Kai-Chun Chiu | PubMed Health

PubMed2004

One-bit-matching conjecture for independent component analysis.

The one-bit-matching conjecture for independent component analysis (ICA) could be understood from different perspectives but is basically stated as "all the sources can be separated as long as there is a one-to-one same-sign-correspondence between the kurtosis signs of all source probability density functions (pdf's) and the kurtosis signs of all model pdf's" (Xu, Cheung, & Amari, 1998a). This conjecture has been widely believed in the ICA community and implicitly supported by many ICA studies, such as the Extended Infomax (Lee, Girolami, & Sejnowski, 1999) and the soft switching algorithm (Welling & Weber, 2001). However, there is no mathematical proof to confirm the conjecture theoretically. In this article, only skewness and kurtosis are considered, and such a mathematical proof is given under the assumption that the skewness of the model densities vanishes. Moreover, empirical experiments are demonstrated on the robustness of the conjecture as the vanishing skewness assumption breaks. As a by-product, we also show that the kurtosis maximization criterion (Moreau & Macchi, 1996) is actually a special case of the minimum mutual information criterion for ICA.

Algorithms↗

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Improved system for object detection and star/galaxy classification via local subspace analysis.

The two traditional tasks of object detection and star/galaxy classification in astronomy can be automated by neural networks because the nature of the problems is that of pattern recognition. A typical existing system can be further improved by using one of the local Principal Component Analysis (PCA) models. Our analysis in the context of object detection and star/galaxy classification reveals that local PCA is not only superior to global PCA in feature extraction, but is also superior to gaussian mixture in clustering analysis. Unlike global PCA which performs PCA for the whole data set, local PCA applies PCA individually to each cluster of data. As a result, local PCA often outperforms global PCA for data of multi-modes. Moreover, since local PCA can effectively avoid the trouble of having to specify a large number of free elements of each covariance matrix of gaussian mixture, it can give a better description of local subspace structures of each cluster when applied on high dimensional data with small sample size. In this paper, the local PCA model proposed by Xu [IEEE Trans. Neural Networks 12 (2001) 822] under the general framework of Bayesian Ying Yang (BYY) normalization learning will be adopted. Endowed with the automatic model selection ability of BYY learning, the BYY normalization learning-based local PCA model can cope with those object detection and star/galaxy classification tasks with unknown model complexity. A detailed algorithm for implementation of the local PCA model will be proposed, and experimental results using both synthetic and real astronomical data will be demonstrated.

Astronomy↗