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.

In the past, in many areas, the best prediction models were linear and nonlinear parametric models. In the last decade, in many application areas, deep learning has shown to lead to more accurate predictions than the parametric models. Deep learning-based predictions are reasonably accurate, but not perfect. How can we achieve better accuracy? To achieve this objective, we propose to combine neural networks with parametric model: namely, to train neural networks not on the original data, but on the differences between the actual data and the predictions of the parametric model. On the example of predicting currency exchange rate, we show that this idea indeed leads to more accurate predictions.

Let p be an odd prime, s and m be positive integers. Cyclic codes of length 2psover Fpmare the ideals ((x-1)i(x+1)j), where 0 ≤ i, j ≤ ps, of the principal ideal ring Fpm[x]/(x2ps- 1). Using this structure, the symbol-pair distances of all cyclic codes of length 2psover Fpmare completely determined. In addition, we establish all MDS symbol-pair cyclic codes of length 2psover Fpm. Some MDS symbol-pair cyclic codes are better than all the known ones. Among others, we discuss possible applications to construct quantum MDS symbol-pair codes.

In this paper, we aim at developing a new collaborative filtering recommender system using soft ratings, which is capable of dealing with both imperfect information about user preferences and the sparsity problem. On the one hand, Dempster-Shafer theory is employed for handling the imperfect information due to its advantage in providing not only a flexible framework for modeling uncertain, imprecise, and incomplete information, but also powerful operations for fusion of information from multiple sources. On the other hand, in dealing with the sparsity problem, community context information that is extracted from the social network containing all users is used for predicting unprovided ratings. As predicted ratings are not a hundred percent accurate, while the provided ratings are actually evaluated by users, we also develop a new method for calculating user-user similarities, in which provided ratings are considered to be more significant than predicted ones. In the experiments, the developed recommender system is tested on two different data sets; and the experiment results indicate that this system is more effective than CoFiDS, a typical recommender system offering soft ratings.

In evidential clustering, cluster-membership uncertainty is represented by Dempster–Shafer mass functions. The notion of evidential partition generalizes other soft clustering structures such as fuzzy, possibilistic, or rough partitions. In this paper, we propose two extensions of the Rand index for evaluating and comparing evidential partitions, called similarity and consistency indices. The similarity index is suitable for measuring the closeness of two soft partitions, whereas the consistency index allows one to assess the agreement, or lack of conflict, between a soft partition and the true hard partition. Simulation experiments illustrate some applications of these indices.

Let p be a prime, and λ be a nonzero element of the finite field Fpm. The λ-constacyclic codes of length psover Fpmare linearly ordered under set-theoretic inclusion, i.e., they are the ideals 〈(x - λ0)i〉, 0 ≤ i ≤ psof the chain ring [(Fpm[x])/((xps- λ))]. This structure is used to establish the symbol-pair distances of all such λ-constacyclic codes. Among others, all maximum distance separable symbol-pair constacyclic codes of length ps are obtained.

Fuzzy techniques have been originally designed to describe imprecise (“fuzzy”) expert knowledge. Somewhat surprisingly, fuzzy techniques have also been successfully used in situations without expert knowledge, when all we have is data. In this paper, we explain this surprising phenomenon by showing that the need for optimal processing of data (including crisp data) naturally leads to fuzzy and neural data processing techniques. This result shows the potential of fuzzy data processing. To maximally utilize this potential, we need to provide an operational meaning of the corresponding fuzzy degrees. We show that such a meaning can be extracted from the above justification of fuzzy techniques. It turns out that, in contrast to probabilistic uncertainty, the natural operational meaning of fuzzy degrees is indirect—similarly to the operational meaning of geometry and physics in general relativity.

One of the most empirically successful tools for studying dependence between different quantities in econometrics is the tool of vine copulas. In this paper, we explain this empirical success by showing that the most widely used vine copulas are, in effect, the results of using the general fuzzy methodology. To be more precise, vine copulas correspond to a natural extension of the traditional fuzzy methodology, when we allow several different “and”-operations (t-norms), and some of these t-norms can be nonassociative.