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Qiao, Xinghao, James, Gareth M. and Sun, Wenguang (2012) Comment. Technometrics, 54 (2). pp. 123-126. ISSN 0040-1706

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Identification Number: 10.1080/00401706.2011.649819


We would like to congratulate the authors on an interesting and stimulating article on spatially correlated clustering of functional data. Reading their work led us to consider the tradeoffs of the functional paradigm in relation to other strategies. In this discussion, we summarize the functional clustering method and suggest an alternative approach to the problem. The situation that is under consideration involves observed data, Yij =Y(sj , ti ), which is a realization of a spatial-temporal process where S={s 1, …, sn } is the collection of spatial locations and T={t 1, …, tm } is the collection of time points. Clustering could be performed directly on the n×m observations. Instead the authors have elected to model the data as functional in the time dimension, taking the view that the Yij ’s are measurements of n spatially interdependent curves {Yj (t), j=1, …, n}. Under this paradigm, the data consist of n functional observations, each with a unique cluster membership; thus a cluster is defined as a collection of locations with similar temporal patterns. The goal is to divide the spatial domain into clusters by extracting information from the shapes of the underlying curves. Clustering of functional data has been previously explored in a number of articles. However, most previous approaches have assumed that cluster memberships for each function are independent. The key contribution that the authors make is to incorporate a spatial correlation structure among the cluster memberships, Z j ={Zjc :c∈C}, which are assumed to follow a multinomial distribution, where C is an index set and . In particular the authors propose the following Gibbs distribution to model Z={Z j :j=1, …, n} as coming from a Markov random field (MRF), where ∂ j denotes the spatial neighbors of sj . This approach has the potential to improve the clustering accuracy by exploiting the local dependency among the cluster memberships. In Section 2, we discuss some possible limitations of the functional approach and consider an alternative method where cluster membership can vary over both temporal and spatial domains. Our method has the advantage of allowing time-varying covariates to be included in the clustering process. Section 3 provides details on a fitting algorithm and some simple simulation results to illustrate the approach. We conclude in Section 4 with a brief discussion.

Item Type: Article
Official URL:
Additional Information: © 2012 American Statistical Association and the American Association for Quality TECHNOMETRICS
Divisions: Statistics
Subjects: H Social Sciences > HA Statistics
Date Deposited: 12 Nov 2019 15:03
Last Modified: 20 Jul 2021 01:22

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