A simple clustering technique to extract subsets of data for function approximation

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.

Clustering is a technique used to classify objects or cases into groups based on their similarity, called clusters or groups. Objects in each group tend to resemble each other and differ greatly (not the same) with objects from other clusters. Public welfare is a condition of fulfilling the material, spiritual and social needs of citizens in order to be able to live properly. Fuzzy Subtractive Clustering (FSC) method is a clustering algorithm that can form the number and centroid of clusters in accordance with data conditions. This study aims to determine the FSC results in grouping the level of welfare of the Indonesian people in 2017. The testing results of the cluster validity index show 2 values of Partition Entropy and Classification Entropy forming into 2 clusters that have the best value, indicating that the provincial group has a high welfare level and the provincial group has a low welfare level.

Deformability of rock masses influencing their behavior is an important geomechanical property for the rock structures design. Due to the problems in determining the deformability of jointed rock masses at the laboratory-scale, various in situ test methods such as plate loading tests, dilatometer etc. have been developed. Although these methods are currently the best techniques, they are expensive and time consuming, and present operational problems. Furthermore, the influence of the test volume on modulus of deformation depending on the technique used is also important. For these reasons, in this paper, the adaptive network-based fuzzy inference system (ANFIS) was used to build a prediction model for the indirect estimation of deformation modulus of a rock mass. Three ANFIS models were implemented by grid partitioning (GP), subtractive clustering method (SCM) and fuzzy c-means clustering method (FCM). The estimation abilities offered using three ANFIS models were presented by using field data of achieved from road and railway construction sites in Korea. In these models, rock mass rating (RMR), depth, uniaxial compressive strength of intact rock (UCS) and elastic modulus of intact rock (Ei) were utilized as the input parameters, while the deformation modulus of a rock mass was the output parameter. Various statistical performance indexes were utilized to compare the performance of those estimation models. The results achieved indicate that the ANFIS-SCM model has strong potential to indirect estimation of deformation modulus of a rock mass with high degree of accuracy and robustness.

In this paper, a novel semi-supervised subtractive clustering method using pair wise constraints is proposed. Because the traditional subtractive clustering method cannot obtain the better clustering accuracies, some pair wise constraints regarded as supervised information are applied to aiding the process of the traditional subtractive clustering. Experimental results show that the new presented semi-supervised clustering method can improve the clustering performance significantly compared to the unsupervised subtractive clustering.

High throughput gene expression analysis using qPCR is commonly used to identify molecular markers of complex cellular processes. However, statistical analysis of multi-dimensional, temporal gene expression data is complicated by limited biological replicates and large number of measurements. Moreover, many available statistical tools for analysis of time series data assume that the data sequence is static and does not evolve over time. With this assumption, the parameters used to model the time series are fixed and thus, can be estimated by pooling data together. However, in many cases, dynamic processes of biological systems involve abrupt changes at unknown time points, making the assumption of stationary time series break down. We addressed this problem using a combination of statistical methods including hierarchical clustering, change point detection, and multiple testing. We applied this multi-step method to multi-dimensional, temporal gene expression data that resulted from our study of colony size-dependent neural cell differentiation of stem cells. The gene expression data were time series as the observations were recorded sequentially over time. Hierarchical clustering segregated the genes into three distinct clusters based on their temporal expression profiles; change point detection identified specific time points at which the entire dataset was divided into several homogenous subsets to allow a separate analysis of each subset; and multiple testing procedure identified the differentially expressed genes in each cluster within each subset of data. We established that our multi-step approach pinpoints specific sets of genes that underlie colony size-mediated neural differentiation of stem cells and demonstrated its advantages over conventional parametric and non-parametric tests that do not take into account temporal dynamics of the data. Importantly, our proposed approach is broadly applicable to any multivariate data sets of limited sample size from high throughput and high content screening such as in drug and biomarker discovery studies.

Support vector machines combining subtractive clustering method are proposed in this paper. Subtractive clustering method is used to select a set of cluster centers which are the data samples themselves as the representation of original massive set of training data. The new training set then is used to construct support vector machines. Two benchmarks on two-class recognition and multi-class problem are tested, and the results show that the support vector machines based on subtractive clustering have better or equal classification accuracy and generalization ability with smaller set of training data and cost less optimization computation time than conventional support vector machines.

Fuzzy model identification based on mixture distribution analysis for bearings remaining useful life estimation using small training data set

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.

