Comparative Assessment of Hierarchical Clustering Methods for Grouping in Singular Spectrum Analysis

Christina Beneki,Hossein Hassani,Mahdi Kalantari

doi:10.3390/appliedmath1010003

Christina Beneki, Hossein Hassani + Show 1 more

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https://doi.org/10.3390/appliedmath1010003

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Abstract

Singular spectrum analysis (SSA) is a popular filtering and forecasting method that is used in a wide range of fields such as time series analysis and signal processing. A commonly used approach to identify the meaningful components of a time series in the grouping step of SSA is the utilization of the visual information of eigentriples. Another supplementary approach is that of employing an algorithm that performs clustering based on the dissimilarity matrix defined by weighted correlation between the components of a time series. The SSA literature search revealed that no investigation has compared the various clustering methods. The aim of this paper was to compare the effectiveness of different hierarchical clustering linkages to identify the appropriate groups in the grouping step of SSA. The comparison was performed based on the corrected Rand (CR) index as a comparison criterion that utilizes various simulated series. It was also demonstrated via two real-world time series how one can proceed, step-by-step, to conduct grouping in SSA using a hierarchical clustering method. This paper is supplemented with accompanying R codes.

Highlights

Singular spectrum analysis (SSA) is a model-free technique that decomposes a time series into a number of meaningful components
The results reported in these tables show that the single, median and centroid linkages can exactly identify the correct groups in FORT series
In this paper, we conducted a comparison study in order to find a proper hierarchical clustering method to identify the appropriate groups at the grouping step of SSA

Summary

Introduction

Singular spectrum analysis (SSA) is a model-free technique that decomposes a time series into a number of meaningful components. Owing to its widespread applications in various fields, this non-parametric method has received much attention in recent years. Examples of the wide variety of SSA applications can be found in [1,2,3,4,5,6,7,8,9]. A whole and precise detailed summary of the theory and applications of SSA can be found in [10,11]. There are other books devoted to SSA; for example, Refs. A comprehensive review of SSA and the description of its modifications and extensions can be found in [15]

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