Typical load profiles in the smart grid context – a clustering methods comparison

The present research paper presents five different clustering methods to identify typical load profiles of medium voltage (MV) electricity consumers. These methods are intended to be used in a smart grid environment to extract useful knowledge about customer’s behaviour. The obtained knowledge can be used to support a decision tool, not only for utilities but also for consumers. Load profiles can be used by the utilities to identify the aspects that cause system load peaks and enable the development of specific contracts with their customers. The framework presented throughout the paper consists in several steps, namely the pre-processing data phase, clustering algorithms application and the evaluation of the quality of the partition, which is supported by cluster validity indices. The process ends with the analysis of the discovered knowledge. To validate the proposed framework, a case study with a real database of 208 MV consumers is used.

Categorical data clustering using a minimum message length criterion

Research on cluster analysis for categorical data continues to develop, new clustering algorithms being proposed. However, in this context, the determination of the number of clusters is rarely addressed. We propose a new approach in which clustering and the estimation of the number of clusters is done simultaneously for categorical data. We assume that the data originate from a finite mixture of multinomial distributions and use a minimum message length criterion (MML) to select the number of clusters (Wallace and Bolton, 1986). For this purpose, we implement an EM-type algorithm (Silvestre et al., 2008) based on the (Figueiredo and Jain, 2002) approach. The novelty of the approach rests on the integration of the model estimation and selection of the number of clusters in a single algorithm, rather than selecting this number based on a set of pre-estimated candidate models. The performance of our approach is compared with the use of Bayesian Information Criterion (BIC) (Schwarz, 1978) and Integrated Completed Likelihood (ICL) (Biernacki et al., 2000) using synthetic data. The obtained results illustrate the capacity of the proposed algorithm to attain the true number of cluster while outperforming BIC and ICL since it is faster, which is especially relevant when dealing with large data sets.

Paired indices for clustering evaluation correction for agreement by chance

In the present paper we focus on the performance of clustering algorithms using indices of paired agreement to measure the accordance between clusters and an a priori known structure. We specifically propose a method to correct all indices considered for agreement by chance - the adjusted indices are meant to provide a realistic measure of clustering performance. The proposed method enables the correction of virtually any index - overcoming previous limitations known in the literature - and provides very precise results. We use simulated datasets under diverse scenarios and discuss the pertinence of our proposal which is particularly relevant when poorly separated clusters are considered. Finally we compare the performance of EM and KMeans algorithms, within each of the simulated scenarios and generally conclude that EM generally yields best results.

Clustering aplicado à Bolsa de Valores de Lisboa

O objetivo desta dissertação foi estudar um conjunto de empresas cotadas na bolsa de valores de Lisboa, para identificar aquelas que têm um comportamento semelhante ao longo do tempo. Para isso utilizamos algoritmos de Clustering tais como K-Means, PAM, Modelos hierárquicos, Funny e C-Means tanto com a distância euclidiana como com a distância de Manhattan. Para selecionar o melhor número de clusters identificado por cada um dos algoritmos testados, recorremos a alguns índices de avaliação/validação de clusters como o Davies Bouldin e Calinski-Harabasz entre outros.

APPLICATION OF GEOMATICS TECHNOLOGIES TO CHARACTERIZE SPATIAL VARIABILITY AT STRATUS VINEYARDS

Vineyards vary over space and time, making geomatics technologies ideally suited to study terroir. This study applied geomatics technologies - GPS, remote sensing and GIS - to characterize the spatial variability at Stratus Vineyards in the Niagara Region. The concept of spatial terroir was used to visualize, monitor and analyze the spatial and temporal variability of variables that influence grape quality. Spatial interpolation and spatial autocorrelation were used to measure the pattern demonstrated by soil moisture, leaf water potential, vine vigour, soil composition and grape composition on two Cabernet Franc blocks and one Chardonnay block. All variables demonstrated some spatial variability within and between the vineyard block and over time. Soil moisture exhibited the most significant spatial clustering and was temporally stable. Geomatics technologies provided valuable spatial information related to the natural spatial variability at Stratus Vineyards and can be used to inform and influence vineyard management decisions.