This study was conducted to assess the performance of a long short-term memory algorithm (LSTM), which was suitable for time series prediction, in the multivariate dataset with missing values. The full dataset for the adopted LSTM model was prepared by running a popular watershed model Hydrological Simulation Program-Fortran (HSPF) in the upper Nam River Basin for 3 years from 2016 to 2018, excluding a one-year warm-up period, on a daily time step. The accuracy of prediction for the LSTM model was evaluated in response to various interpolation methods as well as changes in the number of missing values (for dependent variables) and independent variables (containing a fixed number of missing values for either single or multiple variables). Note that the entire dataset is divided into training and test datasets at a ratio of 7:3. Results showed that different interpolation methods resulted in a considerable variation in performance of the LSTM model. Out of them, StructTS and RPART were selected as the best imputation methods recovering missing values for discharge and total phosphorus, respectively. The prediction error of the LSTM model increased gradually with increasing the number of missing values from 300 to 700. The LSTM model, however, appeared to maintain its performance fairly well even in data sets with a large amount of missing values as long as adequate interpolation methods were adopted for each dependent variable. The performance of the LSTM model degraded further as the number of independent variables containing the fixed number of missing values increased from 1 to 7. We believe that the proposed methodology can be used not only to reconstruct missing values in a real-time monitoring dataset with excellent performance, but also to improve the accuracy of prediction for (time series) deep learning models.

Prediction of residual stress in the welding zone of dissimilar metals using data-based models and uncertainty analysis

Clustering methods have been widely applied to the fault diagnosis of mechanical system, but the characteristic that the number of cluster needs to be determined in advance limits the application range of the method. In this paper, a novel clustering method combining the adaptive resonance theory (ART) with the similarity measure based on the Yu’s norm is presented and applied to the fault diagnosis of rolling element bearings, which can be adaptive to generate the number of cluster by the vigilance parameter test. Time-domain features, frequency-domain features, and time series model parameters are extracted to demonstrate the fault-related information about the bearings, and then considering the irrelevance or redundancy of some features many salient features are selected by an improved distance discriminant technique and input into the proposed clustering method to diagnose the faults of bearings. The experiment results confirmed that the proposed clustering method can diagnose the fault categories accurately and has better diagnosis performance compared with fuzzy ART and Self-Organizing Feature Map (SOFM).

Clustering is an unsupervised learning approach that explores data and seeks groups of similar objects. Many classical clustering models such as k-means and DBSCAN are based on heuristics algorithms and suffer from local optimal solutions and numerical instability. Recently convex clustering has received increasing attentions, which leverages the sparsity inducing norms and enjoys many attractive theoretical properties. However, convex clustering is based on Euclidean distance and is thus not robust against outlier features. Since the outlier features are very common especially when dimensionality is high, the vulnerability has greatly limited the applicability of convex clustering to analyze many real-world datasets. In this paper, we address the challenge by proposing a novel robust convex clustering method that simultaneously performs convex clustering and identifies outlier features. Specifically, the proposed method learns to decompose the data matrix into a clustering structure component and a group sparse component that captures feature outliers. We develop a block coordinate descent algorithm which iteratively performs convex clustering after outliers features are identified and eliminated. We also propose an efficient algorithm for solving the convex clustering by exploiting the structures on its dual problem. Moreover, to further illustrate the statistical stability, we present the theoretical performance bound of the proposed clustering method. Empirical studies on synthetic data and real-world data demonstrate that the proposed robust convex clustering can detect feature outliers as well as improve cluster quality.

To improve hydro-chemical modeling and forecasting, there is a need to better understand flood-induced variability in water chemistry and the processes controlling it in watersheds. In the literature, assumptions are often made, for instance, that stream chemistry reacts differently to rainfall events depending on the season; however, methods to verify such assumptions are not well developed. Often, few floods are studied at a time and chemicals are used as tracers. Grouping similar events from large multivariate datasets using principal component analysis and clustering methods helps to explain hydrological processes; however, these methods currently have some limits (definition of flood descriptors, linear assumption, for instance). Most clustering methods have been used in the context of regionalization, focusing more on mapping results than on understanding processes. In this study, we extracted flood patterns using the probabilistic Latent Dirichlet Allocation (LDA) model, its first use in hydrology, to our knowledge. The LDA method allows multivariate temporal datasets to be considered without having to define explanatory factors beforehand or select representative floods. We analyzed a multivariate dataset from a long-term observatory (Kervidy-Naizin, western France) containing data for four solutes monitored daily for 12 years: nitrate, chloride, dissolved organic carbon, and sulfate. The LDA method extracted four different patterns that were distributed by season. Each pattern can be explained by seasonal hydrological processes. Hydro-meteorological parameters help explain the processes leading to these patterns, which increases understanding of flood-induced variability in water quality. Thus, the LDA method appears useful for analyzing long-term datasets.

A kernel-based subtractive clustering method

SummaryAccurate prediction of the solubility of chemical substances in solvents remains a challenge. The sparsity of high-quality solubility data is recognized as the biggest hurdle in the development of robust data-driven methods for practical use. Nonetheless, the effects of the quality and quantity of data on aqueous solubility predictions have not yet been scrutinized. In this study, the roles of the size and the quality of data sets on the performances of the solubility prediction models are unraveled, and the concepts of actual and observed performances are introduced. In an effort to curtail the gap between actual and observed performances, a quality-oriented data selection method, which evaluates the quality of data and extracts the most accurate part of it through statistical validation, is designed. Applying this method on the largest publicly available solubility database and using a consensus machine learning approach, a top-performing solubility prediction model is achieved.