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<pre><a name="line-1"></a><span class='hs-keyword'>module</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Clustering</span><span class='hs-varop'>.</span><span class='hs-conid'>Hierarchical</span><span class='hs-varop'>.</span><span class='hs-conid'>Internal</span><span class='hs-varop'>.</span><span class='hs-conid'>Types</span>
<a name="line-2"></a> <span class='hs-layout'>(</span> <span class='hs-conid'>Dendrogram</span><span class='hs-layout'>(</span><span class='hs-keyglyph'>..</span><span class='hs-layout'>)</span>
<a name="line-3"></a> <span class='hs-layout'>,</span> <span class='hs-conid'>Linkage</span><span class='hs-layout'>(</span><span class='hs-keyglyph'>..</span><span class='hs-layout'>)</span>
<a name="line-4"></a> <span class='hs-layout'>,</span> <span class='hs-conid'>Distance</span>
<a name="line-5"></a> <span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-6"></a>
<a name="line-7"></a><span class='hs-comment'>-- from base</span>
<a name="line-8"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Control</span><span class='hs-varop'>.</span><span class='hs-conid'>Applicative</span> <span class='hs-layout'>(</span><span class='hs-layout'>(</span><span class='hs-varop'><$></span><span class='hs-layout'>)</span><span class='hs-layout'>,</span> <span class='hs-layout'>(</span><span class='hs-varop'><*></span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
<a name="line-9"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Foldable</span> <span class='hs-layout'>(</span><span class='hs-conid'>Foldable</span> <span class='hs-layout'>(</span><span class='hs-keyglyph'>..</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
<a name="line-10"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Monoid</span> <span class='hs-layout'>(</span><span class='hs-varid'>mappend</span><span class='hs-layout'>)</span>
<a name="line-11"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Traversable</span> <span class='hs-layout'>(</span><span class='hs-conid'>Traversable</span><span class='hs-layout'>(</span><span class='hs-keyglyph'>..</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
<a name="line-12"></a>
<a name="line-13"></a><a name="Dendrogram"></a><span class='hs-comment'>-- | Data structure for storing hierarchical clusters. The</span>
<a name="line-14"></a><a name="Dendrogram"></a><span class='hs-comment'>-- distance between clusters is stored on the branches.</span>
<a name="line-15"></a><a name="Dendrogram"></a><span class='hs-comment'>-- Distances between leafs are the distances between the elements</span>
<a name="line-16"></a><a name="Dendrogram"></a><span class='hs-comment'>-- on those leafs, while distances between branches are defined</span>
<a name="line-17"></a><a name="Dendrogram"></a><span class='hs-comment'>-- by the linkage used (see 'Linkage').</span>
<a name="line-18"></a><a name="Dendrogram"></a><span class='hs-keyword'>data</span> <span class='hs-conid'>Dendrogram</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=</span>
<a name="line-19"></a> <span class='hs-conid'>Leaf</span> <span class='hs-varid'>a</span>
<a name="line-20"></a> <span class='hs-comment'>-- ^ The leaf contains the item @a@ itself.</span>
<a name="line-21"></a> <span class='hs-keyglyph'>|</span> <span class='hs-conid'>Branch</span> <span class='hs-comment'>{-# UNPACK #-}</span> <span class='hs-varop'>!</span><span class='hs-conid'>Distance</span> <span class='hs-layout'>(</span><span class='hs-conid'>Dendrogram</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>Dendrogram</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span>
<a name="line-22"></a> <span class='hs-comment'>-- ^ Each branch connects two clusters/dendrograms that are</span>
<a name="line-23"></a> <span class='hs-comment'>-- @d@ distance apart.</span>
<a name="line-24"></a> <span class='hs-keyword'>deriving</span> <span class='hs-layout'>(</span><span class='hs-conid'>Eq</span><span class='hs-layout'>,</span> <span class='hs-conid'>Ord</span><span class='hs-layout'>,</span> <span class='hs-conid'>Show</span><span class='hs-layout'>)</span>
<a name="line-25"></a>
<a name="line-26"></a><a name="Distance"></a><span class='hs-comment'>-- | A distance is simply a synonym of 'Double' for efficiency.</span>
