A unifying viewpoint of some clustering techniques using Bregman divergences and extensions to mixed data sets

Levasseur, Cecile; Burdge, Brandon; Kreutz-Delgado, Kenneth; Mayer, Uwe

doi:10.1109/iccitechn.2008.4803110

Cited by 1 publication

(3 citation statements)

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“…, m, can be attacked by either using the Expectation-Maximization algorithm [3,6,8,1], as done in particular in the SemiParametric Principal Component Analysis technique [11], or by simply considering the special case of uniform pointmass probabilities, i.e., π l = 1/m ∀l, for which the number of support points equals the number of data samples. It was demonstrated in [7] that this special uniform case corresponds to the exponential Principal Component Analysis technique [2]. We are using this special case in this paper.…”

Section: The Row Vectormentioning

confidence: 99%

“…The NPML estimate is known to be a discrete distribution on a finite number of support points [6,8]. As shown in [7], the NPML approach yields unknown point-mass support pointsā[l], point-mass probability estimates π l , and the…”

Section: The Row Vectormentioning

confidence: 99%

“…The Generalized Linear Statistics (GLS) framework represents a subclass of graphical model techniques and includes as special cases multivariate probabilistic systems such as Principal Component Analysis (PCA), Generalized Linear Models (GLMs) and factor analysis [7]. It This research was partially supported by NSF grant No.…”

Section: Introductionmentioning

confidence: 99%

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Classifying non-gaussian and mixed data sets in their natural parameter space

Levasseur

Mayer

Kreutz-Delgado

2009

2009 IEEE International Workshop on Machine Learning for Signal Processing

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We consider the problem of both supervised and unsupervised classification for multidimensional data that are nongaussian and of mixed types (continuous and/or discrete). An important subclass of graphical model techniques called Generalized Linear Statistics (GLS) is used to capture the underlying statistical structure of these complex data. GLS exploits the properties of exponential family distributions, which are assumed to describe the data components, and constrains latent variables to a lower dimensional parameter subspace. Based on the latent variable information, classification is performed in the natural parameter subspace with classical statistical techniques. The benefits of decision making in parameter space is illustrated with examples of categorical data text categorization and mixed-type data classification. As a text document preprocessing tool, an extension from binary to categorical data of the conditional mutual information maximization based feature selection algorithm is presented.

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Section: The Row Vectormentioning

confidence: 99%