Bayesian Nominal Matrix Factorization for Mining Daily Activity Patterns

With the advent of the Internet of things (IoT) and smart sensor technologies, the data-driven paradigm has been found promising to support human behavioral analysis in a smart home for better healthcare and well-being of senior adults. This work focuses on discovering daily activity routines from sensor data collected in a smart home. By representing the sensor data as a matrix, daily activity routines can be identified using matrix factorization methods. The key challenge rests on the fact that the matrix contains discrete labels as its elements, and decomposing the nominal data matrix into basis vectors of the labels is nontrivial. We propose a novel principled methodology to tackle the nominal matrix factorization problem. Assuming that the similarity matrix of the labels is known, the discrete labels are first projected onto a continuous space with the interlabel distance preserving the given similarity matrix of the labels as far as possible. Then, we extend a hierarchical probabilistic model for ordinal matrix factorization with Bayesian Lasso that the factorization can be more robust to noise and more sparse to ease human interpretation. Our experimental results based on a synthetic data set shows that the factorization results obtained using the proposed methodology outperform those obtained using a number of the state-of-the-art factorization methods in terms of the basis vector reconstruction accuracy. We also applied our model to a publicly available smart home data set to illustrate how the proposed methodology can be used to support daily activity routine analysis.