We introduce a new Blind Source Separation Approach called binNTF which operates on tensor-valued binary datasets. Assuming that several simultaneously acting sources or elementary causes are generating the observed data, the objective of our approach is to uncover the underlying sources as well as their individual contribution to each observation with a minimum number of assumptions in an unsupervised fashion. We motivate, develop and demonstrate our method in the context of binary wafer test data which evolve during microchip fabrication. In this application, we also have to deal with incomplete datasets which can occur due to the commonly used stop-on-first-fail testing procedure or result from the aggregation of several distinct tests into BIN categories.

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.