Feature Selection in Clustering Problems

Neural Information Processing Systems

A novel approach to combining clustering and feature selection is presented. Itimplements a wrapper strategy for feature selection, in the sense that the features are directly selected by optimizing the discriminative powerof the used partitioning algorithm. On the technical side, we present an efficient optimization algorithm with guaranteed local convergence property.The only free parameter of this method is selected by a resampling-based stability analysis. Experiments with real-world datasets demonstrate that our method is able to infer both meaningful partitions and meaningful subsets of features.

Model-Based Clustering and Classification of Functional Data

arXiv.org Machine Learning

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.

Piecewise regression mixture for simultaneous functional data clustering and optimal segmentation

arXiv.org Machine Learning

This paper introduces a novel mixture model-based approach for simultaneous clustering and optimal segmentation of functional data which are curves presenting regime changes. The proposed model consists in a finite mixture of piecewise polynomial regression models. Each piecewise polynomial regression model is associated with a cluster, and within each cluster, each piecewise polynomial component is associated with a regime (i.e., a segment). We derive two approaches for learning the model parameters. The former is an estimation approach and consists in maximizing the observed-data likelihood via a dedicated expectation-maximization (EM) algorithm. A fuzzy partition of the curves in K clusters is then obtained at convergence by maximizing the posterior cluster probabilities. The latter however is a classification approach and optimizes a specific classification likelihood criterion through a dedicated classification expectation-maximization (CEM) algorithm. The optimal curve segmentation is performed by using dynamic programming. In the classification approach, both the curve clustering and the optimal segmentation are performed simultaneously as the CEM learning proceeds. We show that the classification approach is the probabilistic version that generalizes the deterministic K-means-like algorithm proposed in H\'ebrail et al. (2010). The proposed approach is evaluated using simulated curves and real-world curves. Comparisons with alternatives including regression mixture models and the K-means like algorithm for piecewise regression demonstrate the effectiveness of the proposed approach.

A nonparametric framework for inferring orders of categorical data from category-real ordered pairs

arXiv.org Machine Learning

Given a dataset of careers and incomes, how large a difference of income between any pair of careers would be? Given a dataset of travel time records, how long do we need to spend more when choosing a public transportation mode $A$ instead of $B$ to travel? In this paper, we propose a framework that is able to infer orders of categories as well as magnitudes of difference of real numbers between each pair of categories using Estimation statistics framework. Not only reporting whether an order of categories exists, but our framework also reports the magnitude of difference of each consecutive pairs of categories in the order. In large dataset, our framework is scalable well compared with the existing framework. The proposed framework has been applied to two real-world case studies: 1) ordering careers by incomes based on information of 350,000 households living in Khon Kaen province, Thailand, and 2) ordering sectors by closing prices based on 1060 companies' closing prices of NASDAQ stock markets between years 2000 and 2016. The results of careers ordering show income inequality among different careers. The stock market results illustrate dynamics of sector domination that can change over time. Our approach is able to be applied in any research area that has category-real ordered pairs. Our proposed "Dominant-Distribution Network" provides a novel approach to gain new insight of analyzing category orders. The software of this framework is available for researchers or practitioners within R package: EDOIF.

Deep clustering of longitudinal data

arXiv.org Machine Learning

Deep neural networks are a family of computational models that have led to a dramatical improvement of the state of the art in several domains such as image, voice or text analysis. These methods provide a framework to model complex, non-linear interactions in large datasets, and are naturally suited to the analysis of hierarchical data such as, for instance, longitudinal data with the use of recurrent neural networks. In the other hand, cohort studies have become a tool of importance in the research field of epidemiology. In such studies, variables are measured repeatedly over time, to allow the practitioner to study their temporal evolution as trajectories, and, as such, as longitudinal data. This paper investigates the application of the advanced modelling techniques provided by the deep learning framework in the analysis of the longitudinal data provided by cohort studies. Methods: A method for visualizing and clustering longitudinal dataset is proposed, and compared to other widely used approaches to the problem on both real and simulated datasets. Results: The proposed method is shown to be coherent with the preexisting procedures on simple tasks, and to outperform them on more complex tasks such as the partitioning of longitudinal datasets into non-spherical clusters. Conclusion: Deep artificial neural networks can be used to visualize longitudinal data in a low dimensional manifold that is much simpler to interpret than traditional longitudinal plots are. Consequently, practitioners should start considering the use of deep artificial neural networks for the analysis of their longitudinal data in studies to come.