Two-level k-means clustering algorithm for k-tau relationship establishment and linear-time classification

Partitional clustering algorithms, which partition the dataset into a pre-defined number of clusters, can be broadly classified into two types: algorithms which explicitly take the number of clusters as input and algorithms that take the expected size of a cluster as input. In this paper, we propose a variant of the k-means algorithm and prove that it is more efficient than standard k-means algorithms. An important contribution of this paper is the establishment of a relation between the number of clusters and the size of the clusters in a dataset through the analysis of our algorithm. We also demonstrate that the integration of this algorithm as a pre-processing step in classification algorithms reduces their running-time complexity.

A comparison between conceptual clustering and conventional clustering

Clustering is a process of partitioning a given set of patterns into meaningful groups. The clustering process can be viewed as consisting of the following three phases: (i) feature selection phase, (ii) classification phase, and (iii) description generation phase. Conventional clustering algorithms implicitly use knowledge about the clustering environment to a large extent in the feature selection phase. This reduces the need for the environmental knowledge in the remaining two phases, permitting the usage of simple numerical measure of similarity in the classification phase. Conceptual clustering algorithms proposed by Michalski and Stepp [IEEE Trans. PAMI, PAMI-5, 396–410 (1983)] and Stepp and Michalski [Artif. Intell., pp. 43–69 (1986)] make use of the knowledge about the clustering environment in the form of a set of predefined concepts to compute the conceptual cohesiveness during the classification phase. Michalski and Stepp [IEEE Trans. PAMI, PAMI-5, 396–410 (1983)] have argued that the results obtained with the conceptual clustering algorithms are superior to conventional methods of numerical classification. However, this claim was not supported by the experimental results obtained by Dale [IEEE Trans. PAMI, PAMI-7, 241–244 (1985)]. In this paper a theoretical framework, based on an intuitively appealing set of axioms, is developed to characterize the equivalence between the conceptual clustering and conventional clustering. In other words, it is shown that any classification obtained using conceptual clustering can also be obtained using conventional clustering and vice versa.

Regional Flood Frequency Analysis using Two-level Clustering Approach

Clustering techniques are used in regional flood frequency analysis (RFFA) to partition watersheds into natural groups or regions with similar hydrologic responses. The linear Kohonen's self‐organizing feature map (SOFM) has been applied as a clustering technique for RFFA in several recent studies. However, it is seldom possible to interpret clusters from the output of an SOFM, irrespective of its size and dimensionality. In this study, we demonstrate that SOFMs may, however, serve as a useful precursor to clustering algorithms. We present a two‐level. SOFM‐based clustering approach to form regions for FFA. In the first level, the SOFM is used to form a two‐dimensional feature map. In the second level, the output nodes of SOFM are clustered using Fuzzy c‐means algorithm to form regions. The optimal number of regions is based on fuzzy cluster validation measures. Effectiveness of the proposed approach in forming homogeneous regions for FFA is illustrated through application to data from watersheds in Indiana, USA. Results show that the performance of the proposed approach to form regions is better than that based on classical SOFM.

Clustering Based Large Margin Classification: A Scalable Approach using SOCP Formulation

This paper presents a novel Second Order Cone Programming (SOCP) formulation for large scale binary classification tasks. Assuming that the class conditional densities are mixture distributions, where each component of the mixture has a spherical covariance, the second order statistics of the components can be estimated efficiently using clustering algorithms like BIRCH. For each cluster, the second order moments are used to derive a second order cone constraint via a Chebyshev-Cantelli inequality. This constraint ensures that any data point in the cluster is classified correctly with a high probability. This leads to a large margin SOCP formulation whose size depends on the number of clusters rather than the number of training data points. Hence, the proposed formulation scales well for large datasets when compared to the state-of-the-art classifiers, Support Vector Machines (SVMs). Experiments on real world and synthetic datasets show that the proposed algorithm outperforms SVM solvers in terms of training time and achieves similar accuracies.