Assessing the Reproducibility of Clustering of Molecular Dynamics Conformations on Self-Organizing Maps

The goal of most clustering algorithms is to find the optimal number of clusters (i.e. fewest number of clusters). However, analysis of molecular conformations of biological macromolecules obtained from computer simulations may benefit from a larger array of clusters. The Self-Organizing Map (SOM) clustering method has the advantage of generating large numbers of clusters, but often gives ambiguous results. In this work, SOMs have been shown to be reproducible when the same conformational dataset is independently clustered multiple times (~100), with the help of the Cramérs V-index (C_v). The ability of C_v to determine which SOMs are reproduced is generalizable across different SOM source codes. The conformational ensembles produced from MD (molecular dynamics) and REMD (replica exchange molecular dynamics) simulations of the penta peptide Met-enkephalin (MET) and the 34 amino acid protein human Parathyroid Hormone (hPTH) were used to evaluate SOM reproducibility. The training length for the SOM has a huge impact on the reproducibility. Analysis of MET conformational data definitively determined that toroidal SOMs cluster data better than bordered maps due to the fact that toroidal maps do not have an edge effect. For the source code from MATLAB, it was determined that the learning rate function should be LINEAR with an initial learning rate factor of 0.05 and the SOM should be trained by a sequential algorithm. The trained SOMs can be used as a supervised classification for another dataset. The toroidal 10×10 hexagonal SOMs produced from the MATLAB program for hPTH conformational data produced three sets of reproducible clusters (27%, 15%, and 13% of 100 independent runs) which find similar partitionings to those of smaller 6×6 SOMs. The χ^2 values produced as part of the C_v calculation were used to locate clusters with identical conformational memberships on independently trained SOMs, even those with different dimensions. The χ^2 values could relate the different SOM partitionings to each other.

Development of Hierarchical Clustering Techniques for Gridded Data from Mixed Data Sequences

Knowledge discovery in databases is the non-trivial process of identifying valid, novel potentially useful and ultimately understandable patterns from data. The term Data mining refers to the process which does the exploratory analysis on the data and builds some model on the data. To infer patterns from data, data mining involves different approaches like association rule mining, classification techniques or clustering techniques. Among the many data mining techniques, clustering plays a major role, since it helps to group the related data for assessing properties and drawing conclusions. Most of the clustering algorithms act on a dataset with uniform format, since the similarity or dissimilarity between the data points is a significant factor in finding out the clusters. If a dataset consists of mixed attributes, i.e. a combination of numerical and categorical variables, a preferred approach is to convert different formats into a uniform format. The research study explores the various techniques to convert the mixed data sets to a numerical equivalent, so as to make it equipped for applying the statistical and similar algorithms. The results of clustering mixed category data after conversion to numeric data type have been demonstrated using a crime data set. The thesis also proposes an extension to the well known algorithm for handling mixed data types, to deal with data sets having only categorical data. The proposed conversion has been validated on a data set corresponding to breast cancer. Moreover, another issue with the clustering process is the visualization of output. Different geometric techniques like scatter plot, or projection plots are available, but none of the techniques display the result projecting the whole database but rather demonstrate attribute-pair wise analysis

Clustering compositional data trajectories

Our essay aims at studying suitable statistical methods for the clustering of compositional data in situations where observations are constituted by trajectories of compositional data, that is, by sequences of composition measurements along a domain. Observed trajectories are known as “functional data” and several methods have been proposed for their analysis. In particular, methods for clustering functional data, known as Functional Cluster Analysis (FCA), have been applied by practitioners and scientists in many fields. To our knowledge, FCA techniques have not been extended to cope with the problem of clustering compositional data trajectories. In order to extend FCA techniques to the analysis of compositional data, FCA clustering techniques have to be adapted by using a suitable compositional algebra. The present work centres on the following question: given a sample of compositional data trajectories, how can we formulate a segmentation procedure giving homogeneous classes? To address this problem we follow the steps described below. First of all we adapt the well-known spline smoothing techniques in order to cope with the smoothing of compositional data trajectories. In fact, an observed curve can be thought of as the sum of a smooth part plus some noise due to measurement errors. Spline smoothing techniques are used to isolate the smooth part of the trajectory: clustering algorithms are then applied to these smooth curves. The second step consists in building suitable metrics for measuring the dissimilarity between trajectories: we propose a metric that accounts for difference in both shape and level, and a metric accounting for differences in shape only. A simulation study is performed in order to evaluate the proposed methodologies, using both hierarchical and partitional clustering algorithm. The quality of the obtained results is assessed by means of several indices

Dimensionality reduction assisted tensor clustering

This paper is concerned with tensor clustering with the assistance of dimensionality reduction approaches. A class of formulation for tensor clustering is introduced based on tensor Tucker decomposition models. In this formulation, an extra tensor mode is formed by a collection of tensors of the same dimensions and then used to assist a Tucker decomposition in order to achieve data dimensionality reduction. We design two types of clustering models for the tensors: PCA Tensor Clustering model and Non-negative Tensor Clustering model, by utilizing different regularizations. The tensor clustering can thus be solved by the optimization method based on the alternative coordinate scheme. Interestingly, our experiments show that the proposed models yield comparable or even better performance compared to most recent clustering algorithms based on matrix factorization.

