Advances in Data Analysis and Classification最新文献

Modal clustering is an unsupervised learning technique where cluster centers are identified as the local maxima of nonparametric probability density estimates. A natural algorithmic engine for the computation of these maxima is the mean shift procedure, which is essentially an iteratively computed chain of local means. We revisit this technique, focusing on its link to kernel density gradient estimation, in this course proposing a novel concept for bandwidth selection based on the concept of a critical bandwidth. Furthermore, in the one-dimensional case, an inverse version of the mean shift is developed to provide a novel approach for the estimation of antimodes, which is then used to identify cluster boundaries. A simulation study is provided which assesses, in the univariate case, the classification accuracy of the mean-shift based clustering approach. Three (univariate and multivariate) examples from the fields of philately, engineering, and imaging, illustrate how modal clusterings identified through mean shift based methods relate directly and naturally to physical properties of the data-generating system. Solutions are proposed to deal computationally efficiently with large data sets.

After being trained on a fully-labeled training set, where the observations are grouped into a certain number of known classes, novelty detection methods aim to classify the instances of an unlabeled test set while allowing for the presence of previously unseen classes. These models are valuable in many areas, ranging from social network and food adulteration analyses to biology, where an evolving population may be present. In this paper, we focus on a two-stage Bayesian semiparametric novelty detector, also known as Brand, recently introduced in the literature. Leveraging on a model-based mixture representation, Brand allows clustering the test observations into known training terms or a single novelty term. Furthermore, the novelty term is modeled with a Dirichlet Process mixture model to flexibly capture any departure from the known patterns. Brand was originally estimated using MCMC schemes, which are prohibitively costly when applied to high-dimensional data. To scale up Brand applicability to large datasets, we propose to resort to a variational Bayes approach, providing an efficient algorithm for posterior approximation. We demonstrate a significant gain in efficiency and excellent classification performance with thorough simulation studies. Finally, to showcase its applicability, we perform a novelty detection analysis using the openly-available Statlog dataset, a large collection of satellite imaging spectra, to search for novel soil types.

Insurance fraud is a non self-revealing type of fraud. The true historical labels (fraud or legitimate) are only as precise as the investigators’ efforts and successes to uncover them. Popular approaches of supervised and unsupervised learning fail to capture the ambiguous nature of uncertain labels. Imprecisely observed labels can be represented in the Dempster–Shafer theory of belief functions, a generalization of supervised and unsupervised learning suited to represent uncertainty. In this paper, we show that partial information from the historical investigations can add valuable, learnable information for the fraud detection system and improves its performances. We also show that belief function theory provides a flexible mathematical framework for concept drift detection and cost sensitive learning, two common challenges in fraud detection. Finally, we present an application to a real-world motor insurance claim fraud.

Logistic regression is one of the most popular statistical techniques for solving (binary) classification problems in various applications (e.g. credit scoring, cancer detection, ad click predictions and churn classification). Typically, the maximum likelihood estimator is used, which is very sensitive to outlying observations. In this paper, we propose a robust and sparse logistic regression estimator where robustness is achieved by means of the (gamma)-divergence. An elastic net penalty ensures sparsity in the regression coefficients such that the model is more stable and interpretable. We show that the influence function is bounded and demonstrate its robustness properties in simulations. The good performance of the proposed estimator is also illustrated in an empirical application that deals with classifying the type of fuel used by cars.

In finite mixture of regression models, normal assumption for the errors of each regression component is typically adopted. Though this common assumption is theoretically and computationally convenient, it often produces inefficient and undesirable estimates which undermine the applicability of the model particularly in the presence of outliers. To reduce these defects, we propose to use nonparametric Gaussian scale mixture distributions for component error distributions. By this means, we can lessen the risk of misspecification and obtain robust estimators. In this paper, we study the identifiability of the proposed model and develop a feasible estimating algorithm. Numerical studies including simulation studies and real data analysis to demonstrate the performance of the proposed method are also presented.

Motivated by a public suggestion by the famous novelist Kurt Vonnegut, we clustered functional data that represented sentiment curves for famous fictional stories. We analyzed text data from novels written between 1612 and 1925, and transformed them into curves measuring sentiment as a function of the percentage of elapsed contents of the novel. We employed sentence-level sentiment evaluation and nonparametric curve smoothing. Our clustering methods involved finding the optimal number of clusters, aligning curves using different chronological warping functions to account for phase and amplitude variation, and implementing functional K-means algorithms under the square root velocity framework. Our results revealed insights about patterns in fictional narratives that Vonnegut and others have suggested but not analyzed in a functional way.

In order to investigate exchanges between objects, a clustering model for skew-symmetric data is proposed, which relies on the between-cluster effects of the skew-symmetries that represent the imbalances of the observed exchanges between pairs of objects. The aim is to detect clusters of objects that share the same behaviour of exchange so that origin and destination clusters are identified. The proposed model is based on the decomposition of the skew-symmetric matrix pertaining to the imbalances between clusters into a sum of a number of off-diagonal block matrices. Each matrix can be approximated by a skew-symmetric matrix by using a truncated Singular Value Decomposition (SVD) which exploits the properties of the skew-symmetric matrices. The model is fitted in a least-squares framework and an efficient Alternating Least Squares algorithm is provided. Finally, in order to show the potentiality of the model and the features of the resulting clusters, an extensive simulation study and an illustrative application to real data are presented.

Spectral clustering is widely used for detecting clusters in networks for community detection, while a small change on the graph Laplacian matrix could bring a dramatic improvement. In this paper, we propose a dual regularized graph Laplacian matrix and then employ it to the classical spectral clustering approach under the degree-corrected stochastic block model. If the number of communities is known as K, we consider more than K leading eigenvectors and weight them by their corresponding eigenvalues in the spectral clustering procedure to improve the performance. The improved spectral clustering method is dual regularized spectral clustering (DRSC). Theoretical analysis of DRSC shows that under mild conditions it yields stable consistent community detection. Meanwhile, we develop a strategy by taking advantage of DRSC and Newman’s modularity to estimate the number of communities K. We compare the performance of DRSC with several spectral methods and investigate the behaviors of our strategy for estimating K by substantial simulated networks and real-world networks. Numerical results show that DRSC enjoys satisfactory performance and our strategy on estimating K performs accurately and consistently, even in cases where there is only one community in a network.