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https://issues.apache.org/jira/browse/MAHOUT-363?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=12856229#action_12856229
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Shannon Quinn commented on MAHOUT-363:
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I've been getting lot of good feedback, and after discussing my proposal at
length with a few people, I'll submitting changes to the proposal timeline,
particularly regarding the k-means implementation.
Essentially, I'll cut out what is currently sprint 1, shifting sprints 2-4 back
two weeks. I'll start immediately on implementing the EigenCuts algorithm,
relying heavily on test-drive development and full-coverage unit testing to
highlight any bugs in the EigenCuts implementation. Using the extra two weeks,
I'll focus on providing more thorough documentation, including detailed specs
on how to use the algorithm: given that I am working with several PhD students
and professors at CMU who are interested in a map/reduce implementation of this
algorithm, they have massive datasets that are readily available for use. I'll
post an example dataset, along with instructions on how to feed it to Mahout,
and what the output should look like.
If there is extra time at the end, I can work on the user interface and data
visualization.
The schedule aside, there are already a few points of the implementation that I
can probably address in slightly greater detail. Regarding the decomposition of
the similarity matrix and computation of eigenvectors, this is the
computationally difficult part and can be done several different ways. A
stochastic decomposition, as proposed in http://arxiv.org/abs/0909.4061v1 (via
Ted Dunning) would be one of several approaches, though from a performance
perspective this looks to be one of the best. For the mechanics of
parallelizing EigenCuts, the paper from ECML/PKDD 2008, "Parallel spectral
clustering" (via Isabel Drost) provides an excellent starting point, in
addition to using Mahout's existing map/reduce eigensolver.
I hope this helps clarify some points and strengthen the overall feasibility of
the proposal.
> Proposal for GSoC 2010 (EigenCuts clustering algorithm for Mahout)
> ------------------------------------------------------------------
>
> 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. His guidance in highlighting
> the finer points of the underlying theory, coupled with my experience in and
> knowledge of software engineering, makes 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 and Mahout; 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 Mahout and take advantage of
> existing core calculation of transition matrices and associated eigenvectors
> and eigenvalues.
> Sprint 3 (3 weeks; June 28 - July 18): Augment spectral clustering to
> EigenCuts. Fully parallelize with Mahout. 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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