A Unified Framework for Probabilistic Component Analysis

03/13/2013
by   Mihalis A. Nicolaou, et al.
0

We present a unifying framework which reduces the construction of probabilistic component analysis techniques to a mere selection of the latent neighbourhood, thus providing an elegant and principled framework for creating novel component analysis models as well as constructing probabilistic equivalents of deterministic component analysis methods. Under our framework, we unify many very popular and well-studied component analysis algorithms, such as Principal Component Analysis (PCA), Linear Discriminant Analysis (LDA), Locality Preserving Projections (LPP) and Slow Feature Analysis (SFA), some of which have no probabilistic equivalents in literature thus far. We firstly define the Markov Random Fields (MRFs) which encapsulate the latent connectivity of the aforementioned component analysis techniques; subsequently, we show that the projection directions produced by all PCA, LDA, LPP and SFA are also produced by the Maximum Likelihood (ML) solution of a single joint probability density function, composed by selecting one of the defined MRF priors while utilising a simple observation model. Furthermore, we propose novel Expectation Maximization (EM) algorithms, exploiting the proposed joint PDF, while we generalize the proposed methodologies to arbitrary connectivities via parameterizable MRF products. Theoretical analysis and experiments on both simulated and real world data show the usefulness of the proposed framework, by deriving methods which well outperform state-of-the-art equivalents.

READ FULL TEXT
research
01/07/2016

Mixture of Bilateral-Projection Two-dimensional Probabilistic Principal Component Analysis

The probabilistic principal component analysis (PPCA) is built upon a gl...
research
04/13/2019

Self-Paced Probabilistic Principal Component Analysis for Data with Outliers

Principal Component Analysis (PCA) is a popular tool for dimensionality ...
research
01/31/2017

Computational Techniques in Multispectral Image Processing: Application to the Syriac Galen Palimpsest

Multispectral and hyperspectral image analysis has experienced much deve...
research
02/01/2014

Randomized Nonlinear Component Analysis

Classical methods such as Principal Component Analysis (PCA) and Canonic...
research
09/03/2019

Mixture Probabilistic Principal Geodesic Analysis

Dimensionality reduction on Riemannian manifolds is challenging due to t...
research
02/05/2019

Dynamical Component Analysis (DyCA) and its application on epileptic EEG

Dynamical Component Analysis (DyCA) is a recently-proposed method to det...
research
09/03/2019

Mixture Probabilistic Principal GeodesicAnalysis

Dimensionality reduction on Riemannian manifolds is challenging due to t...

Please sign up or login with your details

Forgot password? Click here to reset