Matrix Factorization with Interval-Valued Data

With many applications relying on multidimensional datasets for decision making, matrix factorization (or decomposition) is becoming the basis for many knowledge discovery and machine learning tasks, from clustering, trend detection, anomaly detection, to correlation analysis. Unfortunately, a major shortcoming of matrix analysis operations is that, despite their effectiveness when the data is scalar, these operations become difficult to apply in the presence of non-scalar data, as they are not designed for data that include non-scalar observations, such as intervals. In this paper, we propose matrix decomposition techniques that consider the existence of interval-valued data. We show that naive ways to deal with such imperfect data may introduce errors in analysis and present factorization techniques that are especially effective when the amount of imprecise information is large.