Hierarchical Clustering Algorithm for Land Cover Mapping Using Satellite Images

This paper presents hierarchical clustering algorithms for land cover mapping problem using multi-spectral satellite images. In unsupervised techniques, the automatic generation of number of clusters and its centers for a huge database is not exploited to their full potential. Hence, a hierarchical clustering algorithm that uses splitting and merging techniques is proposed. Initially, the splitting method is used to search for the best possible number of clusters and its centers using Mean Shift Clustering (MSC), Niche Particle Swarm Optimization (NPSO) and Glowworm Swarm Optimization (GSO). Using these clusters and its centers, the merging method is used to group the data points based on a parametric method (k-means algorithm). A performance comparison of the proposed hierarchical clustering algorithms (MSC, NPSO and GSO) is presented using two typical multi-spectral satellite images - Landsat 7 thematic mapper and QuickBird. From the results obtained, we conclude that the proposed GSO based hierarchical clustering algorithm is more accurate and robust.

Cross-Guided Clustering: Transfer of Relevant Supervision across Tasks

Lack of supervision in clustering algorithms often leads to clusters that are not useful or interesting to human reviewers. We investigate if supervision can be automatically transferred for clustering a target task, by providing a relevant supervised partitioning of a dataset from a different source task. The target clustering is made more meaningful for the human user by trading-off intrinsic clustering goodness on the target task for alignment with relevant supervised partitions in the source task, wherever possible. We propose a cross-guided clustering algorithm that builds on traditional k-means by aligning the target clusters with source partitions. The alignment process makes use of a cross-task similarity measure that discovers hidden relationships across tasks. When the source and target tasks correspond to different domains with potentially different vocabularies, we propose a projection approach using pivot vocabularies for the cross-domain similarity measure. Using multiple real-world and synthetic datasets, we show that our approach improves clustering accuracy significantly over traditional k-means and state-of-the-art semi-supervised clustering baselines, over a wide range of data characteristics and parameter settings.

Novel Biobjective Clustering (BiGC) Based on Cooperative Game Theory

We propose a new approach to clustering. Our idea is to map cluster formation to coalition formation in cooperative games, and to use the Shapley value of the patterns to identify clusters and cluster representatives. We show that the underlying game is convex and this leads to an efficient biobjective clustering algorithm that we call BiGC. The algorithm yields high-quality clustering with respect to average point-to-center distance (potential) as well as average intracluster point-to-point distance (scatter). We demonstrate the superiority of BiGC over state-of-the-art clustering algorithms (including the center based and the multiobjective techniques) through a detailed experimentation using standard cluster validity criteria on several benchmark data sets. We also show that BiGC satisfies key clustering properties such as order independence, scale invariance, and richness.

Agrupamento espacial em robótica de enxame.

Os Sistemas Multi-Robôs proporcionam vantagens sobre um robô individual, quando da realização de uma tarefa com maiores velocidade, precisão e tolerância a falhas. Os estudos dos comportamentos sociais na natureza têm permitido desenvolver algoritmos bio-inspirados úteis na área da robótica de enxame. Seguindo instruções simples e repetitivas, grupos de robôs, fisicamente limitados, conseguem solucionar problemas complexos. Quando existem duas ou mais tarefas a serem realizadas e o conjunto de robôs é heterogêneo, é possível agrupá-los de acordo com as funcionalidades neles disponíveis. No caso em que o conjunto de robôs é homogêneo, o agrupamento pode ser realizado considerando a posição relativa do robô em relação a uma tarefa ou acrescentando alguma característica distintiva. Nesta dissertação, é proposta uma técnica de clusterização espacial baseada simplesmente na comunicação local de robôs. Por meio de troca de mensagens entre os robôs vizinhos, esta técnica permite formar grupos de robôs espacialmente próximos sem precisar movimentar os robôs. Baseando-se nos métodos de clusterização de fichas, a técnica proposta emprega a noção de fichas virtuais, que são chamadas de cargas, sendo que uma carga pode ser estática ou dinâmica. Se uma carga é estática permite determinar a classe à qual um robô pertence. Dependendo da quantidade e do peso das cargas disponíveis no sistema, os robôs intercambiam informações até alcançar uma disposição homogênea de cargas. Quando as cargas se tornam estacionárias, é calculada uma densidade que permite guiar aquelas que estão ainda em movimento. Durante as experiências, foi observado visualmente que as cargas com maior peso acabam se agrupando primeiro enquanto aquelas com menor peso continuam se deslocando no enxame, até que estas cargas formem faixas de densidades diferenciadas para cada classe, alcançando assim o objetivo final que é a clusterização dos robôs.

