We consider the problem of choosing new focal elements to supplement the given evidence within the framework of the Dempster-Shafer evidence theory. We propose and analyze some selection rules to solve this problem under the assumption that the final goal is to add evidence to make the pignistic transformation of the new body of evidence as representative as possible of the underlying distribution of evidence. Given the current absence of selection rules, we used the random choice of the next focal element as a benchmark, and then we formalized some possible selection rules, some of them based on the maximization or minimization of uncertainty. Then, we used a Monte Carlo simulation to compare the proposed selection rules with the benchmark represented by the random selection. Numerical results show that the selection rule that balances the occurrence of elements of the frame of discernment within the set of focal elements outperforms the others, on average, as well as in a worst-case scenario, and consequently may reasonably serve as a guiding rule for the selection of new focal elements. • The problem of updating evidence as additional data is available is addressed. • A framework based on the Dempster-Shafer theory is proposed. • Within the proposed framework we focus on the Transferable Belief Model. • Several rules for selection of the “best” new focal elements are introduced. • The rule balancing the occurrence of elementary events outperforms the others.

Seeking an efficient solution for the problem of dynamic user preferences on social networks is challenging because the input data areshort textsand user preferences usuallychangeover time. This work proposes a novel framework that tackles these challenges based on deep neural networks and the Dempster-Shafer theory of evidence. The framework consists of three primary phases: (1) learning the hidden space of user texts; (2) word generation and mass inference; and (3) mass combination and keyword extraction. In the first phase, user texts are grouped into small batches according to timestamps. Each batch is used for separately training two types of neural networks, the Variational Autoencoder (VAE) and the Generative Adversarial Network (GAN). In the second phase, the generators in the trained VAE and GAN work independently as twoexpertsto generate bunches of tokens for modeling user preferences. Each bunch is considered as one piece of evidence, and is transformed into the so-called mass function in Dempster-Shafer theory by maximum a posterior estimation. In the final phase, Dempster’s rule of combination is utilized for fusing the two independent pieces of evidence into an overall mass. This mass is used for extracting top keywords to form the user preferences within a specific time span. The experiments on short text datasets verified that the proposed method outperforms baseline models on many evaluation metrics. Additionally, the output of the proposed framework could be used for visualization, which is useful in many practical applications.

This paper proposes a novel framework for clustering mixed numerical and categorical data with missing values. It integrates the imputation and clustering steps into a single process, which results in an algorithm named Clustering Mixed Numerical and Categorical Data with Missing Values (k-CMM). The algorithm consists of three phases. The initialization phase splits the input dataset into two parts based on missing values in objects and attributes types. The imputation phase uses the decision-tree-based method to find the set of correlated data objects. The clustering phase uses the mean and kernel-based methods to form cluster centers at numerical and categorical attributes, respectively. The algorithm also uses the squared Euclidean and information-theoretic-based dissimilarity measure to compute the distances between objects and cluster centers. An extensive experimental evaluation was conducted on real-life datasets to compare the clustering quality of k-CMM with state-of-the-art clustering algorithms. The execution time, memory usage, and scalability of k-CMM for various numbers of clusters or data sizes were also evaluated. Experimental results show that k-CMM can efficiently cluster missing mixed datasets as well as outperform other algorithms when the number of missing values increases in the datasets.