A k-means procedure based on a Mahalanobis type distance for clustering multivariate functional data

Martino, Andrea; Ghiglietti, Andrea; Ieva, Francesca; Paganoni, Anna Maria

doi:10.1007/s10260-018-00446-6

Cited by 29 publications

(34 citation statements)

References 17 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…There are several studies concerning clustering functional data, that show the interest this topic arouses. Here, we have considered two recent works: The distance based k-means procedure (functional k-means) appearing in Martino et al (2019) and the test based kmeans from Zambom et al (2019).…”

Section: The Benchmark For Clustering Functional Datamentioning

confidence: 99%

“…In Martino et al (2019), a clustering procedure based on k-means clustering with the generalized Mahalanobis distance, d ρ , previously defined in Ghiglietti and Paganoni (2017),…”

Section: The Benchmark For Clustering Functional Datamentioning

confidence: 99%

“…(2018) and Franco-Pereira and Lillo ( 2019). The second one consist of two scenarios studied in Martino et al (2019).…”

Section: Simulation Study A: Two Clustersmentioning

confidence: 99%

“…Nevertheless, choosing the correct number of clusters before applying a clustering technique is a challenge. In Martino et al (2019) and Zambom et al (2019) they both fix the number of clusters before performing the classification.…”

Section: Case Study: Growth Data Setmentioning

confidence: 99%

“…In Jacques and Preda (2014) the functional clustering techniques are classified into four categories: raw data methods, which consist on considering the functional data set as a multivariate one and apply there the clustering techniques studied for multivariate data (Boullé (2012)); the filtering methods, that firstly apply a basis to the functional data and then use clustering techniques to the obtained data (Abraham et al (2003), Rossi et al (2004), Peng, Müller, et al (2008), Kayano et al (2010)); adaptive methods, where dimensionality reduction and clustering are performed at the same time (James and Sugar (2003), Jacques and Preda (2013), Giacofci et al (2013), Traore et al (2019)); and distancebased methods, which apply a clustering technique based on distances with a specific distance for functional data (Tarpey and Kinateder (2003), Ieva et al (2011), Martino et al (2019). Recent works which perform different strategies for clustering functional data are Zambom et al (2019) that propose a new method applying k-means, assigning each element to a cluster or another based on a combination of an hypothesis test of parallelism and a test for equality of means, and Schmutz et al (2020) that presents a new strategy for clustering functional data based on applying model based techniques when a principal component analysis is previously performed.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Functional clustering via multivariate clustering

Pulido,

Franco-Pereira,

Lillo

2021

Preprint

View full text Add to dashboard Cite

Clustering techniques applied to multivariate data are a very useful tool in Statistics and have been fully studied in the literature. Nevertheless, these clustering methodologies are less well known when dealing with functional data. Our proposal consists of introducing a clustering procedure for functional data using the very well known techniques for clustering multivariate data. The idea is to reduce a functional data problem to a multivariate data problem by applying the epigraph and the hypograph indexes to the original data and to its first and second derivatives.All the information given by the functional data is therefore transformed to the multivariate context, being sufficiently informative for the usual multivariate clustering techniques to be efficient. The performance of this new methodology is evaluated through a simulation study and it is also illustrated through real data sets.

show abstract

Section: The Benchmark For Clustering Functional Datamentioning

confidence: 99%

“…In Martino et al (2019), a clustering procedure based on k-means clustering with the generalized Mahalanobis distance, d ρ , previously defined in Ghiglietti and Paganoni (2017),…”

Section: The Benchmark For Clustering Functional Datamentioning

confidence: 99%

“…(2018) and Franco-Pereira and Lillo ( 2019). The second one consist of two scenarios studied in Martino et al (2019).…”

Section: Simulation Study A: Two Clustersmentioning

confidence: 99%

Section: Case Study: Growth Data Setmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Functional clustering via multivariate clustering

Pulido,

Franco-Pereira,

Lillo

2021

Preprint

View full text Add to dashboard Cite

show abstract

Multivariate functional data clustering using adaptive density peak detection

Ren

Fang

Zhang

et al. 2023

Statistics in Medicine

View full text Add to dashboard Cite

Clustering for multivariate functional data is a challenging problem since the data are represented by a set of curves and functions belonging to an infinite‐dimensional space. In this article, we propose a novel clustering method for multivariate functional data using an adaptive density peak detection technique. It is a quick cluster center identification algorithm based on the two measures of each functional data observation: the functional density estimate and the distance to the closest observation with a higher functional density. We suggest two types of functional density estimators for multivariate functional data. The first one is a functional k$$ k $$‐nearest neighbor density estimator based on (a) an L2 distance between raw functional curves, or (b) a semimetric of multivariate functional principal components. The second one is a k$$ k $$‐nearest neighbor density estimator based on multivariate functional principal scores. Our clustering method is computationally fast since it does not need an iterative process. The flexibility and advantages of the method are examined by comparing it with other existing clustering methods in simulation studies. A user‐friendly R package FADPclust is developed for public use. Finally, our method is applied to a real case study in lung cancer research.

show abstract

Functional clustering on a sphere via Riemannian functional principal components

Kim

Lim

2023

Stat

View full text Add to dashboard Cite

We propose the functional clustering algorithm applicable to the sphere‐valued random curves, called ‐centres Riemannian functional clustering (kCRFC). It is based on Riemannian functional principal component scores and ‐centres functional clustering algorithm; thus, we can obtain accurate clustering results by reflecting the geometry of the sphere. Our method shows better clustering performances than existing multivariate functional clustering methods in various simulation settings. We apply the proposed method to the migration trajectories of Egyptian Vultures in the Middle East and East Africa and fruit fly behaviours, containing the curves lied on two‐dimensional and three‐dimensional sphere, respectively.

show abstract

A k-means procedure based on a Mahalanobis type distance for clustering multivariate functional data

Cited by 29 publications

References 17 publications

Functional clustering via multivariate clustering

Functional clustering via multivariate clustering

Multivariate functional data clustering using adaptive density peak detection

Functional clustering on a sphere via Riemannian functional principal components

Contact Info

Product

Resources

About