In many fields of computer science, tensor decomposition techniques are increasingly being adopted as the core of many applications that rely on multi-dimensional datasets for implementing knowledge discovery tasks. Unfortunately, a major shortcoming of state-of-the-art tensor analyses is that, despite their effectiveness when the data is certain, these operations become difficult to apply, or altogether inapplicable, in the presence of uncertainty in the data, a circumstance common to many real-world scenarios. In this paper we propose a way to address this issue by extending the known Tensor-Train technique for tensor factorization in order to deal with uncertain data, here modeled as intervals. Working with interval-valued data, however, presents numerous challenges, since many algebraic operations that form the building blocks of the factorization process, as well as the properties that make these procedures useful for knowledge discovery, cannot be easily extended from their scalar counterparts, and often require some approximation (including, though it is not only the case, for keeping computational costs manageable). These challenges notwithstanding, our proposed techniques proved to be reasonably effective, and are supported by a thorough experimental validation.

With many applications relying on multi-dimensional datasets for decision making, matrix factorization (or decomposition) is becoming the basis for many knowledge discoveries 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. Yet, in many applications, the available data are inherently non-scalar for various reasons, including imprecision in data collection, conflicts in aggregated data, data summarization, or privacy issues, where one is provided with a reduced, clustered, or intentionally noisy and obfuscated version of the data to hide information. 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.

With many applications relying on multi-dimensional 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.

Many realistic life scenarios require dealing with deadlines and action durations. Such constraints, together with propositional and resource conditions must be taken into account in order to make plans which are actually feasible. In order to combine these aspects, the paper deals with the entailed temporal constrained planning problem by using the framework of numeric planning, based on an action centred philosophy a-la PDDL. The approach is motivated by the necessity of integrating scheduling and planning in the context of a multi-modal journey planning problem. In order to evaluate the feasibility of the approach, the paper presents JoPA, a web service architecture which has been thoroughly evaluated employing two state of the art numeric planning systems, i.e. Metric-FF and Colin. Results show that the approach is feasible considering (un) constrained and optimization tasks.