We consider an adversarially-trained version of the nonnegative matrix factorization, a popular latent dimensionality reduction technique. In our formulation, attacker adds arbitrary bounded norm to given data matrix. design efficient algorithms inspired by adversarial training optimize for dictionary and coefficient matrices with enhanced generalization abilities. Extensive simulations on synt...

A long-term campaign for monitoring the concentration of atmospheric Particulate Matter (PM) was conducted at multiple sites located in the center and suburbs of the Tokyo Metropolitan Area in Japan. The concentration of fine PM has shown a declining trend over the last two decades. A positive matrix factorization model elucidated that the contribution of combustion sources was drastically redu...

This paper addresses the QR decomposition and UD factorization based square-root algorithms of the recursive least-squares (RLS) Wiener fixed-point smoother and filter. In the RLS Wiener estimators, the Riccati-type difference equations for the auto-variance function of the filtering estimate are included. Hence, by the roundoff errors, in the case of the small value of the observation noise va...

In this paper, a constructive general matrix factorization scheme is developed for extracting a nontrivial factor from a given nD (n > 2) polynomial matrix whose maximal order minors satisfy certain conditions. It is shown that three classes of nD polynomial matrices admit this kind of general matrix factorization. It turns out that minor prime factorization and determinantal factorization are ...

It is today accepted that matrix factorization models allow a high quality of rating prediction in recommender systems. However, a major drawback of matrix factorization is its static nature that results in a progressive declining of the accuracy of the predictions after each factorization. This is due to the fact that the new obtained ratings are not taken into account until a new factorizatio...