<a name="line-27"></a><a name="Distance"></a><span class='hs-keyword'>type</span> <span class='hs-conid'>Distance</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Double</span>
<a name="line-28"></a>
<a name="line-29"></a><a name="instance%20Functor%20Dendrogram"></a><span class='hs-comment'>-- | Does not recalculate the distances!</span>
<a name="line-30"></a><a name="instance%20Functor%20Dendrogram"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Functor</span> <span class='hs-conid'>Dendrogram</span> <span class='hs-keyword'>where</span>
<a name="line-31"></a> <span class='hs-varid'>fmap</span> <span class='hs-varid'>f</span> <span class='hs-layout'>(</span><span class='hs-conid'>Leaf</span> <span class='hs-varid'>d</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Leaf</span> <span class='hs-layout'>(</span><span class='hs-varid'>f</span> <span class='hs-varid'>d</span><span class='hs-layout'>)</span>
<a name="line-32"></a> <span class='hs-varid'>fmap</span> <span class='hs-varid'>f</span> <span class='hs-layout'>(</span><span class='hs-conid'>Branch</span> <span class='hs-varid'>s</span> <span class='hs-varid'>c1</span> <span class='hs-varid'>c2</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Branch</span> <span class='hs-varid'>s</span> <span class='hs-layout'>(</span><span class='hs-varid'>fmap</span> <span class='hs-varid'>f</span> <span class='hs-varid'>c1</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>fmap</span> <span class='hs-varid'>f</span> <span class='hs-varid'>c2</span><span class='hs-layout'>)</span>
<a name="line-33"></a>
<a name="line-34"></a><a name="instance%20Foldable%20Dendrogram"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Foldable</span> <span class='hs-conid'>Dendrogram</span> <span class='hs-keyword'>where</span>
<a name="line-35"></a> <span class='hs-varid'>foldMap</span> <span class='hs-varid'>f</span> <span class='hs-layout'>(</span><span class='hs-conid'>Leaf</span> <span class='hs-varid'>d</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>f</span> <span class='hs-varid'>d</span>
<a name="line-36"></a> <span class='hs-varid'>foldMap</span> <span class='hs-varid'>f</span> <span class='hs-layout'>(</span><span class='hs-conid'>Branch</span> <span class='hs-keyword'>_</span> <span class='hs-varid'>c1</span> <span class='hs-varid'>c2</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>foldMap</span> <span class='hs-varid'>f</span> <span class='hs-varid'>c1</span> <span class='hs-varop'>`mappend`</span> <span class='hs-varid'>foldMap</span> <span class='hs-varid'>f</span> <span class='hs-varid'>c2</span>
<a name="line-37"></a>
<a name="line-38"></a><a name="instance%20Traversable%20Dendrogram"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Traversable</span> <span class='hs-conid'>Dendrogram</span> <span class='hs-keyword'>where</span>
<a name="line-39"></a> <span class='hs-varid'>traverse</span> <span class='hs-varid'>f</span> <span class='hs-layout'>(</span><span class='hs-conid'>Leaf</span> <span class='hs-varid'>d</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Leaf</span> <span class='hs-varop'><$></span> <span class='hs-varid'>f</span> <span class='hs-varid'>d</span>
<a name="line-40"></a> <span class='hs-varid'>traverse</span> <span class='hs-varid'>f</span> <span class='hs-layout'>(</span><span class='hs-conid'>Branch</span> <span class='hs-varid'>s</span> <span class='hs-varid'>c1</span> <span class='hs-varid'>c2</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Branch</span> <span class='hs-varid'>s</span> <span class='hs-varop'><$></span> <span class='hs-varid'>traverse</span> <span class='hs-varid'>f</span> <span class='hs-varid'>c1</span> <span class='hs-varop'><*></span> <span class='hs-varid'>traverse</span> <span class='hs-varid'>f</span> <span class='hs-varid'>c2</span>
<a name="line-41"></a>
<a name="line-42"></a>
<a name="line-43"></a><a name="Linkage"></a><span class='hs-comment'>-- | The linkage type determines how the distance between</span>
<a name="line-44"></a><a name="Linkage"></a><span class='hs-comment'>-- clusters will be calculated. These are the linkage types</span>
<a name="line-45"></a><a name="Linkage"></a><span class='hs-comment'>-- currently available on this library.</span>
<a name="line-46"></a><a name="Linkage"></a><span class='hs-keyword'>data</span> <span class='hs-conid'>Linkage</span> <span class='hs-keyglyph'>=</span>
<a name="line-47"></a> <span class='hs-conid'>SingleLinkage</span>
