Gen Hori

Extended SMART algorithms for non-negative matrix factorization

In this paper we derive a family of new extended SMART (Simultaneous Multiplicative Algebraic Reconstruction Technique) algorithms for Non-negative Matrix Factorization (NMF). The proposed algorithms are characterized by improved efficiency and convergence rate and can be applied for various distributions of data and additive noise. Information theory and information geometry play key roles in the derivation of new algorithms. We discuss several loss functions used in information theory which allow us to obtain generalized forms of multiplicative NMF learning adaptive algorithms. We also provide flexible and relaxed forms of the NMF algorithms to increase convergence speed and impose an additional constraint of sparsity. The scope of these results is vast since discussed generalized divergence functions include a large number of useful loss functions such as the Amari α– divergence, Relative entropy, Bose-Einstein divergence, Jensen-Shannon divergence, J-divergence, Arithmetic-Geometric (AG) Taneja divergence, etc. We applied the developed algorithms successfully to Blind (or semi blind) Source Separation (BSS) where sources may be generally statistically dependent, however are subject to additional constraints such as nonnegativity and sparsity. Moreover, we applied a novel multilayer NMF strategy which improves performance of the most proposed algorithms.

Isolation of gene sets affected specifically by polyglutamine expression: implication of the TOR signaling pathway in neurodegeneration

Transcriptional dysregulation as a result of sequestration of essential transcription factors into protein aggregates formed by polyglutamine (polyQ) expansions can lead to late-onset progressive neurodegeneration. DNA microarray analysis of Drosophila expressing polyQ in the compound eye over time revealed large numbers of transcriptional changes at the earliest stages of the disease including repression of the transient receptor potential calcium channels in a polyQ-induced cell death specific manner. While significant differences in expression profiles were found between the Drosophila compound eye and polyQ-sensitive neural cells, a number of possible key overlapping regulators were extracted. Among these, PDK1 was shown to act as a mediator for polyQ-toxicity, suggesting the involvement of the TOR pathway in polyQ-induced neurodegeneration.

Gene interaction in DNA microarray data is decomposed by information geometric measure

MOTIVATION Given the vast amount of gene expression data, it is essential to develop a simple and reliable method of investigating the fine structure of gene interaction. We show how an information geometric measure achieves this. RESULTS We introduce an information geometric measure of binary random vectors and show how this measure reveals the fine structure of gene interaction. In particular, we propose an iterative procedure by using this measure (called IPIG). The procedure finds higher-order dependencies which may underlie the interaction between two genes of interest. To demonstrate the method, we investigate the interaction between the two genes of interest in the data from human acute lymphoblastic leukemia cells. The method successfully discovered biologically known findings and also selected other genes as hidden causes that constitute the interaction. AVAILABILITY Softwares are currently not available but are possibly made available in future at http://www.mns.brain.riken.go.jp/~nakahara/DNA_pub.html where all the related information is also linked.

Improved Parameter Estimation for Variance-Stabilizing Transformation of Gene-Expression Microarray Data

A gene-expression microarray datum is modeled as an exponential expression signal (log-normal distribution) and additive noise. Variance-stabilizing transformation based on this model is useful for improving the uniformity of variance, which is often assumed for conventional statistical analysis methods. However, the existing method of estimating transformation parameters may not be perfect because of poor management of outliers. By employing an information normalization technique, we have developed an improved parameter estimation method, which enables statistically more straightforward outlier exclusion and works well even in the case of small sample size. Validation of this method with experimental data has suggested that it is superior to the conventional method.

Comparison of Two Main Approaches to Joint SVD

An initially flat sheet of a fan cylinder assembly is formed to an exact cylindrical configuration in such a manner that less than 20% of the material comprising the sheet in a direction along the thickness of the same is exposed to stress above the yield strength of the material. The sheet is provided with tabs bent to a perpendicular orientation relative to remaining regions of the sheet, and holes are punched in certain of the tabs at precise, predefined locations and which are related to precise, predefined locations of apertures spaced around the periphery of an exact circular opening in an upright support panel of the tower housing. The sheet is formed to a true cylinder by causing the major region of the sheet to bear against the periphery of the circular opening of the support panel so that the flat panel functions as a guide both during forming of the cylinder and also thereafter to retain the sheet in its proper cylindrical configuration. In an alternate embodiment of the invention, an annular member comprised of expanded foam material is secured to the support panel opposite the fan cylinder for reducing turbulence of the air flowing from the fill structure and through the fan cylinder.

Isospectral Gradient Flows for Non-symmetric Eigenvalue Problem

We derive the general formula of isospectral gradient flows on adjoint orbits which are related to the theory of solitons and matrix eigenvalue problem. The general formula includes some known examples of isospectral flows. Using the general formula, we obtain new dynamical systems which provide new computational algorithm for solving the eigenvalue problem of non-symmetric matrices.

Isospectral flows expressed in multiple bracket forms

It is shown that gradient equations on adjoint orbits with respect to certain metrics have multiple bracket representation. This is a generalization of Brockett’s dynamical system of double bracket formH = [H, [H, N]].

Global analysis of log likelihood criterion

This paper introduces and investigates a gradient flow of the log likelihood function restricted on the isospectral submanifold and proves that the flow globally converges to diagonal matrices for almost all positive definite initial matrices. This result shows that the log likelihood function does not have any spurious stable fixed point and ensures the global convergence of ICA algorithms based on the log likelihood function.