Topographic Analysis of Correlated Components

Hiroaki Sasaki; Michael U. Gutmann; Hayaru Shouno; Aapo Hyvärinen

Topographic Analysis of Correlated Components

Hiroaki Sasaki, Michael U. Gutmann, Hayaru Shouno, Aapo Hyvärinen ;

Proceedings of the Asian Conference on Machine Learning, PMLR 25:365-378, 2012.

Abstract

Independent component analysis (ICA) is a method to estimate components which are as statistically independent as possible. However, in many practical applications, the estimated components are not independent. Recent variants of ICA have made use of such residual dependencies to estimate an ordering (topography) of the components. Like in ICA, the components in those variants are assumed to be uncorrelated, which might be a rather strict condition. In this paper, we address this shortcoming. We propose a generative model for the source where the components can have linear and higher order correlations, which generalizes models in use so far. Based on the model, we derive a method to estimate topographic representations. In numerical experiments on artificial data, the new method is shown to be more widely applicable than previously proposed extensions of ICA. We learn topographic representations for two kinds of real data sets: for outputs of simulated complex cells in the primary visual cortex and for text data.

Related Material

Download PDF

@InProceedings{pmlr-v25-sasaki12, title = {Topographic Analysis of Correlated Components}, author = {Hiroaki Sasaki and Michael U. Gutmann and Hayaru Shouno and Aapo Hyvärinen}, booktitle = {Proceedings of the Asian Conference on Machine Learning}, pages = {365--378}, year = {2012}, editor = {Steven C. H. Hoi and Wray Buntine}, volume = {25}, series = {Proceedings of Machine Learning Research}, address = {Singapore Management University, Singapore}, month = {04--06 Nov}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v25/sasaki12/sasaki12.pdf}, url = {http://proceedings.mlr.press/v25/sasaki12.html}, abstract = {Independent component analysis (ICA) is a method to estimate components which are as statistically independent as possible. However, in many practical applications, the estimated components are not independent. Recent variants of ICA have made use of such residual dependencies to estimate an ordering (topography) of the components. Like in ICA, the components in those variants are assumed to be uncorrelated, which might be a rather strict condition. In this paper, we address this shortcoming. We propose a generative model for the source where the components can have linear and higher order correlations, which generalizes models in use so far. Based on the model, we derive a method to estimate topographic representations. In numerical experiments on artificial data, the new method is shown to be more widely applicable than previously proposed extensions of ICA. We learn topographic representations for two kinds of real data sets: for outputs of simulated complex cells in the primary visual cortex and for text data.} }

%0 Conference Paper %T Topographic Analysis of Correlated Components %A Hiroaki Sasaki %A Michael U. Gutmann %A Hayaru Shouno %A Aapo Hyvärinen %B Proceedings of the Asian Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2012 %E Steven C. H. Hoi %E Wray Buntine %F pmlr-v25-sasaki12 %I PMLR %J Proceedings of Machine Learning Research %P 365--378 %U http://proceedings.mlr.press %V 25 %W PMLR %X Independent component analysis (ICA) is a method to estimate components which are as statistically independent as possible. However, in many practical applications, the estimated components are not independent. Recent variants of ICA have made use of such residual dependencies to estimate an ordering (topography) of the components. Like in ICA, the components in those variants are assumed to be uncorrelated, which might be a rather strict condition. In this paper, we address this shortcoming. We propose a generative model for the source where the components can have linear and higher order correlations, which generalizes models in use so far. Based on the model, we derive a method to estimate topographic representations. In numerical experiments on artificial data, the new method is shown to be more widely applicable than previously proposed extensions of ICA. We learn topographic representations for two kinds of real data sets: for outputs of simulated complex cells in the primary visual cortex and for text data.

TY - CPAPER TI - Topographic Analysis of Correlated Components AU - Hiroaki Sasaki AU - Michael U. Gutmann AU - Hayaru Shouno AU - Aapo Hyvärinen BT - Proceedings of the Asian Conference on Machine Learning PY - 2012/11/17 DA - 2012/11/17 ED - Steven C. H. Hoi ED - Wray Buntine ID - pmlr-v25-sasaki12 PB - PMLR SP - 365 DP - PMLR EP - 378 L1 - http://proceedings.mlr.press/v25/sasaki12/sasaki12.pdf UR - http://proceedings.mlr.press/v25/sasaki12.html AB - Independent component analysis (ICA) is a method to estimate components which are as statistically independent as possible. However, in many practical applications, the estimated components are not independent. Recent variants of ICA have made use of such residual dependencies to estimate an ordering (topography) of the components. Like in ICA, the components in those variants are assumed to be uncorrelated, which might be a rather strict condition. In this paper, we address this shortcoming. We propose a generative model for the source where the components can have linear and higher order correlations, which generalizes models in use so far. Based on the model, we derive a method to estimate topographic representations. In numerical experiments on artificial data, the new method is shown to be more widely applicable than previously proposed extensions of ICA. We learn topographic representations for two kinds of real data sets: for outputs of simulated complex cells in the primary visual cortex and for text data. ER -