<a name="line-48"></a> <span class='hs-comment'>-- ^ The distance between two clusters @a@ and @b@ is the</span>
<a name="line-49"></a> <span class='hs-comment'>-- /minimum/ distance between an element of @a@ and an element</span>
<a name="line-50"></a> <span class='hs-comment'>-- of @b@.</span>
<a name="line-51"></a> <span class='hs-keyglyph'>|</span> <span class='hs-conid'>CompleteLinkage</span>
<a name="line-52"></a> <span class='hs-comment'>-- ^ The distance between two clusters @a@ and @b@ is the</span>
<a name="line-53"></a> <span class='hs-comment'>-- /maximum/ distance between an element of @a@ and an element</span>
<a name="line-54"></a> <span class='hs-comment'>-- of @b@.</span>
<a name="line-55"></a> <span class='hs-keyglyph'>|</span> <span class='hs-conid'>CLINK</span>
<a name="line-56"></a> <span class='hs-comment'>-- ^ The same as 'CompleteLinkage', but using the CLINK</span>
<a name="line-57"></a> <span class='hs-comment'>-- algorithm. It's much faster however doesn't always give the</span>
<a name="line-58"></a> <span class='hs-comment'>-- best complete linkage dendrogram.</span>
<a name="line-59"></a> <span class='hs-keyglyph'>|</span> <span class='hs-conid'>UPGMA</span>
<a name="line-60"></a> <span class='hs-comment'>-- ^ Unweighted Pair Group Method with Arithmetic mean, also</span>
<a name="line-61"></a> <span class='hs-comment'>-- called \"average linkage\". The distance between two</span>
<a name="line-62"></a> <span class='hs-comment'>-- clusters @a@ and @b@ is the /arithmetic average/ between the</span>
<a name="line-63"></a> <span class='hs-comment'>-- distances of all elements in @a@ to all elements in @b@.</span>
<a name="line-64"></a> <span class='hs-keyglyph'>|</span> <span class='hs-conid'>FakeAverageLinkage</span>
<a name="line-65"></a> <span class='hs-comment'>-- ^ This method is usually wrongly called \"average linkage\".</span>
<a name="line-66"></a> <span class='hs-comment'>-- The distance between cluster @a = a1 U a2@ (that is, cluster</span>
<a name="line-67"></a> <span class='hs-comment'>-- @a@ was formed by the linkage of clusters @a1@ and @a2@) and</span>
<a name="line-68"></a> <span class='hs-comment'>-- an old cluster @b@ is @(d(a1,b) + d(a2,b)) / 2@. So when</span>
<a name="line-69"></a> <span class='hs-comment'>-- clustering two elements to create a cluster, this method is</span>
<a name="line-70"></a> <span class='hs-comment'>-- the same as UPGMA. However, in general when joining two</span>
<a name="line-71"></a> <span class='hs-comment'>-- clusters this method assigns equal weights to @a1@ and @a2@,</span>
<a name="line-72"></a> <span class='hs-comment'>-- while UPGMA assigns weights proportional to the number of</span>
<a name="line-73"></a> <span class='hs-comment'>-- elements in each cluster. See, for example:</span>
<a name="line-74"></a> <span class='hs-comment'>--</span>
<a name="line-75"></a> <span class='hs-comment'>-- *</span>
<a name="line-76"></a> <span class='hs-comment'>-- <<a href="http://www.cs.tau.ac.il/~rshamir/algmb/00/scribe00/html/lec08/node21.html">http://www.cs.tau.ac.il/~rshamir/algmb/00/scribe00/html/lec08/node21.html</a>>,</span>
<a name="line-77"></a> <span class='hs-comment'>-- which defines the real UPGMA and gives the equation to</span>
<a name="line-78"></a> <span class='hs-comment'>-- calculate the distance between an old and a new cluster.</span>
<a name="line-79"></a> <span class='hs-comment'>--</span>
<a name="line-80"></a> <span class='hs-comment'>-- *</span>
<a name="line-81"></a> <span class='hs-comment'>-- <<a href="http://github.com/JadeFerret/ai4r/blob/master/lib/ai4r/clusterers/average_linkage.rb">http://github.com/JadeFerret/ai4r/blob/master/lib/ai4r/clusterers/average_linkage.rb</a>>,</span>
<a name="line-82"></a> <span class='hs-comment'>-- code for \"average linkage\" on ai4r library implementing</span>
<a name="line-83"></a> <span class='hs-comment'>-- what we call here @FakeAverageLinkage@ and not UPGMA.</span>
<a name="line-84"></a> <span class='hs-keyword'>deriving</span> <span class='hs-layout'>(</span><span class='hs-conid'>Eq</span><span class='hs-layout'>,</span> <span class='hs-conid'>Ord</span><span class='hs-layout'>,</span> <span class='hs-conid'>Show</span><span class='hs-layout'>,</span> <span class='hs-conid'>Enum</span><span class='hs-layout'>)</span>
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