SIAM Undergraduate Research Online
Volume 5
In This Volume

Spectral Clustering: An empirical study of Approximation Algorithms and its Application to the Attrition Problem
Published electronically December 21, 2012DOI: 10.1137/12S012094
Authors
A. Thompson (University of Nebraska – Lincoln), B. Cung (University of Nebraska – Lincoln), T. Jin (University of Nebraska – Lincoln), J. Ramirez (University of Nebraska – Lincoln)
Project Advisors
D. Needell (Claremont McKenna College), C. Boutsidis (Claremont McKenna College)
Abstract
Clustering is the problem of separating a set of objects into groups (called clusters) so that objects within the same cluster are more similar to each other than to those in different clusters. Spectral clustering is a now wellknown method for clustering which utilizes the spectrum of the data similarity matrix to perform this separation. Since the method relies on solving an eigenvector problem, it is computationally expensive for large datasets. To overcome this constraint, approximation methods have been developed which aim to reduce running time while maintaining accurate classification. In this article, we summarize and experimentally evaluate several approximation methods for spectral clustering. From an applications standpoint, we employ spectral clustering to solve the socalled attrition problem, where one aims to identify from a set of employees those who are likely to voluntarily leave the company from those who are not. Our study sheds light on the empirical performance of existing approximate spectral clustering methods and shows the applicability of these methods in an important business optimization related problem.

Study of Free Alternative Numerical Computation Packages
Published electronically December 18, 2012 
An Approach to Identify the Number of Clusters
Published electronically December 17, 2012 
Geographic Profiling Through SixDimensional Nonparametric Density Estimation
Published electronically November 5, 2012 
A MultiNumeric Method for Parabolic Problems Using an Adaptive RegionSwapping Approach
Published electronically August 30, 2012 
The Alignment of Arbitrary Contours Using Area Difference Distance Measurement
Published electronically August 13, 2012 
Finding Eigenvalues for Matrices Acting on Subspaces
Published electronically July 30, 2012 
Moody's Mega Math Challenge 2012 Champion PaperAll Aboard: Can High Speed Rail Get Back on Track?
Published electronically July 19, 2012 
A Quantile Regression Study of Climate Change in Chicago, 19602010
Published electronically July 11, 2012 
Solving a NonLinear Partial Differential Equation for the Simulation of Tumour Oxygenation
Published electronically June 21, 2012 
Statistical Modeling through Analytical and Monte Carlo Methods of the Fat Fraction in Magnetic Resonance Imaging (MRI)
Published electronically June 21, 2012 
Modeling and Numerical Simulation of the Nonlinear Dynamics of the Parametrically Forced String Pendulum
Published electronically June 14, 2012 
A Maple Application for Testing SelfAdjointness on Quantum Graphs
Published electronically June 12, 2012 
Instability of Gravity Driven Flow of Liquid Crystal Films
Published electronically May 25, 2012 
What Moves You: Using Legs for Vehicular Transportation
Published electronically April 24, 2012 
Nonautonomous Logistic Equations and Optimization of Renewable Resources Management
Published electronically March 28, 2012 
Tracking the movement of eigenvalues via a corresponding Evans function
Published electronically March 27, 2012
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