , "600-700 MOUNTAIN AVE" + , "100 DIAMOND HILL RD" + , "100 DIAMOND HILL ROAD" + , "123 SPRINGFIELD AVENUE" + , "123 SPRINFGIELD AVE" + ] + +exampleItems :: V.Vector String +exampleItems = V.fromList exampleData + +-- | Add beginning and ending symbols. +addBorders :: String -> String +addBorders x = "##" <> x <> "$$" + +-- | Generate qgrams for a string. +getQGrams :: Int -> String -> [QGram] +getQGrams n = + fmap QGram . filter ((== n) . length) . fmap (take n) . tails . addBorders + +-- | Get mapping of qgrams to indices. +getQGramMap :: [QGram] -> QGramMap +getQGramMap = QGramMap . Map.fromList . flip zip [0,1..] + +-- | Convert a record to a vector. +recordToRow :: Int -> QGramMap -> String -> S.SpVector Double +recordToRow n (QGramMap qgramMap) = S.fromListSV (Map.size qgramMap) + . Map.toAscList + . Map.fromListWith (+) + . flip zip [1,1..] + . fromMaybe (error "Invalid qgram.") + . mapM (flip Map.lookup qgramMap) + . getQGrams n + +-- | Generate the matrix of qgrams from a list of records and qgram length. +exampleMatrix :: Int -> [String] -> S.SpMatrix Double +exampleMatrix n records = + S.transposeSM . S.fromColsL . fmap (recordToRow n qgramMap) $ records + where + qgramMap = getQGramMap + . Set.toList + . Set.fromList + . concatMap (getQGrams n) + $ records + +clusterExample = hierarchicalSpectralCluster + SignGroup + True + Nothing + Nothing + Nothing + exampleItems + (Left $ exampleMatrix 3 exampleData) + +clusterKExample = hierarchicalSpectralCluster + KMeansGroup + True + (Just 2) + Nothing + Nothing + exampleItems + (Left $ exampleMatrix 3 exampleData) + +clusterAdjExample = hierarchicalSpectralClusterAdj + SignGroup + Nothing + Nothing + Nothing + exampleItems + adjacencyExample + +clusterKAdjExample = hierarchicalSpectralClusterAdj + KMeansGroup + (Just 2) + Nothing + Nothing + exampleItems + adjacencyExample + +adjacencyExample :: S.SpMatrix Double +adjacencyExample = S.filterSM (\i j _ -> i /= j) $ (unB b) S.##^ (unB b) + where + b = getB True $ exampleMatrix 3 exampleData + +denseAdjacencyExample :: H.Matrix Double +denseAdjacencyExample = H.assoc (S.dimSM adjacencyExample) 0 + . fmap (\(!x, !y, !z) -> if x == y then ((x, y), 0) else ((x, y), z)) + . S.toListSM + $ adjacencyExample + +denseClusterExample = Dense.hierarchicalSpectralCluster + SignGroup + Nothing + Nothing + Nothing + exampleItems + denseAdjacencyExample + +denseClusterKExample = Dense.hierarchicalSpectralCluster + KMeansGroup + (Just 2) + Nothing + Nothing + exampleItems + denseAdjacencyExample + +-- | Generate the matrix of qgrams from a list of records and qgram length. +exampleEigenMatrix :: Int -> [String] -> E.SparseMatrixXd +exampleEigenMatrix n records = E.fromList (S.nrows mat) (S.ncols mat) . S.toListSM $ mat + where + mat = exampleMatrix n records + +adjacencyEigenExample :: E.SparseMatrixXd +adjacencyEigenExample = E._imap (\i j v -> if i == j then 0 else v) + $ (EF.unB b) * E.transpose (EF.unB b) + where + b = EF.getB True $ exampleEigenMatrix 3 exampleData + +clusterEigenExample = EF.hierarchicalSpectralCluster + SignGroup + True + Nothing + Nothing + Nothing + exampleItems + (Left $ exampleEigenMatrix 3 exampleData) + +clusterKEigenExample = EF.hierarchicalSpectralCluster + KMeansGroup + True + (Just 2) + Nothing + Nothing + exampleItems + (Left $ exampleEigenMatrix 3 exampleData) + +clusterAdjEigenExample = EA.hierarchicalSpectralCluster + SignGroup + Nothing + Nothing + Nothing + exampleItems + adjacencyEigenExample + +clusterKAdjEigenExample = EA.hierarchicalSpectralCluster + KMeansGroup + (Just 2) + Nothing + Nothing + exampleItems + adjacencyEigenExample diff --git a/src/Math/Clustering/Hierarchical/Spectral/Types.hs b/src/Math/Clustering/Hierarchical/Spectral/Types.hs