[CONF] Apache Mahout > Spectral Clustering

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Space: Apache Mahout (https://cwiki.apache.org/confluence/display/MAHOUT)
Page: Spectral Clustering (https://cwiki.apache.org/confluence/display/MAHOUT/Spectral+Clustering)

Added by Shannon Quinn:
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Spectral clustering is a more powerful and specialized algorithm (compared to K-means) which has significant use in photo editing, hence its name. Each object to be clustered can initially be represented as an _n_\-dimensional numeric vector, but the difference with this algorithm is that there must also be some method for performing a comparison between each object and expressing this comparison as a scalar.

This _n_ by _n_ comparison of all objects with all others forms the _affinity_ matrix, which can be intuitively thought of as a rough representation of an underlying undirected, weighted, and fully-connected graph whose edges express the relative relationships, or affinities, between each pair of objects in the original data. This affinity matrix forms the basis from which the two spectral clustering algorithms operate.

The equation by which the affinities are calculated can vary depending on the user's circumstances; typically, the equation takes the form of:

_d{_}{^}2^ / _c_

where _d_ is the Euclidean distance between a pair of points, and _c_ is a scaling factor. _c_ is often calculated relative to a _k_\-neighborhood of closest points to the current point; all other affinities are set to 0 outside of the neighborhood. Again, this formula can vary depending on the situation (e.g. a fully-connected graph would ignore the _k_\-neighborhood and calculate affinities for all pairs of points).

h2. K-Means Spectral Clustering

h3. Overview

h3. Implementation

h2. Eigencuts Spectral Clustering

h3. Overview

h3. Implementation

h2. Quickstart

h2. Examples

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