Unsupervised Curve Clustering using B‐Splines

By Christophe Abraham, P. Cornillon, É. Matzner-Lober, N. Molinari. 2003

387 citations recorded by the source corpus.

Subfields: Analytical Chemistry, Applied Mathematics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/f5a325397f8517e02a43fc6095eda0535d089a3f

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In Analytical Chemistry

In Applied Mathematics

In Statistics and Probability

Citations in the corpus

Classification of non‐parametric regression functions in longitudinal data models (2017, methodology): “There is a vast amount of references which deal with this problem in different model set-ups; see for example Abraham et al. (2003) and Tarpey and Kinateder (2003) for procedures based on k-means clustering, James and Sugar (2003) and Chiou and Li (2007) for so-called model-based clustering…”
Applications of functional data analysis: A systematic review (2013, background): “Application of FDA has also been published across various scientific fields including analysis of child size evolution [9], climatic variation [4,13], handwriting in Chinese [14], acidification processes [15], land usage prediction based on satellite images [16], medical research [17-19], behavioral”
Functional Data Analysis (2016, methodology): “Abraham et al. (2003) derived the strong consistency property of this clustering method, which has been implemented with various basis functions, such as P splines (Coﬀey, Hinde & Holian 2014), a Gaussian orthonormalized basis (Kayano, Dozono & Konishi 2010), and the wavelet basis (Giacofci et al.…”
On the Kernel Rule for Function Classification (2006, methodology): “Key references on this topic are Rice and Silverman [26], Kneip and Gasser [16], Kulkarni and Posner [18], Ramsay and Silverman [25], Bosq [5], Ferraty and Vieu [12], [13], [14], Diabo-Niang and Rhomari [11], Hall, Poskitt and Pres-nell [15], Abraham, Cornillon, Matzner-Løber and Molinari [1], Anton”
Functional clustering and identifying substructures of longitudinal data (2007, methodology): “Reasons for this include, but are not limited to, the fact that index sets or recording times are not always the same for curves as they are for irregular designs, the number of measurements in index sets are very large and measurement errors may be present (Abraham et al., 2003).”
A survey of functional principal component analysis (2014, methodology): “Due to its practical advantages, functional data analysis has received considerable attention in diverse areas of application, such as: the study of acidification processes (Abraham et al. 2003), the analysis of growth curve (Rao 1958), the analysis of handwritten statistics in Chinese (Ramsay 2000)”
Model-based clustering for multivariate functional data (2013, methodology): “Recently, several new approaches considers the k-means algorithm applied to a B-spline fitting (Abraham et al., 2003), to defined principal points of curves (Tarpey and Kinateder, 2003) or to a truncation of the Karhunen-Loeve expansion (Chiou and Li, 2007). Sangalli et al. (2010) also use a k-means”
Functional data clustering: a survey (2013, methodology): “In Abraham et al. (2003) and Peng and Müller (2008) the k-means algorithm is used on B-splines coefﬁcients (Abraham et al. 2003) and on principal component scores (Peng and Müller 2008).”