Values Of Multivariate Time Series Research Articles

Multivariate time series clustering based on common principal component analysis

Time series clustering is often applied to pattern recognition and also as the basis of the tasks in the field of time series data mining including dimensionality reduction, feature extraction, classification and visualization. Due to the high dimensionality of multivariate time series and most of the previous work concentrating on univariate time series clustering, a novel method which is based on common principal component analysis, is proposed to achieve multivariate time series clustering more fast and accurately. It is inspired by the traditional clustering method K-Means and can construct a common projection axes as prototype of each cluster. Moreover, the reconstruction error of each multivariate time series projected on the corresponding common projection axes are used to reassign the member of the cluster. The detailed algorithm of the proposed method Mc2PCA is given and the time complexity is analyzed, which shows that the proposed method is very fast and its time complexity is linear to the number of multivariate time series objects. Unlike the traditional methods, the proposed method considers the relationship among variables and the distribution of the original data values of multivariate time series. The experimental results in the various datasets demonstrate that Mc2PCA is superior to the traditional methods for multivariate time series clustering.

Short-term load forecasting by using a combined method of convolutional neural networks and fuzzy time series

We propose a combined method that is based on the fuzzy time series (FTS) and convolutional neural networks (CNN) for short-term load forecasting (STLF). Accordingly, in the proposed method, multivariate time series data which include hourly load data, hourly temperature time series and fuzzified version of load time series, was converted into multi-channel images to be fed to a proposed deep learning CNN model with proper architecture. By using images which have been created from the sequenced values of multivariate time series, the proposed CNN model could determine and extract related important parameters, in an implicit and automatic way, without any need for human interaction and expert knowledge, and all by itself. By following this strategy, it was shown how employing the proposed method is easier than some traditional STLF models. Therefore it could be seen as one of the big difference between the proposed method and some state-of-the-art methodologies of STLF. Moreover, using fuzzy logic had great contribution to control over-fitting by expressing one dimension of time series by a fuzzy space, in a spectrum, and a shadow instead of presenting it with exact numbers. Various experiments on test data-sets support the efficiency of the proposed method.

How to model multivariate extremes if one must?

In this paper we discuss some approaches to modeling extremely large values in multivariate time series. In particular, we discuss the notion of multivariate regular variation as a key to modeling multivariate heavy‐tailed phenomena. The latter notion has found a variety of applications in queuing theory, stochastic networks, telecommunications, insurance, finance and other areas. We contrast this approach with modeling multivariate extremes by using the multivariate student distribution and copulas.