We investigate the problem of discovering and forecasting regular regime switches in a financial ecosystem comprising multiple time series. Such regime switches, indicative of varying market behaviors across distinct time intervals, are pivotal for a nuanced understanding of market dynamics, which in turn allows informed model selection for forecasting and enhanced interpretability of predictive outcomes. Despite strides in this domain, prevailing methodologies often falter due to: (1) an inability to effectively model the temporal behaviors inherent in financial series; and (2) neglecting the interdependencies among series when discovering regimes. In this paper, we propose RHINE, a Regime-switcHIng model with Nonlinear rEpresentation. RHINE stands out with its kernel-based representation, adept at capturing the dynamic shifts in market regimes. This representation encapsulates the nonlinear interplay across multiple financial time series. By leveraging the kernel representation, we introduce an eigengap thresholding measure, designed to automatically discern the optimal number of financial market regimes, enhancing the model's adaptability to market fluctuations. Empirical assessments on both synthetic and real-world stock market datasets underscore RHINE's prowess. The findings illuminate that the inherent structures governing financial market behaviors are dynamic, and harnessing these dynamics via RHINE leads to a regime-based model that outperforms both conventional and state-of-the-art neural network models in predictive capabilities.

The linguistic intuitionistic fuzzy sets (LIFSs) and linguistic Pythagorean fuzzy sets (LPFSs) are two linguistic orthopair fuzzy sets whose membership grades are pairs of linguistic terms from the predefined linguistic term sets (LTSs). One linguistic term indicates the membership degree (MD), while the other one gives the nonmembership degree (NMD). In each LIFS, the sum of the subscripts of MD and NMD is less than the cardinality of LTS. In the LPFSs, the sum of the squares of the subscripts of MD and NMD is less than the square of the cardinality of LTS. In this paper, we propose a general form of these two linguistic orthopair fuzzy sets, which can be named linguistic q-rung orthopair fuzzy sets. We devise the operational laws, based on which, the linguistic q-rung orthopair fuzzy weighted averaging (LqROFWA) operator and linguistic q-rung orthopair fuzzy weighted geometric (LqROFWG) operator are developed to aggregate the linguistic q-rung orthopair fuzzy numbers (LqROFNs). Then, the novel interactional operational laws that consider the interactions between the MD and NMD from different LqROFNs are given. The partitioned geometric Heronian mean (PGHM) operator can effectively solve the decision-making problems in which the attributes grouped into the same clusters have interrelationships and the attributes belonging to different clusters have no interrelationship. Based on these novel operational laws and PGHM operator, the linguistic q-rung orthopair fuzzy interactional PGHM (LqROFIPGHM) operator and linguistic q-rung orthopair fuzzy interactional weighted PGHM (LqROFIWPGHM) operator are proposed and their properties are discussed. Based on the LqROFIWPGHM operator, an efficient multiattribute group decision-making model is given to deal with the linguistic q-rung orthopair fuzzy information. Finally, the superiorities of the interactional operational laws and LqROFIWPGHM operator are tested using some illustrative examples.

Chronic obstructive pulmonary disease (COPD) accounts for the highest rate of hospital readmissions and is the third leading cause of death in Canada, the United States and worldwide. Predicting COPD failure provides a prognostic warning of death or readmission, and is crucial to early intervention and decision-making. The aim of this study is to perform COPD failure prediction on longitudinal data. To address the inappropriate estimation of Cox hazard in current approaches, we propose a new representation of hazard to capture the relationship between survival probability and time-varying risk factors in a concise but effective way. To optimize model parameters, we design and maximize a new joint likelihood that comprises two components used to estimate survival status separately for failure and censored patients. A regularized optimization is performed on the joint likelihood to prevent overfitting arising from model learning. Our approach is applied to a real-life COPD data set and outperforms the current state-of-the-art prediction models in terms of the survival AUC, concordance index and Birer score metrics, this reveals that the great promise of our approach for clinical prediction.

The discovery of circle of friends has risen rapidly in recent years. Traditional methods are mainly based on social network analysis which relies heavily on self-report data, such that these methods have isolated successes with limited accuracy, breadth, and depth. In this paper, we propose a new method which combines clustering technique to automatically discover the circle of friends on mobile data. In our method, the circle of friends is modeled as non-overlapping subspace clusters on mobile data with a Vector Space Model (VSM) based representation, for which a new subspace clustering algorithm is proposed to mine the underlying friend-relationship. The experimental studies on real mobile data demonstrate the effectiveness of the new method, and the results show that our clustering algorithm achieves better performance than the existing clustering algorithms.

Naive Bayes (NB for short) is one of the popular methods for supervised classification in a knowledge management system. Currently, in many real-world applications, high-dimensional data pose a major challenge to conventional NB classifiers, due to noisy or redundant features and local relevance of these features to classes. In this paper, an automated feature weighting solution is proposed to result in a NB method effective in dealing with high-dimensional data. We first propose a locally weighted probability model, for Bayesian modeling in high-dimensional spaces, to implement a soft feature selection scheme. Then we propose an optimization algorithm to find the weights in linear time complexity, based on the Logitnormal priori distribution and the Maximum a Posteriori principle. Experimental studies show the effectiveness and suitability of the proposed model for high-dimensional data classification.

Clustering high-dimensional data is a major challenge due to the curse of dimensionality. To solve this problem, projective clustering has been defined as an extension to traditional clustering that attempts to find projected clusters in subsets of the dimensions of a data space. In this paper, a probability model is first proposed to describe projected clusters in high-dimensional data space. Then, we present a model-based algorithm for fuzzy projective clustering that discovers clusters with overlapping boundaries in various projected subspaces. The suitability of the proposal is demonstrated in an empirical study done with synthetic data set and some widely used real-world data set.

Clustering high dimensional data is a big challenge in data mining due to the curse of dimensionality. To solve this problem, projective clustering has been defined as an extension of traditional clustering that seeks to find projected clusters in subsets of dimensions of a data space. In this paper, the problem of modeling projected clusters is first discussed, and an extended Gaussian model is proposed. Second, a general objective criterion used with k-means type projective clustering is presented based on the model. Finally, the expressions to learn model parameters are derived and then used in a new algorithm named FPC to perform fuzzy clustering on high dimensional data. The experimental results on document clustering show the effectiveness of the proposed clustering model.