Heterogeneous tensor decomposition for clustering via manifold optimization

Tensor clustering is an important tool that exploits intrinsically rich structures in real-world multiarray or Tensor datasets. Often in dealing with those datasets, standard practice is to use subspace clustering that is based on vectorizing multiarray data. However, vectorization of tensorial data does not exploit complete structure information. In this paper, we propose a subspace clustering algorithm without adopting any vectorization process. Our approach is based on a novel heterogeneous Tucker decomposition model taking into account cluster membership information. We propose a new clustering algorithm that alternates between different modes of the proposed heterogeneous tensor model. All but the last mode have closed-form updates. Updating the last mode reduces to optimizing over the multinomial manifold for which we investigate second order Riemannian geometry and propose a trust-region algorithm. Numerical experiments show that our proposed algorithm compete effectively with state-of-the-art clustering algorithms that are based on tensor factorization.

Malaria on the Amazonian frontier: Transmission dynamics, risk factors, spatial distribution, and prospects for control

Little follow-up data on malaria transmission in communities originating from frontier settlements in Amazonia are available. Here we describe a cohort study in a frontier settlement in Acre, Brazil, where 509 subjects contributed 489.7 person-years of follow-up. The association between malaria morbidity during the follow-up and individual, household, and spatial covariates was explored with mixed-effects logistic regression models and spatial analysis. Incidence rates for Plasmodium vivax and Plasmodium falciparum malaria were 30.0/100 and 16.3/100 person-years at risk, respectively. Malaria morbidity was strongly associated with land clearing and farming, and decreased after five years of residence in the area, suggesting that clinical immunity develops among subjects exposed to low malaria endemicity. Significant spatial clustering of malaria was observed in the areas of most recent occupation, indicating that the continuous influx of nonimmune settlers to forest-fringe areas perpetuates the cycle of environmental change and colonization that favors malaria transmission in rural Amazonia.

Evolutionary fuzzy clustering of relational data

This paper is concerned with the computational efficiency of fuzzy clustering algorithms when the data set to be clustered is described by a proximity matrix only (relational data) and the number of clusters must be automatically estimated from such data. A fuzzy variant of an evolutionary algorithm for relational clustering is derived and compared against two systematic (pseudo-exhaustive) approaches that can also be used to automatically estimate the number of fuzzy clusters in relational data. An extensive collection of experiments involving 18 artificial and two real data sets is reported and analyzed. (C) 2011 Elsevier B.V. All rights reserved.

Investigation of a new GRASP-based clustering algorithm applied to biological data

A large amount of biological data has been produced in the last years. Important knowledge can be extracted from these data by the use of data analysis techniques. Clustering plays an important role in data analysis, by organizing similar objects from a dataset into meaningful groups. Several clustering algorithms have been proposed in the literature. However, each algorithm has its bias, being more adequate for particular datasets. This paper presents a mathematical formulation to support the creation of consistent clusters for biological data. Moreover. it shows a clustering algorithm to solve this formulation that uses GRASP (Greedy Randomized Adaptive Search Procedure). We compared the proposed algorithm with three known other algorithms. The proposed algorithm presented the best clustering results confirmed statistically. (C) 2009 Elsevier Ltd. All rights reserved.

A maximal frequent itemset approach for web document clustering

To efficiently and yet accurately cluster Web documents is of great interests to Web users and is a key component of the searching accuracy of a Web search engine. To achieve this, this paper introduces a new approach for the clustering of Web documents, which is called maximal frequent itemset (MFI) approach. Iterative clustering algorithms, such as K-means and expectation-maximization (EM), are sensitive to their initial conditions. MFI approach firstly locates the center points of high density clusters precisely. These center points then are used as initial points for the K-means algorithm. Our experimental results tested on 3 Web document sets show that our MFI approach outperforms the other methods we compared in most cases, particularly in the case of large number of categories in Web document sets.

Enhancing the effectiveness of clustering with spectra analysis

For many clustering algorithms, such as K-Means, EM, and CLOPE, there is usually a requirement to set some parameters. Often, these parameters directly or indirectly control the number of clusters, that is, k, to return. In the presence of different data characteristics and analysis contexts, it is often difficult for the user to estimate the number of clusters in the data set. This is especially true in text collections such as Web documents, images, or biological data. In an effort to improve the effectiveness of clustering, we seek the answer to a fundamental question: How can we effectively estimate the number of clusters in a given data set? We propose an efficient method based on spectra analysis of eigenvalues (not eigenvectors) of the data set as the solution to the above. We first present the relationship between a data set and its underlying spectra with theoretical and experimental results. We then show how our method is capable of suggesting a range of k that is well suited to different analysis contexts. Finally, we conclude with further  empirical results to show how the answer to this fundamental question enhances the clustering process for large text collections.