Canopy Clustering

Canopy Clustering is a very simple, fast and surprisingly accurate method for grouping objects into clusters. All objects are represented as a point in a multidimensional feature space. The algorithm uses a fast approximate distance metric and two distance thresholds T1 > T2 for processing. The basic algorithm is to begin with a set of points and remove one at random. Create a Canopy containing this point and iterate through the remainder of the point set. At each point, if its distance from the first point is < T1, then add the point to the cluster. If, in addition, the distance is < T2, then remove the point from the set. This way points that are very close to the original will avoid all further processing. The algorithm loops until the initial set is empty, accumulating a set of Canopies, each containing one or more points. A given point may occur in more than one Canopy.

Canopy Clustering is often used as an initial step in more rigorous clustering techniques, such as k-Means. By starting with an initial clustering the number of more expensive distance measurements can be significantly reduced by ignoring points outside of the initial canopies.

Strategy for parallelization

Looking at the sample Hadoop implementation in http://code.google.com/p/canopy-clustering/ the processing is done in 3 M/R steps:

1. The data is massaged into suitable input format
2. Each mapper performs canopy clustering on the points in its input set and outputs its canopies' centers
3. The reducer clusters the canopy centers to produce the final canopy centers
4. The points are then clustered into these final canopies

Some ideas can be found in Cluster computing and MapReduce lecture video series [by Google(r)]; Canopy Clustering is discussed in lecture #4. Slides can be found here. Finally here is the Wikipedia page.

Design of implementation

The initial implementation accepts input files containing multidimensional points (Float[]) that are comma-terminated values enclosed in brackets (e.g. "[1.5,2.5,]"). Processing is done in two phases: Canopy generation and Clustering.

Canopy generation phase

During the map step, each mapper processes a subset of the total points and applies the chosen distance measure and thresholds to generate canopies. In the mapper, each point which is found to be within an existing canopy will be output using that canopy's id to a combiner. After sorting by canopyId keys has occurred, the combiner will see an iterator of all points for each canopyId key. The combiner sums all of the points having that key and normalizes the total to produce a canopy centroid which is output, using a constant key ("centroid") to a single reducer. The reducer receives all of the initial centroids and again applies the canopy measure and thresholds to produce a final set of canopy centroids which is output (i.e. clustering the cluster centroids). The reducer output format is: canopyId\t[<canopy-centroid-coordinates>].

Clustering phase

During the clustering phase, each mapper reads the canopy centroids produced by the first phase. Since all mappers have the same canopy definitions, their outputs will be combined during the shuffle so that each reducer (many are allowed here) will see all of the points assigned to one or more canopies. The output format will then be: <canopy-definition>\t[<member-point-coordinates>] <payload>. My plan is to include the canopyId, measure, thresholds and centroid in the <canopy-definition> so that the output will be self-descriptive. The plan is also to allow any information encoded in the input points after the coordinate delimiter ']' to be treated as payload and passed through the clustering phase without modification.