Learning fuzzy systems: an ojective function-approach

One of the most important aspects of fuzzy systems is that they are easily understandable and interpretable. This property, however, does not come for free but poses some essential constraints on the parameters of a fuzzy system (like the linguistic terms), which are sometimes overlooked when learning fuzzy system automatically from data. In this paper, an objective function-based approach to learn fuzzy systems is developed, taking these constraints explicitly into account. Starting from fuzzy c-means clustering, several modifications of the basic algorithm are proposed, affecting the shape of the membership functions, the partition of individual variables and the coupling of input space partitioning and local function approximation

Online Modeling and Monitoring of Dependent Processes under Resource Constraints

Adaptive monitoring of a large population of dynamic processes is critical for the timely detection of abnormal events under limited resources in many healthcare and engineering systems. Examples include the risk-based disease screening and condition-based process monitoring. However, existing adaptive monitoring models either ignore the dependency among processes or overlook the uncertainty in process modeling. To design an optimal monitoring strategy that accurately monitors the processes with poor health conditions and actively collects information for uncertainty reduction, a novel online collaborative learning method is proposed in this study. The proposed method designs a collaborative learning-based upper confidence bound (CL-UCB) algorithm to optimally balance the exploitation and exploration of dependent processes under limited resources. Efficiency of the proposed method is demonstrated through theoretical analysis, simulation studies and an empirical study of adaptive cognitive monitoring in Alzheimer's disease

Model-Based Clustering and Classification of Functional Data

The problem of complex data analysis is a central topic of modern statistical science and learning systems and is becoming of broader interest with the increasing prevalence of high-dimensional data. The challenge is to develop statistical models and autonomous algorithms that are able to acquire knowledge from raw data for exploratory analysis, which can be achieved through clustering techniques or to make predictions of future data via classification (i.e., discriminant analysis) techniques. Latent data models, including mixture model-based approaches are one of the most popular and successful approaches in both the unsupervised context (i.e., clustering) and the supervised one (i.e, classification or discrimination). Although traditionally tools of multivariate analysis, they are growing in popularity when considered in the framework of functional data analysis (FDA). FDA is the data analysis paradigm in which the individual data units are functions (e.g., curves, surfaces), rather than simple vectors. In many areas of application, the analyzed data are indeed often available in the form of discretized values of functions or curves (e.g., time series, waveforms) and surfaces (e.g., 2d-images, spatio-temporal data). This functional aspect of the data adds additional difficulties compared to the case of a classical multivariate (non-functional) data analysis. We review and present approaches for model-based clustering and classification of functional data. We derive well-established statistical models along with efficient algorithmic tools to address problems regarding the clustering and the classification of these high-dimensional data, including their heterogeneity, missing information, and dynamical hidden structure. The presented models and algorithms are illustrated on real-world functional data analysis problems from several application area