Quantile-based fuzzy C-means clustering of multivariate time series: Robust techniques

Hard and soft clustering of categorical time series based on two novel distances with an application to biological sequences

“…There are at least three interesting ways through which this work could be extended. First, robust versions of the proposed methods could be constructed by considering the so-called metric, noise, and trimmed approaches [54,10,17], which adjust the objective function of the clustering algorithm in a suitable manner so that outlier series do not pervert the resulting partition. Second, a spatial penalisation term could be incorporated in the objective function of the procedures in order to deal with OTS data sets containing geographical information [39,38], like the one considered in Section 5.1.…”

“…Once the membership degrees are obtained through (17), the C series minimising the objective function in (16) are selected as the new medoids. Specifically, for each c ∈ {1, .…”

“…As in the case of d ACF , in an ordinal context, the computation of d QAF must be based on the corresponding count time series. Several time series clustering procedures using quantile-based features have been proposed in the literature [40,15,16,17]. These methods usually show a great performance when the clusters are characterised by different nonlinear structures.…”

“…Some other works propose to replace each series in the collection by a vector of model-free features describing its behaviour in a suitable way. Then, the computed vectors are used as input to a standard clustering method [11,12,13,14,15,16,17]. Alternative techniques are based on reducing the dimensionality of the original time series as a preliminary step [18,19,20].…”

“…On the contrary, a structure-based dissimilarity is desirable if the target is to compare underlying dependence models. Examples of this type of distances are metrics comparing the autocorrelations [10], the quantile autocovariances [11], the quantile cross-spectral densities [12,13,14,15], the wavelet representations [16] or the wavelet coefficients [17] of two time series. Additional types of dissimilarities are based on dimensionality reduction techniques [18,19] or levels of shared information [20,21].…”