Reinhard Schachtner

Knowledge-based gene expression classification via matrix factorization

Motivation: Modern machine learning methods based on matrix decomposition techniques, like independent component analysis (ICA) or non-negative matrix factorization (NMF), provide new and efficient analysis tools which are currently explored to analyze gene expression profiles. These exploratory feature extraction techniques yield expression modes (ICA) or metagenes (NMF). These extracted features are considered indicative of underlying regulatory processes. They can as well be applied to the classification of gene expression datasets by grouping samples into different categories for diagnostic purposes or group genes into functional categories for further investigation of related metabolic pathways and regulatory networks. Results: In this study we focus on unsupervised matrix factorization techniques and apply ICA and sparse NMF to microarray datasets. The latter monitor the gene expression levels of human peripheral blood cells during differentiation from monocytes to macrophages. We show that these tools are able to identify relevant signatures in the deduced component matrices and extract informative sets of marker genes from these gene expression profiles. The methods rely on the joint discriminative power of a set of marker genes rather than on single marker genes. With these sets of marker genes, corroborated by leave-one-out or random forest cross-validation, the datasets could easily be classified into related diagnostic categories. The latter correspond to either monocytes versus macrophages or healthy vs Niemann Pick C disease patients. Supplementary information: Supplementary data are available at Bioinformatics online. Contact: elmar.lang@biologie.uni-regensburg.de

Towards unique solutions of non-negative matrix factorization problems by a determinant criterion

We propose a determinant criterion to constrain the solutions of non-negative matrix factorization problems and achieve unique and optimal solutions in a general setting, provided an exact solution exists. We demonstrate how optimal solutions are obtained by a heuristic named detNMF in an illustrative example and discuss the difference to sparsity constraints. Furthermore, an intuitive explanation of multi-layer techniques is discussed also.

A Nonnegative Blind Source Separation Model for Binary Test Data

A novel method called binNMF is introduced which aimed to extract hidden information from multivariate binary data sets. The method treats the problem in the spirit of blind source separation: The data are assumed to be generated by a superposition of several simultaneously acting sources or elementary causes which are not observable directly. The superposition process is based on a minimum of assumptions and reversed to identify the underlying sources. The method is motivated, developed, and demonstrated in the context of binary wafer test data which evolve during microchip fabrication.

A Bayesian approach to the Lee–Seung update rules for NMF

Abstract NMF is a Blind Source Separation technique decomposing multivariate non-negative data sets into meaningful non-negative basis components and non-negative weights. In its canonical form an NMF algorithm was proposed by Lee and Seung (1999) [31] employing multiplicative update rules. In this study we show how the latter follow from a new variational Bayes NMF algorithm VBNMF employing a Gaussian noise kernel.

How to extract marker genes from microarray data sets

In this study we focus on classification tasks and apply matrix factorization techniques like principal component analysis (PCA), independent component analysis (ICA) and non-negative matrix factorization ( NMF) to a microarray data set. The latter monitors the gene expression levels (GEL) of mononcytes and macrophages during and after differentiation. We show that these tools are able to identify relevant signatures in the deduced matrices and extract marker genes from these gene expression profiles (GEPs) without the need for extensive data bank search for appropriate functional annotations. With these marker genes corresponding test data sets can then easily be classified into related diagnostic categories.

Binary Nonnegative Matrix Factorization Applied to Semi-conductor Wafer Test Sets

A method of forming a fiber reinforced synthetic resin rod-like molding including a rod-like core portion having at least in the outer portion thereof a reinforcing fiber bundle integrally adhered together by a thermosetting resin and a thermoplastic resin layer coating the core portion is disclosed. The outer surface portion of the core portion and the inner surface portion of the thermoplastic resin layer are integrally adhered together due to an anchor effect generated by contacting between the thermosetting resin and the thermoplastic resin in a semifluid state under pressure.

Blind matrix decomposition techniques to identify marker genes from microarrays

Exploratory matrix factorization methods like PCA, ICA and sparseNMF are applied to identify marker genes and classify gene expression data sets into different categories for diagnostic purposes or group genes into functional categories for further investigation of related regulatory pathways. Gene expression levels of either human breast cancer (HBC) cell lines [6] or the famous leucemia data set [10] are considered.

Routes to identify marker genes for microarray classification

Support vector machines are applied to extract marker genes from various microarray data sets: breast cancer, leukemia and monocyte - macrophage differentiation to ease classification of related pathologies or characterize related gene regulation pathways.

Bayesian extensions of non-negative matrix factorization

Although non-negative matrix factorization has become a popular data analysis tool for non-negative data sets, there are still some issues remaining partly unsolved. We investigate the potential of Bayesian techniques towards the solution of two important open questions concerning uniqueness and actual number of sources underlying the data. We derive a general Bayesian optimality condition for NMF solutions and elaborate on the criterion for the Gaussian likelihood case. We further derive a variational Bayes NMF algorithm for the Gaussian likelihood using rectified Gaussian prior distributions and study its ability to estimate the true number of sources in a toy data set.

Nonnegative Matrix Factorization for Binary Data to Extract Elementary Failure Maps from Wafer Test Images

We introduce a probabilistic variant of nonnegative matrix factorization (NMF) applied to binary datasets. Hence we consider binary coded images as a probabilistic superposition of underlying continuous-valued basic patterns. An extension of the well-known NMF procedure to binary-valued datasets is provided to solve the related optimization problem with nonnegativity constraints. We demonstrate the performance of our method by applying it to the detection and characterization of hidden causes for failures during wafer processing. Therefore, we decompose binary coded (pass/fail) wafer test data into underlying elementary failure patterns and study their influence on the quality of single wafers.