A \(k\)-means procedure based on a Mahalanobis type distance for clustering multivariate functional data. (English) Zbl 1427.62054
Summary: This paper proposes a clustering procedure for samples of multivariate functions in \((L^2(I))^{J}\), with \(J\ge 1\). This method is based on a \(k\)-means algorithm in which the distance between the curves is measured with a metric that generalizes the Mahalanobis distance in Hilbert spaces, considering the correlation and the variability along all the components of the functional data. The proposed procedure has been studied in simulation and compared with the \(k\)-means based on other distances typically adopted for clustering multivariate functional data. In these simulations, it is shown that the \(k\)-means algorithm with the generalized Mahalanobis distance provides the best clustering performances, both in terms of mean and standard deviation of the number of misclassified curves. Finally, the proposed method has been applied to two case studies, concerning ECG signals and growth curves, where the results obtained in simulation are confirmed and strengthened.
MSC:
| 62H30 | Classification and discrimination; cluster analysis (statistical aspects) |
| 62H20 | Measures of association (correlation, canonical correlation, etc.) |
| 62P10 | Applications of statistics to biology and medical sciences; meta analysis |
Keywords:
distances in \(L^2\); \(k\)-means algorithm; multivariate functional data; correlation; Mahalanobis distanceReferences:
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