A Bayesian Boolean Matrix Factorization for Analyzing Copy Number Abnormalities for Multiple Myeloma Disease

Music City Center 

Chromosomal alterations in multiple myeloma are pivotal in understanding the disease's patho-
genesis, progression, and therapeutic response. Multiple myeloma, a cancer of plasma cells, is char-
acterized by various genomic abnormalities, including chromosomal translocations, deletions, dupli-
cations, and aneuploidy. Studying the latent factors behind these events of deletion and insertion is
very helpful in understanding the disease's prognosis and evolution. One possible approach would be
the use of Boolean Matrix Factorization algorithms to unravel the complexities of these events. This
study aimed to develop a novel algorithm Bayesian Boolean Matrix Factorization (BBooMF) for
decomposing binary (0, 1) datasets into a two binary factor matrices. We propose a simple novel de-
composition method for categorical data based on logical conditions, yielding to easily interpretable
factors. We utilize the Bayesian approach in addition to boolean algebra to carry out probabilistic
inference to address uncertainty and noise in the data,improving the accuracy and interpretability of
matrix factorization. We iteratively optimize the factorization process using the Gibbs sampler, pro-
viding valuable insights into the underlying patterns and structures of complex discrete datasets. The
proposed algorithm is compared with the existing classical methods like Asso, GRENCOND, GRENCOND+
and topFiberM. Our algorithm perform better or as well as these classical methods. The developed
algorithms will have potential applications in other fields which have data sets that are naturally
represented using binary structures .

Boolean factorization