Model-based clustering for multivariate functional data
Julien Jacques,Cristian Preda +1 more
TLDR
The first model-based clustering algorithm for multivariate functional data is proposed, based on the assumption of normality of the principal component scores, and it ability to take into account the dependence among curves.About:
This article is published in Computational Statistics & Data Analysis.The article was published on 2014-03-01 and is currently open access. It has received 239 citations till now. The article focuses on the topics: Correlation clustering & Cluster analysis.read more
Figures
Figure 5: Temperature and precipitation curves for 35 locations in Canada, averaged over 1960 to 1994. The top figures are the original curves and the bottom figures are the reduced ones. 
Figure 1: Kneading, Growth and ECG datasets. 
Figure 6: Convergence of the pseudo EM algorithm (top: pseudo likelihood evolution, bottom: approximation orders evolutions). The red part in the pseudo likelihood stops when the maximum is achieved. 
Figure 7: Funclust clustering using the reduced curves into 4 groups. 
Figure 8: K-means clustering using the reduced curves into 4 groups, with distance d1 (left) and d2 right. 
Figure 4: Convergence of the pseudo EM algorithm (top: pseudo likelihood evolution, bottom: approximation orders evolutions). The red part in the pseudo likelihood stops when the maximum is achieved.
Citations
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Journal ArticleDOI
Functional Data Analysis
TL;DR: In this article, the authors provide an overview of FDA, starting with simple statistical notions such as mean and covariance functions, then covering some core techniques, the most popular of which is functional principal component analysis (FPCA).
Journal ArticleDOI
Functional data clustering: a survey
Julien Jacques,Cristian Preda +1 more
TL;DR: Four groups of clustering algorithms for functional data are proposed, composed of methods which perform simultaneously dimensionality reduction of the curves and clustering, leading to functional representation of data depending on clusters.
Journal ArticleDOI
Multivariate Functional Principal Component Analysis for Data Observed on Different (Dimensional) Domains
Clara Happ,Sonja Greven +1 more
TL;DR: In this paper, the theoretical basis for multivariate functional principal component analysis is given in terms of a Karhunen-Loeve Theorem and a relationship between univariate and multivariate FP analysis is established.
Journal ArticleDOI
k-mean alignment for curve clustering
TL;DR: A novel algorithm is described, which jointly clusters and aligns curves and efficiently decouples amplitude and phase variability; in particular, it is able to detect amplitude clusters while simultaneously disclosing clustering structures in the phase.
Book
Model-Based Clustering and Classification for Data Science
TL;DR: In this paper, the authors frame cluster analysis and classification in terms of statistical models, thus yielding principled estimation, testing and prediction methods, and sound answers to the central questions, such as how many clusters are there? which method should I use? How should I handle outliers.
References
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Maximum likelihood from incomplete data via the EM algorithm
Journal ArticleDOI
Estimating the Dimension of a Model
TL;DR: In this paper, the problem of selecting one of a number of models of different dimensions is treated by finding its Bayes solution, and evaluating the leading terms of its asymptotic expansion.
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The scree test for the number of factors
TL;DR: The Scree Test for the Number Of Factors this paper was first proposed in 1966 and has been used extensively in the field of behavioral analysis since then, e.g., in this paper.
Book
Finite Mixture Models
Geoffrey J. McLachlan,David Peel +1 more
TL;DR: The important role of finite mixture models in the statistical analysis of data is underscored by the ever-increasing rate at which articles on mixture applications appear in the mathematical and statistical literature.
Book
Statistical analysis of finite mixture distributions
TL;DR: This course discusses Mathematical Aspects of Mixtures, Sequential Problems and Procedures, and Applications of Finite Mixture Models.