Time Series Clustering Method Based on Principal Component Analysis

Time series clustering via matrix profile and community detection

Time series clustering has been applied in many scientific domains and has attracted much attention in recent years. In this paper, a novel hypergraph based clustering method for time series is proposed, combining multiple similarity measures and hypergraph partitioning. We firstly build the hypergraph for time series dataset using multiple similarity measures, where each time series is represented by vertex and hyperedge is formed based on the similarity relation among time series. Then, the vertices in the constructed hypergraph are grouped by the hypergraph partitioning method to identify the clusters of time series. Two different strategies for hypergraph construction are presented in detail, resulting in two specific methods. Empirical experiments of time series clustering with the UCR archive are conducted for the purpose of evaluation. The results demonstrate that the proposed methods outperform contrast clustering methods in most of the tested datasets and also achieve better performance than the network based methods under consideration, owe to the combination of advantages of hypergraph and various similarity measures.

Improved time series clustering based on new geometric frameworks

Identifying the module structure of swarms using a new framework of network-based time series clustering

The time series clustering is one of the important research contents in the time series data mining. Since the dimension of time series is common high, the performance of direct raw time series data clustering is not ideal. How to improve the clustering performance of time series is the main research point of this paper. Firstly, use Locality Preserving Projection (LPP) to time series samples for dimensionality reduction; secondly, carry out clustering ensemble to the lowdimension data; finally, compare the clustering performance with the existing methods such as Principal Component Analysis (PCA) and Piecewise Aggregate Approximation (PAA). Experiment results show that the proposed method is superior to the compared methods.

The high dimension of multivariate time series (MTS) is one of the major factors that impact on the efficiency and effectiveness of data mining. It has two kinds of dimensions, time-based dimensionality, and variable-based dimensionality. They often cause most of the algorithms and techniques applied to the field of MTS data mining to be a failure. In view of the importance of the correlation between any two variables in an MTS, the covariances between any two variables are applied to analyze the extraction of the features for every MTS. In this way, a covariance sequence can be constructed to represent the characteristic of the MTS. Furthermore, an excellent method of dimensionality reduction, principal component analysis (PCA), is used to extract the features of the covariance sequences that derived from an MTS dataset. Thus Euclidean distance is suitable to measure the similarity between the features fast. The experimental results demonstrate that the proposed method not only can handle multivariate time series with different lengths but also is more efficient and effective than the existing methods for the MTS data mining.

One of the main challenging subjects of data mining is fuzzy-clustering time series in real-world applications. Its reason can be time-series data characteristics that include high dimensional, large volume and existence of temporal ordering in data. So far, many studies have performed about issues such as addressing time-series data high dimension and applying a different effect of each dimension in clustering results. In many of the recent published resources, feature-weighting process in time-series data has employed as one effective way to overcome mentioned problems. Appropriate weight's assignment can discuss as one challenge in mentioned resources. Hence, aim of this paper is optimization of the feature-weighting process in time series clustering task. For this aim, a technique is proposed based on the combination of two fundamental concepts, including features effect-based weighting and optimization in order to optimize weight's assignment in time series clustering. Proposed technique is made possibility use of the merits of two concepts in order to improving performance fuzzy-clustering task in time-series data. Fuzzy Particle Swarm Optimization (FPSO) is used as a population-based technique for optimization of feature-weighting process and enhancing performance of clustering. Proposed technique is evaluated based on three indexes validity that includes Partition Coefficient (PC), Partition Entropy (PE) and Davios-Bouldin (DB). Experimental results are indicated that our proposed technique is efficient and can represent encouraging results. Also, clustering results by population-based a proposed technique is demonstrated the improvement of performance of fuzzy-clustering time series than other conventional techniques.

Time series clustering finds applications in diverse fields of science and technology. Kernel based clustering methods like kernel K-means method need number of clusters as input and cannot handle outliers or noise. In this paper, we propose a density based clustering method in kernel feature space for clustering multivariate time series data of varying length. This method can also be used for clustering any type of structured data, provided a kernel which can handle that kind of data is used. We present heuristic methods to find the initial values of the parameters used in our proposed algorithm. To show the effectiveness of this method, this method is applied to two different online handwritten character data sets which are multivariate time series data of varying length, as a real world application. The performance of the proposed method is compared with the spectral clustering and kernel k-means clustering methods. Besides handling outliers, the proposed method performs as well as the spectral clustering method and outperforms the kernel k-means clustering method.

The study is focused on experimental comparison of time series models of two classes, namely, artificial neural networks and fuzzy time series models. In each class, three basic models of the time series were selected to compare their predictive abilities, which were evaluated by the MAPE criterion. To the class of models using artificial neural networks, multilayer perceptron networks, as well as RNNs, containing LSTM or GRU blocks in the hidden layer, were investigated. In this study, three basic fuzzy time series models were used: the model with fuzzified time series values, the model with fuzzified first differences of time series values, and the model based on the elementary fuzzy tendency. A comparative study was conducted based on dataset of time series, which were divided into two groups relative to the length of time series. An experimental study showed that for medium-term time series on the test interval, the RNNs based on LSTM showed the smallest error on average (MAPE = 3.0013%), and for the short-term time series, the fuzzy models showed the smallest error on average (MAPE = 5.7313%), while models of the ANN class predicted the short-term time series with MAPE > 9.8% in average.

