scholarly journals Using Permutations for Hierarchical Clustering of Time Series

Entropy ◽  
2019 ◽  
Vol 21 (3) ◽  
pp. 306 ◽  
Author(s):  
Jose Cánovas ◽  
Antonio Guillamón ◽  
María Ruiz-Abellón
Keyword(s):  
Time Series ◽  
Hierarchical Clustering ◽  
Real Data ◽  
Distance Measures ◽  
Data Series ◽  
Clustering Methods ◽  
Linkage Method ◽  
Hierarchical Clustering Methods ◽  
Simulated Time ◽  
Simulated Time Series

Two distances based on permutations are considered to measure the similarity of two time series according to their strength of dependency. The distance measures are used together with different linkages to get hierarchical clustering methods of time series by dependency. We apply these distances to both simulated theoretical and real data series. For simulated time series the distances show good clustering results, both in the case of linear and non-linear dependencies. The effect of the embedding dimension and the linkage method are also analyzed. Finally, several real data series are properly clustered using the proposed method.

scholarly journals Weighted Linear Recurrent Forecasting in Singular Spectrum Analysis

2019 ◽  
Vol 19 (01) ◽  
pp. 2050010
Author(s):  
Mahdi Kalantari ◽  
Hossein Hassani ◽  
Emmanuel Sirimal Silva
Keyword(s):  
Time Series ◽  
Spectrum Analysis ◽  
Singular Spectrum Analysis ◽  
Real Data ◽  
Recurrent Relation ◽  
Singular Spectrum ◽  
Viable Solution ◽  
Simulated Time ◽  
Simulated Time Series

Singular Spectrum Analysis (SSA) is an increasingly popular time series filtering and forecasting technique. Owing to its widespread applications in a variety of fields, there is a growing interest towards improving its forecasting capabilities. As such, this paper takes into consideration the Recurrent forecasting approach in SSA (SSA-R) and presents a new mechanism for improving the accuracy of forecasts attainable via this method. The proposed Recurrent SSA-R approach is referred to as Weighted SSA-R (W:SSA-R), and we propose using a weighting algorithm for weigthing the coefficients of the Linear Recurrent Relation (LRR). The performance of forecasts from the W:SSA-R approach are compared with forecasts from the established SSA-R approach. We exploit real data and various simulated time series for the comparison, so as to provide the reader with more conclusive findings. Our results confirm that the W:SSA-R approach can provide comparatively more accurate forecasts and is indeed a viable solution for improving forecasts by SSA.

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

AppliedMath ◽  
2021 ◽  
Vol 1 (1) ◽  
pp. 18-36
Author(s):  
Hossein Hassani ◽  
Mahdi Kalantari ◽  
Christina Beneki
Keyword(s):  
Time Series ◽  
Hierarchical Clustering ◽  
Spectrum Analysis ◽  
Visual Information ◽  
Singular Spectrum Analysis ◽  
Clustering Methods ◽  
Dissimilarity Matrix ◽  
Singular Spectrum ◽  
Wide Range ◽  
Hierarchical Clustering Methods

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.

scholarly journals Scale-dependent intrinsic entropies of complex time series

2016 ◽  
Vol 374 (2065) ◽  
pp. 20150204 ◽  
Author(s):  
Jia-Rong Yeh ◽  
Chung-Kang Peng ◽  
Norden E. Huang
Keyword(s):  
Time Series ◽  
Time Scales ◽  
Spatial Scales ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Complex Time ◽  
Multi Scale ◽  
Mode Decomposition ◽  
Simulated Time ◽  
Simulated Time Series

Multi-scale entropy (MSE) was developed as a measure of complexity for complex time series, and it has been applied widely in recent years. The MSE algorithm is based on the assumption that biological systems possess the ability to adapt and function in an ever-changing environment, and these systems need to operate across multiple temporal and spatial scales, such that their complexity is also multi-scale and hierarchical. Here, we present a systematic approach to apply the empirical mode decomposition algorithm, which can detrend time series on various time scales, prior to analysing a signal’s complexity by measuring the irregularity of its dynamics on multiple time scales. Simulated time series of fractal Gaussian noise and human heartbeat time series were used to study the performance of this new approach. We show that our method can successfully quantify the fractal properties of the simulated time series and can accurately distinguish modulations in human heartbeat time series in health and disease.

scholarly journals Machine-learning identification of asteroid groups

2019 ◽  
Vol 488 (1) ◽  
pp. 1377-1386 ◽  
Author(s):  
V Carruba ◽  
S Aljbaae ◽  
A Lucchini
Keyword(s):  
Machine Learning ◽  
Hierarchical Clustering ◽  
Clustering Algorithms ◽  
Family Members ◽  
Parent Body ◽  
Clustering Methods ◽  
New Family ◽  
Hierarchical Clustering Methods ◽  
Rotational Failure ◽  
Asteroid Families

