Dictionary Learning on a Manifold Outline Introduction: Background Introduction: Background Introduction: Motivation

Dictionary Learning on a Manifold Outline Introduction: Background Introduction: Background Introduction: Motivation www.phwiki.com

Dictionary Learning on a Manifold Outline Introduction: Background Introduction: Background Introduction: Motivation

Sterling, Dwayne, Host has reference to this Academic Journal, PHwiki organized this Journal Dictionary Learning on a Manifold 1Mingyuan Zhou, 2Hongxia Yang, 3Guillermo Sapiro, 2David Dunson in addition to 1Lawrence Carin 1Department of Electrical & Computer Engineering, Duke University 2Department of Statistical Science, Duke University 3Department of Electrical & Computer Engineering, University of Minnesota Zhou 2011 Outline Introduction Dependent Hierarchical Beta Process (dHBP) Dictionary Learning with dHBP Image Interpolation in addition to Denoising Conclusions Introduction: Background Dictionary learning in addition to sparse coding Sparse factor analysis model (Factor/feature/dish/dictionary atom) Indian Buffet process in addition to beta process

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Introduction: Background Beta process in addition to Bernoulli process (Thibaux & Jordan AISTATS2007) Indian Buffet process (Griffiths & Ghahramani 2005) Introduction: Motivation Exchangeability assumption is not true Image interpolation with BPFA (Zhou et al. 2009) 80% pixels are missing at r in addition to om Introduction: Covariate Dependence Dependent Dirichlet process MacEachern (1999), Duan et al. (2007), Griffin & Steel (2006) Non-exchangeable IBP Phylogenetic IBP (Miller, Griffiths & Jordan 2008) Dependent IBP (Williamson, Orbanz & Ghahramani 2010) Bayesian density regression (Dunson & Pillai 2007)

Review of Beta Process (Thibaus & Jordan 2007) A beta process is a positive Levy process, whose Levy measure lives on in addition to can be expressed as If the base measure is continuous, then is drawn from a degenerate beta distribution parameterized by If , then Dependent Hierarchical Beta Process R in addition to om walk matrix dHBP Covariate-dependent correlations Dictionary Learning with dHBP BP dHBP

Missing data Full data: Observed: , Missing: Sparse spiky noise Recoverd data: Missing Data in addition to Outliers Independence chain Metropolis-Hastings Slice sampling Gibbs sampling MCMC Inference Experiments Image interpolation Missing pixels Locations of missing pixels are known Image denoising WGN + sparse spiky noise Amplitudes unknown Locations of spiky noise are unknown Covariates: patch spatial locations

Image Interpolation: BP vs. dHBP BP: 26.9 dB dHBP: 29.92 dB 80% pixels missing at r in addition to om BP atom usage dHBP atom usage BP dictionary dHBP dictionary Dictionary atom activation probability map dHBP recovery Image Interpolation: BP vs. dHBP Observed (20%) BP recovery dHBP recovery Original dHBP recovery Image Interpolation: BP vs. dHBP

Image Interpolation: BP vs. dHBP Observed (20%) BP recovery dHBP recovery Original dHBP recovery Spiky Noise Removal: BP vs. dHBP BP denoised image Noisy image (WGN + Sparse Spiky noise) BP dictionary dHBP denoised image Original image dHBP dictionary Spiky Noise Removal: BP vs. dHBP BP denoised image Noisy image (WGN + Sparse Spiky noise) dHBP denoised image Original image dHBP dictionary BP dictionary

Future Work L in addition to mark-dHBP J l in addition to marks J N Locality constraint as long as manifold learning Covariates: cosine distance between samples Dictionary atoms look like the data Variational inference, online learning Other applications Super-resolution Deblurring Video background & as long as eground modeling A dependent hierarchical beta process is proposed Efficient hybrid MCMC inference is presented Encouraging per as long as mance is demonstrated on image-processing applications Conclusions

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