Model-based clustering for multivariate functional data
Julien Jacques,Cristian Preda +1 more
TL;DR: 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.
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About: This article is published in Computational Statistics & Data Analysis. The article was published on 01 Mar 2014. and is currently open access. The article focuses on the topics: Correlation clustering & Cluster analysis.
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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
Regularization and variable selection via the elastic net
Hui Zou,Trevor Hastie +1 more
TL;DR: It is shown that the elastic net often outperforms the lasso, while enjoying a similar sparsity of representation, and an algorithm called LARS‐EN is proposed for computing elastic net regularization paths efficiently, much like algorithm LARS does for the lamba.
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).
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.
441
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.
342
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Model-Based Clustering and Classification for Data Science
Charles Bouveyron,Gilles Celeux,T. Brendan Murphy,Adrian E. Raftery +3 more
- 01 Jul 2019
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.
223
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