Time series clustering is a pivotal technique for efficiently mining the structure of data. However, time series data possess unique characteristics such as periodicity, nonlinearity and sensitivity to high-frequency noise in dynamic environments, which significantly impact the performance of clustering methods. Recently, deep clustering has garnered widespread attention for its outstanding performance in capture multi-scale temporal dependencies. Despite this, existing methods struggle to effectively captured the similarities and diverse temporal patterns in noisy time series. Accordingly, we propose a novel deep time series clustering framework integrating spectral-adaptive masking with hierarchical contrastive learning. First, an enhanced encoder is designed to generate representations of time series through the incorporation of a frequency-domain adaptive noise filter, which dynamically suppress high-frequency fluctuations by learning threshold parameters from spectral power distributions. Second, hierarchical contrastive information is captured at both the temporal-level alignment within overlapping segments and instance-level comparisons across augmented subsequences, while simultaneously performing clustering on low-dimensional space and utilizing a novel fuzzy clustering loss to improve robustness against outlier interference. Finally, the network architecture is optimized through the integration of contrastive loss and clustering loss, which achieves end-to-end joint representation learning and clustering assignment. Extensive experiments on various time series datasets demonstrate that our approach outperforms state-of-the-art clustering methods.

In finance, cluster analysis is a tool particularly useful for classifying stock market multivariate time series data related to daily returns, volatility daily stocks returns, commodity prices, volume trading, index, enhanced index tracking portfolio, and so on. In the literature, following different methodological approaches, several clustering methods have been proposed for clustering multivariate time series. In this paper by adopting a fuzzy approach and using the Partitioning Around Medoids strategy, we suggest to cluster multivariate financial time series by considering the dynamic time warping distance. In particular, we proposed a robust clustering method capable to neutralize the negative effects of possible outliers in the clustering process. The clustering method achieves its robustness by adopting a suitable trimming procedure to identify multivariate financial time series more distant from the bulk of data. The proposed clustering method is applied to the stocks composing the FTSE MIB index to identify common time patterns and possible outliers.

Subsequence clustering of multivariate time series is a useful tool for discovering repeated patterns in temporal data. Once these patterns have been discovered, seemingly complicated datasets can be interpreted as a temporal sequence of only a small number of states, or clusters. However, discovering these patterns is challenging because it requires simultaneous segmentation and clustering of the time series. Here we propose a new method of model-based clustering, which we call Toeplitz Inverse Covariance-based Clustering (TICC). Each cluster in the TICC method is defined by a correlation network, or Markov random field (MRF), characterizing the interdependencies between different observations in a typical subsequence of that cluster. Based on this graphical representation, TICC simultaneously segments and clusters the time series data. We solve the TICC problem through a scalable algorithm that is able to efficiently solve for tens of millions of observations. We validate our approach by comparing TICC to several state-of-the-art baselines in a series of synthetic experiments, and we then demonstrate on an automobile dataset how TICC can be used to learn interpretable clusters in real-world scenarios.

The common mode error (CME) and optimal noise model are the two most important factors affecting the accuracy of time series in regional Global Navigation Satellite System (GNSS) networks. Removing the CME and selecting the optimal noise model can effectively improve the accuracy of GNSS coordinate time series. The CME, a major source of error, is related to the spatiotemporal distribution; hence, its detrimental effects on time series can be effectively reduced through spatial filtering. Independent component analysis (ICA) is used to filter the time series recorded by 79 GPS stations in Antarctica from 2010 to 2018. After removing stations exhibiting strong local effects using their spatial responses, the filtering results of residual time series derived from principal component analysis (PCA) and ICA are compared and analyzed. The Akaike information criterion (AIC) is then used to determine the optimal noise model of the GPS time series before and after ICA/PCA filtering. The results show that ICA is superior to PCA regarding both the filter results and the consistency of the optimal noise model. In terms of the filtering results, ICA can extract multisource error signals. After ICA filtering, the root mean square (RMS) values of the residual time series are reduced by 14.45%, 8.97%, and 13.27% in the east (E), north (N), and vertical (U) components, respectively, and the associated speed uncertainties are reduced by 13.50%, 8.06% and 11.82%, respectively. Furthermore, different GNSS time series in Antarctica have different optimal noise models with different noise characteristics in different components. The main noise models are the white noise plus flicker noise (WN+FN) and white noise plus power law noise (WN+PN) models. Additionally, the spectrum index of most PN is close to that of FN. Finally, there are more stations with consistent optimal noise models after ICA filtering than there are after PCA filtering.

Dynamic Time Warping (DTW) is a widely used distance measurement in time series clustering. DTW distance is invariant to time series phase perturbations but has a quadratic complexity. An effective acceleration method must reduce the DTW utilization ratio during time series clustering; for example, TADPole uses both upper and lower bounds to prune off a large ratio of expensive DTW calculations. To further reduce the DTW utilization ratio, we find that the linear-complexity L1-norm distance (Manhattan distance) is effective enough when the time series only comprise small phase perturbations. Therefore, we propose a novel time series clustering by Minimizing Dynamic Time Warping Utilization (MiniDTW) algorithm to accelerate time series clustering. In MiniDTW, the dataset is first greedily summarized into seed clusters, which comprise time series of small phase perturbations, by L1-norm distance. Then, we develop a new Sparse Symmetric Non-negative Matrix Factorization (SSNMF) algorithm, which factorizes the DTW distance matrix of seed cluster centers, to merge the seed clusters into the final clusters. The experiments on UCR time series datasets demonstrate that MiniDTW, pruning 98.52% of the DTW utilization, is better than the counterpart method, TADPole, which only prunes 75.56% of the DTW utilization; and thus MiniDTW is 10 times faster than TADPole.

Deep time-series clustering via latent representation alignment