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Conference Paper

#### Boolean Tensor Factorization

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##### Citation

Miettinen, P. (2011). Boolean Tensor Factorization. In D. Cook, J. Pei, W. Wang, O.
Zaïane, & X. Wu (*11th IEEE International Conference
on Data Mining* (pp. 447-456). Los Alamitos, CA: IEEE. doi:10.1109/ICDM.2011.28.

Cite as: http://hdl.handle.net/11858/00-001M-0000-0010-1427-1

##### Abstract

Tensors are multi-way generalizations of matrices, and similarly to matrices,
they can also be factorized, that is, represented (approximately) as a product
of factors. These factors are typically either all matrices or a mixture of
matrices and tensors. With the widespread adoption of matrix factorization
techniques in data mining, also tensor factorizations have started to gain
attention.
In this paper we study the Boolean tensor factorizations. We assume that the
data is binary multi-way data, and we want to factorize it to binary factors
using Boolean arithmetic (i.e.\ defining that $1+1=1$). Boolean tensor
factorizations are, therefore, natural generalization of the Boolean matrix
factorizations. We will study the theory of Boolean tensor factorizations and
show that at least some of the benefits Boolean matrix factorizations have over
normal matrix factorizations carry over to the tensor data. We will also
present algorithms for Boolean variations of CP and Tucker decompositions, the
two most-common types of tensor factorizations. With experimentation done with
synthetic and real-world data, we show that Boolean tensor factorizations are a
viable alternative when the data is naturally binary.