ABSTRACT Asteroid families are groups of asteroids that share a common origin. They can be the outcome of a collision or be the result of the rotational failure of a parent body or its satellites. Collisional asteroid families have been identified for several decades using hierarchical clustering methods (HCMs) in proper elements domains. In this method, the distance of an asteroid from a reference body is computed, and, if it is less than a critical value, the asteroid is added to the family list. The process is then repeated with the new object as a reference, until no new family members are found. Recently, new machine-learning clustering algorithms have been introduced for the purpose of cluster classification. Here, we apply supervised-learning hierarchical clustering algorithms for the purpose of asteroid families identification. The accuracy, precision, and recall values of results obtained with the new method, when compared with classical HCM, show that this approach is able to found family members with an accuracy above 89.5 per cent, and that all asteroid previously identified as family members by traditional methods are consistently retrieved. Values of the areas under the curve coefficients below Receiver Operating Characteristic curves are also optimal, with values consistently above 85 per cent. Overall, we identify 6 new families and 13 new clumps in regions where the method can be applied that appear to be consistent and homogeneous in terms of physical and taxonomic properties. Machine-learning clustering algorithms can, therefore, be very efficient and fast tools for the problem of asteroid family identification.

scholarly journals Using hierarchical clustering to explore patterns of deprivation among English local authorities

2019 ◽  
Vol 42 (4) ◽  
pp. 772-777
Author(s):  
Steven L Senior
Keyword(s):  
Hierarchical Clustering ◽  
Demographic Characteristics ◽  
Homogeneous Group ◽  
Statistical Testing ◽  
Clustering Methods ◽  
Local Authorities ◽  
Multiple Deprivation ◽  
Hierarchical Clustering Methods ◽  
Different Levels ◽  
Indices Of Multiple Deprivation

Abstract Background The English Indices of Multiple Deprivation (IMD) is widely used as a measure of deprivation. However, similarly ranked areas can differ substantially in the underlying domains of deprivation. These domains contain a richer set of data that might be useful for classifying local authorities. Clustering methods offer a set of techniques to identify groups of areas with similar patterns of deprivation. Methods Hierarchical agglomerative (i.e. bottom-up) clustering methods were applied to domain scores for 152 upper tier local authorities. Advances in statistical testing allow clusters to be identified that are unlikely to have arisen from random partitioning of a homogeneous group. The resulting clusters are described in terms of their subdomain scores and basic geographic and demographic characteristics. Results Five statistically significant clusters of local authorities were identified. These clusters only partially reflect different levels of overall deprivation. In particular, two clusters share similar overall IMD scores but have contrasting patterns of deprivation. Conclusion Hierarchical clustering methods identify five distinct clusters that do not correspond closely to quintiles of deprivation. This approach may help to distinguish between places that face similar underlying challenges, and places that appear similar in terms of overall deprivation scores, but that face different challenges.

Research on NMF Based Hierarchical Clustering Methods

2010 ◽  
Vol 439-440 ◽  
pp. 1306-1311
Author(s):  
Fang Li ◽  
Qun Xiong Zhu
Keyword(s):  
Hierarchical Clustering ◽  
Clustering Algorithm ◽  
Clustering Methods ◽  
Agglomerative Clustering ◽  
Clustering Method ◽  
Hierarchical Agglomerative Clustering ◽  
Hierarchical Clustering Methods

LSI based hierarchical agglomerative clustering algorithm is studied. Aiming to the problems of LSI based hierarchical agglomerative clustering method, NMF based hierarchical clustering method is proposed and analyzed. Two ways of implementing NMF based method are introduced. Finally the result of two groups of experiment based on the TanCorp document corpora show that the method proposed is effective.

Singular Spectrum Analysis Based on L1-Norm

2016 ◽  
Vol 15 (01) ◽  
pp. 1650009 ◽  
Author(s):  
Mahdi Kalantari ◽  
Masoud Yarmohammadi ◽  
Hossein Hassani
Keyword(s):  
Time Series ◽  
Spectrum Analysis ◽  
Singular Spectrum Analysis ◽  
Frobenius Norm ◽  
L1 Norm ◽  
Empirical Results ◽  
Singular Spectrum ◽  
Simulated Time ◽  
Simulated Time Series ◽  
Basic Version

In recent years, the singular spectrum analysis (SSA) technique has been further developed and increasingly applied to solve many practical problems. The aim of this research is to introduce a new version of SSA based on [Formula: see text]-norm. The performance of the proposed approach is assessed by applying it to various real and simulated time series, especially with outliers. The results are compared with those obtained using the basic version of SSA which is based on the Frobenius norm or [Formula: see text]-norm. Different criteria are also examined including reconstruction errors and forecasting performances. The theoretical and empirical results confirm that SSA based on [Formula: see text]-norm can provide better reconstruction and forecasts in comparison to basic SSA when faced with time series which are polluted by outliers.

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