Recent Developments in Boolean Matrix Factorization

Miettinen, Pauli; Neumann, Stefan

doi:10.24963/ijcai.2020/685

Cited by 21 publications

(11 citation statements)

References 34 publications

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“…The non-symmetric variants of these matrix problems known as Binary Matrix Factorization, have been receiving a lot of attention recently [25,15,16,1,19,3]. Here the objective is to minimize A − BC , where A is an m × n input matrix, B is an m × k output binary matrix and C is a k×n output binary matrix.…”

Section: Weighted Edge Clique Partitionmentioning

confidence: 99%

Parameterized algorithms for identifying gene co-expression modules via weighted clique decomposition

Cooley¹,

Greene²,

Issac³

et al. 2021

SIAM Conference on Applied and Computational Discrete Algorithms (ACDA21)

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We present a new combinatorial model for identifying regulatory modules in gene co-expression data using a decomposition into weighted cliques. To capture complex interaction effects, we generalize the previously-studied weighted edge clique partition problem. As a first step, we restrict ourselves to the noise-free setting, and show that the problem is fixed parameter tractable when parameterized by the number of modules (cliques). We present two new algorithms for finding these decompositions, using linear programming and integer partitioning to determine the clique weights. Further, we implement these algorithms in Python and test them on a biologically-inspired synthetic corpus generated using real-world data from transcription factors and a latent variable analysis of co-expression in varying cell types.

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Section: Weighted Edge Clique Partitionmentioning

confidence: 99%

Parameterized algorithms for identifying gene co-expression modules via weighted clique decomposition

Cooley¹,

Greene²,

Issac³

et al. 2021

SIAM Conference on Applied and Computational Discrete Algorithms (ACDA21)

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“…There is a big body of work done on Low Boolean-Rank Approximation. We refer to [27,29,31,30] for further references on this interesting problem. Parameterized algorithms for Low Boolean-Rank Approximation (without outliers) were studied in [18].…”

Section: K-clustering With Column Outliersmentioning

confidence: 99%

Parameterized Complexity of Feature Selection for Categorical Data Clustering

Bandyapadhyay,

Fomin,

Golovach

et al. 2021

Preprint

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We develop new algorithmic methods with provable guarantees for feature selection in regard to categorical data clustering. While feature selection is one of the most common approaches to reduce dimensionality in practice, most of the known feature selection methods are heuristics. We study the following mathematical model. We assume that there are some inadvertent (or undesirable) features of the input data that unnecessarily increase the cost of clustering. Consequently, we want to select a subset of the original features from the data such that there is a small-cost clustering on the selected features. More precisely, for given integers ℓ (the number of irrelevant features) and k (the number of clusters), budget B, and a set of n categorical data points (represented by m-dimensional vectors whose elements belong to a finite set of values Σ), we want to select m − ℓ relevant features such that the cost of any optimal k-clustering on these features does not exceed B. Here the cost of a cluster is the sum of Hamming distances (ℓ0-distances) between the selected features of the elements of the cluster and its center. The clustering cost is the total sum of the costs of the clusters.We use the framework of parameterized complexity to identify how the complexity of the problem depends on parameters k, B, and |Σ|. Our main result is an algorithm that solves the Feature Selection problem in time f (k, B, |Σ|) • m g (k,|Σ|) • n 2 for some functions f and g. In other words, the problem is fixed-parameter tractable parameterized by B when |Σ| and k are constants. Our algorithm for Feature Selection is based on a solution to a more general problem, Constrained Clustering with Outliers. In this problem, we want to delete a certain number of outliers such that the remaining points could be clustered around centers satisfying specific constraints. One interesting fact about Constrained Clustering with Outliers is that besides Feature Selection, it encompasses many other fundamental problems regarding categorical data such as Robust Clustering, Binary and Boolean Low-rank Matrix Approximation with Outliers, and Binary Robust Projective Clustering. Thus as a byproduct of our theorem, we obtain algorithms for all these problems. We also complement our algorithmic findings with complexity lower bounds.

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“…Chandran et al [11] showed that under a standard assumption in complexity theory, any approximation algorithm for BMF requires time 2 2 Ω(k) or (mn) ω (1) ; this essentially rules out practical algorithms for BMF with approximation guarantees. For a recent survey on BMF see [30].…”

Section: Proof Of Propositionmentioning

confidence: 99%

Biclustering and Boolean Matrix Factorization in Data Streams

Neumann¹,

Miettinen²

2020

Preprint

Self Cite

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We study the clustering of bipartite graphs and Boolean matrix factorization in data streams. We consider a streaming setting in which the vertices from the left side of the graph arrive one by one together with all of their incident edges. We provide an algorithm that, after one pass over the stream, recovers the set of clusters on the right side of the graph using sublinear space; to the best of our knowledge, this is the first algorithm with this property. We also show that after a second pass over the stream, the left clusters of the bipartite graph can be recovered and we show how to extend our algorithm to solve the Boolean matrix factorization problem (by exploiting the correspondence of Boolean matrices and bipartite graphs). We evaluate an implementation of the algorithm on synthetic data and on real-world data. On real-world datasets the algorithm is orders of magnitudes faster than a static baseline algorithm while providing quality results within a factor 2 of the baseline algorithm. Our algorithm scales linearly in the number of edges in the graph. Finally, we analyze the algorithm theoretically and provide sufficient conditions under which the algorithm recovers a set of planted clusters under a standard random graph model.

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Recent Developments in Boolean Matrix Factorization

Cited by 21 publications

References 34 publications

Parameterized algorithms for identifying gene co-expression modules via weighted clique decomposition

Parameterized algorithms for identifying gene co-expression modules via weighted clique decomposition

Parameterized Complexity of Feature Selection for Categorical Data Clustering

Biclustering and Boolean Matrix Factorization in Data Streams

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