new file mode 100644 --- /dev/null +++ b/src/Math/Clustering/Hierarchical/Spectral/Types.hs @@ -0,0 +1,90 @@ +{- Math.Clustering.Hierarchical.Types +Gregory W. Schwartz + +Collects the types used in hierarchical clustering. +-} + +{-# LANGUAGE BangPatterns #-} +{-# LANGUAGE DeriveGeneric #-} +{-# LANGUAGE StandaloneDeriving #-} + +module Math.Clustering.Hierarchical.Spectral.Types + ( ClusteringTree (..) + , ClusteringVertex (..) + , EigenGroup (..) + , clusteringTreeToDendrogram + , clusteringTreeToDendrogramCumulative + , getClusterItemsDend + , getClusterItemsTree + , Q (..) + , NumEigen (..) + ) where + +-- Remote +import Data.Clustering.Hierarchical (Dendrogram (..)) +import Data.Monoid ((<>)) +import Data.Tree (Tree (..)) +import GHC.Generics (Generic) +import Math.Modularity.Types (Q (..)) +import Math.TreeFun.Tree (leaves) +import qualified Data.Aeson as A +import qualified Data.Foldable as F +import qualified Data.Vector as V + +-- Local + +type Items a = V.Vector a +type ClusteringTree a = Tree (ClusteringVertex a) +type NumEigen = Int + +data EigenGroup = SignGroup | KMeansGroup deriving (Read, Show, Generic) + +data ClusteringVertex a = ClusteringVertex + { _clusteringItems :: !(Items a) + , _ngMod :: !Q + } deriving (Eq, Ord, Read, Show, Generic) + +-- | Convert a ClusteringTree to a Dendrogram. Modularity is the distance. +clusteringTreeToDendrogram :: ClusteringTree a -> Dendrogram (Items a) +clusteringTreeToDendrogram = go + where + go (Node { rootLabel = !n, subForest = []}) = Leaf $ _clusteringItems n + go (Node { rootLabel = !n, subForest = [x, y]}) = + Branch (unQ . _ngMod $ n) (go x) (go y) + go (Node { subForest = xs}) = + error $ "Clustering tree has " + <> (show $ length xs) + <> " children. Requires two or none." + +-- | Convert a ClusteringTree to a Dendrogram. Modularity is the distance, such +-- that the distance is the modularity plus the maximum distance of each branch. +clusteringTreeToDendrogramCumulative :: ClusteringTree a -> Dendrogram (Items a) +clusteringTreeToDendrogramCumulative = fst . go + where + go (Node { rootLabel = !n, subForest = []}) = + (Leaf (_clusteringItems n), 0) + go (Node { rootLabel = !n, subForest = [x, y]}) = + (Branch newD l r, newD) + where + newD = (unQ . _ngMod $ n) + max lDist rDist + (!l, !lDist) = go x + (!r, !rDist) = go y + go (Node { subForest = xs}) = + error $ "Clustering tree has " + <> (show $ length xs) + <> " children. Requires two or none." + +-- | Gather clusters (leaves) from the dendrogram. +getClusterItemsDend :: Foldable t => t (Items a) -> [Items a] +getClusterItemsDend = F.toList + +-- | Gather clusters (leaves) from the tree. +getClusterItemsTree :: ClusteringTree a -> [Items a] +getClusterItemsTree = fmap _clusteringItems . leaves + +deriving instance (Read a) => Read (Dendrogram a) +deriving instance Generic (Dendrogram a) + +instance (A.ToJSON a) => A.ToJSON (Dendrogram a) where + toEncoding = A.genericToEncoding A.defaultOptions +instance (A.FromJSON a) => A.FromJSON (Dendrogram a) diff --git a/src/Math/Clustering/Hierarchical/Spectral/Utility.hs b/src/Math/Clustering/Hierarchical/Spectral/Utility.hs new file mode 100644 --- /dev/null +++ b/src/Math/Clustering/Hierarchical/Spectral/Utility.hs @@ -0,0 +1,28 @@ +{- Math.Clustering.Hierarchical.Spectral.Utility +Gregory W. Schwartz + +Collects utility functions for the clustering section of the program. +-} + +{-# LANGUAGE BangPatterns #-} + +module Math.Clustering.Hierarchical.Spectral.Utility + ( subsetVector + ) where + +-- Remote +import Data.Maybe (fromMaybe) +import qualified Data.Foldable as F +import qualified Data.Vector as V + +-- Local + + +subsetVector :: V.Vector a -> [Int] -> V.Vector a +subsetVector xs = + V.fromList + . F.foldr' (\ !i !acc + -> ( fromMaybe (error "Out of bounds in subsetVector.") + $ xs V.!? i + ) : acc + ) [] diff --git a/src/Math/Graph/Components.hs b/src/Math/Graph/Components.hs new file mode 100644 --- /dev/null +++ b/src/Math/Graph/Components.hs @@ -0,0 +1,37 @@ +{- Math.Graph.Components +Gregory W. Schwartz + +Find connected components of matrices. +-} + +{-# LANGUAGE BangPatterns #-} + +module Math.Graph.Components + ( getComponentMats + , getComponentMatsItems + ) where + +-- Remote +import Data.List (sort) +import qualified Data.Graph.Inductive as G +import qualified Data.Vector as V + +-- Local +import Math.Graph.Types +import Math.Clustering.Hierarchical.Spectral.Utility + +-- | Get the components of a graphable object, an adjacency matrix. +getComponentMats :: (Graphable a) => a -> [a] +getComponentMats mat = fmap (fromGraph . flip G.subgraph gr) . G.components $ gr + where + gr = toGraph mat + +-- | Get the components of a graphable object, an adjacency matrix with the +-- associated items. +getComponentMatsItems :: (Graphable b) => V.Vector a -> b -> [(V.Vector a, b)] +getComponentMatsItems items mat = + fmap (\ !xs -> (subsetVector items . sort $ xs, fromGraph . G.subgraph xs $ gr)) + . G.components + $ gr + where + gr = toGraph mat diff --git a/src/Math/Graph/Types.hs b/src/Math/Graph/Types.hs new file mode 100644 --- /dev/null +++ b/src/Math/Graph/Types.hs @@ -0,0 +1,71 @@ +{- Math.Graph.Types +Gregory W. Schwartz + +Types used for graph sections of the program. +-} + +{-# LANGUAGE BangPatterns #-} +{-# LANGUAGE TypeSynonymInstances #-} +{-# LANGUAGE FlexibleInstances #-} + +module Math.Graph.Types where + +-- Remote +import Data.List (sort) +import qualified Data.Eigen.SparseMatrix as E +import qualified Data.Map.Strict as Map +import qualified Data.Graph.Inductive as G +import qualified Data.Sparse.Common as S +import qualified Data.Vector.Unboxed as V +import qualified Math.Clustering.Spectral.Dense as D +import qualified Numeric.LinearAlgebra as H +import qualified Numeric.LinearAlgebra.Sparse as S + +-- Local +import qualified Math.Clustering.Spectral.Dense as D +import qualified Math.Clustering.Spectral.Eigen.AdjacencyMatrix as E +import qualified Math.Clustering.Spectral.Sparse as S + +-- | Get a re-mapped edge list with nodes ordered from 0 to the number of nodes +-- in the graph. +orderedEdges :: G.Gr Int a -> [(Int, Int, a)] +orderedEdges gr = + fmap (\(!i, !j, !v) -> (getUpdate i, getUpdate j, v)) . G.labEdges $ gr + where + nodeMap = Map.fromList . flip zip [0..] . sort . G.nodes $ gr + getUpdate = flip ( Map.findWithDefault + (error "Unexpected missing node in orderedEdges.") + ) + nodeMap + +-- | Graphable class for converting matrices to and from a graph. +class Graphable a where + toGraph :: a -> G.Gr Int Double + fromGraph :: G.Gr Int Double -> a + +instance Graphable D.AdjacencyMatrix where + toGraph mat = G.mkGraph (zip [0 .. H.rows mat - 1] [0 .. H.rows mat - 1]) + . filter (\(_, _, x) -> x /= 0) + . concatMap (\(!i, !xs) -> fmap (\(!j, !v) -> (i, j, v)) xs) + . zip [0..] + . fmap (zip [0..] . H.toList) + . H.toRows + $ mat + fromGraph gr = H.assoc (G.noNodes gr, G.noNodes gr) 0 + . fmap (\(!i, !j, !v) -> ((i, j), v)) + . orderedEdges + $ gr + +instance Graphable S.AdjacencyMatrix where + toGraph mat = G.mkGraph (zip [0 .. S.nrows mat - 1] [0 .. S.nrows mat - 1]) + . filter (\(_, _, x) -> x /= 0) + . S.toListSM + $ mat + fromGraph gr = S.fromListSM (G.noNodes gr, G.noNodes gr) . orderedEdges $ gr + +instance Graphable E.AdjacencyMatrix where + toGraph mat = G.mkGraph (zip [0 .. E.rows mat - 1] [0 .. E.rows mat - 1]) + . filter (\(_, _, x) -> x /= 0) + . E.toList + $ mat + fromGraph gr = E.fromList (G.noNodes gr) (G.noNodes gr) . orderedEdges $ gr