Proposal for GSoC 2010 (EigenCuts clustering algorithm for Mahout)
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Key: MAHOUT-363
URL: https://issues.apache.org/jira/browse/MAHOUT-363
Project: Mahout
Issue Type: Task
Reporter: Shannon Quinn
Proposal Title: EigenCuts spectral clustering implementation on map/reduce for
Apache Mahout (addresses issue Mahout-328)
Student Name: Shannon Quinn
Student E-mail: mag...@gmail.com
Organization/Project:Assigned Mentor:
Proposal Abstract:
Clustering algorithms are advantageous when the number of classes are not known
a priori. However, most techniques still require an explicit K to be chosen,
and most spectral algorithms' use of piecewise constant approximation of
eigenvectors breaks down when the clusters are tightly coupled. EigenCuts[1]
solves both these problems by choosing an eigenvector to create a new cluster
boundary and iterating until no more edges are cut.
Detailed Description
Clustering techniques are extremely useful unsupervised methods, particularly
within my field of computational biology, for situations where the number (and
often the characteristics as well) of classes expressed in the data are not
known a priori. K-means is a classic technique which, given some K, attempts to
label data points within a cluster as a function of their distance (e.g.
Euclidean) from the cluster's mean, iterating to convergence.
Another approach is spectral clustering, which models the data as a weighted,
undirected graph in some n-dimensional space, and creates a matrix M of
transition probabilities between nodes. By computing the eigenvalues and
eigenvectors of this matrix, most spectral clustering techniques take advantage
of the fact that, for data with loosely coupled clusters, the K leading
eigenvectors will identify the roughly piecewise constant regions in the data
that correspond to clusters.
However, these techniques all suffer from drawbacks, the two most significant
of which are having to choose an arbitrary K a priori, and in the situation of
tightly coupled clusters where the piecewise constant approximation on the
eigenvectors no longer holds.
The EigenCuts algorithm addresses both these issues. As a type of spectral
clustering algorithm it works by constructing a Markov chain representation of
the data and computing the eigenvectors and eigenvalues of the transition
matrix. Eigenflows, or flow of probability by eigenvector, have an associated
half life of flow decay called eigenflow. By perturbing the weights between
nodes, it can be observed where bottlenecks exist in the eigenflow's halflife,
allowing for the identification of boundaries between clusters. Thus, this
algorithm iterates until no more cuts between clusters need to be made,
eliminating the need for an a prior K, and conferring the ability to separate
tightly coupled clusters.
The only disadvantage of EigenCuts is the need to recompute eigenvectors and
eigenvalues at each iterative step, incurring a large computational overhead.
This problem can be adequately addressed within the map/reduce framework and on
a Hadoop cluster by parallelizing the computation of each eigenvector and its
associated eigenvalue. Apache Hama in particular, with its specializations in
graph and matrix data, will be crucial in parallelizing the computations of
transition matrices and their corresponding eigenvalues and eigenvectors at
each iteration.
Since Dr Chennubhotla is currently a member of the faculty at the University of
Pittsburgh, I have been in contact with him for the past few weeks, and we both
envision and eagerly anticipate continued collaboration over the course of the
summer and this project's implementation. He has thus far been instrumental in
highlighting the finer points of the underlying theory, and coupled with my
experience in and knowledge of software engineering, this is a project we are
both extremely excited about implementing.
Timeline
At the end of each sprint, there should be a concrete, functional deliverable.
It may not do much, but what it does will work and have full coverage
accompanying unit tests.
Sprint 0 (April 26 - May 23): Work with mentor on any pre-coding tasks -
familiarization with and dev deployments of Hadoop, Mahout, Hama; reading up on
documentation, fine-tuning the project plan and requirements. This part will
kick into high gear after May 6 (my last final exam and final academic
obligation, prior to the actual graduation ceremony), but likely nothing before
April 29 (the day of my thesis defense).
Sprint 1 (2 weeks; May 24 - June 6): Implement basic k-means clustering
algorithm and parallelize on Mahout over Hadoop. Preliminary interface allows
for dataset selection and visualization of resulting clusters.
Sprint 2 (3 weeks; June 7 - 27): Modify k-means algorithm to spectral
clustering. Integrate map/reduce framework via Hama for calculating of
transition matrices and associated eigenvectors and eigenvalues.
Sprint 3 (3 weeks; June 28 - July 18): Augment spectral clustering to
EigenCuts. Fully parallelize with Hama. Also, mid-term evaluations.
Sprint 4 (3 weeks; July 19 - August 8): Fix any remaining issues with
EigenCuts. Finalize interface for running the algorithm, selecting datasets and
visualizing results.
Sprint 5 (1 week; August 9 - 15): Tidy up documentation, write final unit
tests, fix outstanding bugs.
Other Information
I am finishing up my last semester as a master's student in computational
biology at Carnegie Mellon, prior to beginning the PhD program in CompBio at
Carnegie Mellon this coming fall. I have worked extensively with clustering
techniques as a master's student, as a significant amount of my work has
involved bioimage analysis within Dr Robert Murphy's lab. Previous work has
involved using HMMs to detect patterns in tuberculosis genomes and use CLUSTALW
to cluster those patterns according to geographic location. My master's thesis
involves use of matrix completion to infer linear transformations of proteins
and their associated subcellular locations across varying cell conditions
(drugs, cell lines, etc).
I unfortunately have limited experience with Apache Mahout and Hadoop, but with
an undergraduate computer science degree from Georgia Tech, and after an
internship with IBM ExtremeBlue, I feel I am extremely adept at picking up new
frameworks quickly.
References
[1] Chakra Chennubhotla and Allan D. Jepson. Half-Lives of EigenFlows for
Spectral Clustering. NIPS 2002.
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