Data.Clustering.Hierarchical.Internal.Types

Documentation

data Dendrogram a

Data structure for storing hierarchical clusters. The distance between clusters is stored on the branches. Distances between leafs are the distances between the elements on those leafs, while distances between branches are defined by the linkage used (see Linkage).

Constructors

Leaf a

The leaf contains the item a itself.

Branch !Distance (Dendrogram a) (Dendrogram a)

Each branch connects two clusters/dendrograms that are d distance apart.

Instances

Functor Dendrogram

Does not recalculate the distances!

Defined in Data.Clustering.Hierarchical.Internal.Types

Methods

fmap :: (a -> b) -> Dendrogram a -> Dendrogram b

(<$) :: a -> Dendrogram b -> Dendrogram a

Foldable Dendrogram

Defined in Data.Clustering.Hierarchical.Internal.Types

Methods

fold :: Monoid m => Dendrogram m -> m

foldMap :: Monoid m => (a -> m) -> Dendrogram a -> m

foldr :: (a -> b -> b) -> b -> Dendrogram a -> b

foldr' :: (a -> b -> b) -> b -> Dendrogram a -> b

foldl :: (b -> a -> b) -> b -> Dendrogram a -> b

foldl' :: (b -> a -> b) -> b -> Dendrogram a -> b

foldr1 :: (a -> a -> a) -> Dendrogram a -> a

foldl1 :: (a -> a -> a) -> Dendrogram a -> a

toList :: Dendrogram a -> [a]

null :: Dendrogram a -> Bool

length :: Dendrogram a -> Int

elem :: Eq a => a -> Dendrogram a -> Bool

maximum :: Ord a => Dendrogram a -> a

minimum :: Ord a => Dendrogram a -> a

sum :: Num a => Dendrogram a -> a

product :: Num a => Dendrogram a -> a

Traversable Dendrogram

Defined in Data.Clustering.Hierarchical.Internal.Types

Methods

traverse :: Applicative f => (a -> f b) -> Dendrogram a -> f (Dendrogram b)

sequenceA :: Applicative f => Dendrogram (f a) -> f (Dendrogram a)

mapM :: Monad m => (a -> m b) -> Dendrogram a -> m (Dendrogram b)

sequence :: Monad m => Dendrogram (m a) -> m (Dendrogram a)

Eq a => Eq (Dendrogram a)

Defined in Data.Clustering.Hierarchical.Internal.Types

Methods

(==) :: Dendrogram a -> Dendrogram a -> Bool

(/=) :: Dendrogram a -> Dendrogram a -> Bool

Ord a => Ord (Dendrogram a)

Defined in Data.Clustering.Hierarchical.Internal.Types

Methods

compare :: Dendrogram a -> Dendrogram a -> Ordering

(<) :: Dendrogram a -> Dendrogram a -> Bool

(<=) :: Dendrogram a -> Dendrogram a -> Bool

(>) :: Dendrogram a -> Dendrogram a -> Bool

(>=) :: Dendrogram a -> Dendrogram a -> Bool

max :: Dendrogram a -> Dendrogram a -> Dendrogram a

min :: Dendrogram a -> Dendrogram a -> Dendrogram a

Show a => Show (Dendrogram a)

Defined in Data.Clustering.Hierarchical.Internal.Types

Methods

showsPrec :: Int -> Dendrogram a -> ShowS

show :: Dendrogram a -> String

showList :: [Dendrogram a] -> ShowS

data Linkage

The linkage type determines how the distance between clusters will be calculated. These are the linkage types currently available on this library.

Constructors

SingleLinkage

The distance between two clusters a and b is the minimum distance between an element of a and an element of b.

CompleteLinkage

The distance between two clusters a and b is the maximum distance between an element of a and an element of b.

CLINK

The same as CompleteLinkage, but using the CLINK algorithm. It's much faster however doesn't always give the best complete linkage dendrogram.

UPGMA

Unweighted Pair Group Method with Arithmetic mean, also called "average linkage". The distance between two clusters a and b is the arithmetic average between the distances of all elements in a to all elements in b.

FakeAverageLinkage

This method is usually wrongly called "average linkage". The distance between cluster a = a1 U a2 (that is, cluster a was formed by the linkage of clusters a1 and a2) and an old cluster b is (d(a1,b) + d(a2,b)) / 2. So when clustering two elements to create a cluster, this method is the same as UPGMA. However, in general when joining two clusters this method assigns equal weights to a1 and a2, while UPGMA assigns weights proportional to the number of elements in each cluster. See, for example:

• http://www.cs.tau.ac.il/~rshamir/algmb/00/scribe00/html/lec08/node21.html, which defines the real UPGMA and gives the equation to calculate the distance between an old and a new cluster.
• http://github.com/JadeFerret/ai4r/blob/master/lib/ai4r/clusterers/average_linkage.rb, code for "average linkage" on ai4r library implementing what we call here FakeAverageLinkage and not UPGMA.

Instances

Enum Linkage

Defined in Data.Clustering.Hierarchical.Internal.Types

Methods

succ :: Linkage -> Linkage

pred :: Linkage -> Linkage

toEnum :: Int -> Linkage

fromEnum :: Linkage -> Int

enumFrom :: Linkage -> [Linkage]

enumFromThen :: Linkage -> Linkage -> [Linkage]

enumFromTo :: Linkage -> Linkage -> [Linkage]

enumFromThenTo :: Linkage -> Linkage -> Linkage -> [Linkage]

Eq Linkage

Defined in Data.Clustering.Hierarchical.Internal.Types

Methods

(==) :: Linkage -> Linkage -> Bool

(/=) :: Linkage -> Linkage -> Bool

Ord Linkage

Defined in Data.Clustering.Hierarchical.Internal.Types

Methods

compare :: Linkage -> Linkage -> Ordering

(<) :: Linkage -> Linkage -> Bool

(<=) :: Linkage -> Linkage -> Bool

(>) :: Linkage -> Linkage -> Bool

(>=) :: Linkage -> Linkage -> Bool

max :: Linkage -> Linkage -> Linkage

min :: Linkage -> Linkage -> Linkage

Show Linkage

Defined in Data.Clustering.Hierarchical.Internal.Types

Methods

showsPrec :: Int -> Linkage -> ShowS

show :: Linkage -> String

showList :: [Linkage] -> ShowS

type Distance = Double

A distance is simply a synonym of Double for efficiency.