Locally Constraint Support Vector Clustering
Roberts-Grey, Gina, Freelance Writer has reference to this Academic Journal, PHwiki organized this Journal Locally Constraint Support Vector Clustering Dragomir Yankov, Eamonn Keogh, Kin Fai Kan Computer Science & Eng. Dept. University of Cali as long as nia, Riverside Outline On the need of improving the Support Vector Clustering (SVC) algorithm. Motivation Problem as long as mulation Locally constrained SVC An overview of SVC Applying factor analysis as long as local outlier detection Regularizing the decision function of SVC Experimental evaluation Motivation as long as improving SVC SVC trans as long as ms the data in a high dimensional feature space, where a decision function is computed The support-vectors define contours in the original space representing higher density regions The method is theoretically sound in addition to useful as long as detecting non-convex as long as mations original data detected clusters
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Motivation as long as improving SVC (cont) Parametrizing SVC incorrectly may either disguise some objectively present clusters, or produce multiple unintuitive clusters Correct parametrization is especially hard in the presence of noise (frequently encountered when learning from embedded manifolds) large kernel widths merge the clusters small kernel widths produce multiple unintuitive clusters Problem as long as mulation How can we make Support Vector Clustering: Less susceptible to noise in the data More resilient to imprecise parametrization Locally constrained SVC one class classification Support Vector density estimation Primal as long as mulation Dual as long as mulation
Locally constrained SVC labeling the closed contours Support Vector Clustering decision function Labeling the individual classes Build an affinity matrix in addition to find the connected components Locally constrained SVC detecting local outliers Factor analysis: Mixture of factor analyzers We can adapt MFA to pinpoint local outliers Points like P1 in addition to P2 that deviate a lot from the FA are among the true outliers Locally constrained SVC regularizing the decision function To compute the local deviation of each point we use their Mahalanobis distances with respect to the corresponding FA New primal as long as mulation (weighting the slack variables) New dual as long as mulation
Locally constrained SVC discussion Difference SVC in addition to LSVC Tuning the parameters cannot achieve the same result SVC tries to accommodate all outliers building complex boundaries Small kernel width detects the outliers but produces multiple unintuitive clusters LSVC SVC SVC SVC Experimental evaluation synthetic data Gaussian with radial Gaussian distributions Good parameter values as long as LSVC are detected automatically. The right clusters are detected SVC is harder to parametrize. The detected clusters are incorrect LSVC SVC Experimental evaluation synthetic data Swiss roll data with added Gaussian noise Most of the noise is identified as bounded SVs by LSVC. The correct clusters are detected SVC tends to merge the two large clusters. With supervision the clusters are eventually identified LSVC SVC
Experimental evaluation face images Frey face dataset LSVC discriminates the two objectively interesting manifolds embedding the data Even with supervision we could not find parameters that separate the two major manifolds with SVC LSVC SVC Experimental evaluation shape clustering Arrowheads dataset Some of the classes are similar. There are multiple elements bridging their shape manifolds LSVC achieves 73% accuracy vs 60% as long as SVC LSVC SVC Conclusion The LSVC method combines both a global in addition to a local view of the data It computes a decision function that defines a global measure of density support MFA complements this with a local view based on the individual analyzers The algorithm improves significantly on the stability of SVC in the presence of noise LSVC allows as long as easier automatic parameterization of one-class SVMs
All datasets in addition to the code as long as LSVC can be obtained by writing to the first author: firstname.lastname@example.org THANK YOU!
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