A dependent partition-valued process for multitask clustering and time evolving network modelling

The fundamental aim of clustering algorithms is to partition data points. We consider tasks where the discovered partition is allowed to vary with some covariate such as space or time. One approach would be to use fragmentation-coagulation processes, but these, being Markov processes, are restricted to linear or tree structured covariate spaces. We define a partition-valued process on an arbitrary covariate space using Gaussian processes. We use the process to construct a multitask clustering model which partitions datapoints in a similar way across multiple data sources, and a time series model of network data which allows cluster assignments to vary over time. We describe sampling algorithms for inference and apply our method to defining cancer subtypes based on different types of cellular characteristics, finding regulatory modules from gene expression data from multiple human populations, and discovering time varying community structure in a social network.

On Clustering Images Using Compression

The need for the ability to cluster unknown data to better understand its relationship to know data is prevalent throughout science. Besides a better understanding of the data itself or learning about a new unknown object, cluster analysis can help with processing data, data standardization, and outlier detection. Most clustering algorithms are based on known features or expectations, such as the popular partition based, hierarchical, density-based, grid based, and model based algorithms. The choice of algorithm depends on many factors, including the type of data and the reason for clustering, nearly all rely on some known properties of the data being analyzed. Recently, Li et al. proposed a new universal similarity metric, this metric needs no prior knowledge about the object. Their similarity metric is based on the Kolmogorov Complexity of objects, the objects minimal description. While the Kolmogorov Complexity of an object is not computable, in "Clustering by Compression," Cilibrasi and Vitanyi use common compression algorithms to approximate the universal similarity metric and cluster objects with high success. Unfortunately, clustering using compression does not trivially extend to higher dimensions. Here we outline a method to adapt their procedure to images. We test these techniques on images of letters of the alphabet.

Eliminating Redundant Training Data Using Unsupervised Clustering Techniques

Training data for supervised learning neural networks can be clustered such that the input/output pairs in each cluster are redundant. Redundant training data can adversely affect training time. In this paper we apply two clustering algorithms, ART2 -A and the Generalized Equality Classifier, to identify training data clusters and thus reduce the training data and training time. The approach is demonstrated for a high dimensional nonlinear continuous time mapping. The demonstration shows six-fold decrease in training time at little or no loss of accuracy in the handling of evaluation data.

Clustering and synchrony in laying hens: The effect of environmental resources on social dynamics

Laying hens generally choose to aggregate, but the extent to which the environments in which we house them impact on social group dynamics is not known. In this paper the effect of pen environment on spatial clustering is considered. Twelve groups of four laying hens were studied under three environmental conditions: wire floor (W), shavings (Sh) and perches, peat, nestbox and shavings (PPN). Groups experienced each environment twice, for five weeks each time, in a systematic order that varied from group to group. Video recordings were made one day per week for 30 weeks. To determine level of clustering, we recorded positional data from a randomly selected 20-min excerpt per video (a total of 20 min x 360 videos analysed). On screen, pens were divided into six equal areas. In addition, PPN pens were divided into an additional four (sub) areas, to account for the use of perches (one area per half perch). Every 5 s, we recorded the location of each bird and calculated location use over time, feeding synchrony and cluster scores for each environment. Feeding synchrony and cluster scores were compared against unweighted and weighted (according to observed proportional location use) Poisson distributions to distinguish between resource and social attraction.

Interpretable and Reconfigurable Clustering of Document Datasets by Deriving Word-based Rules

Clusters of text documents output by clustering algorithms are often hard to interpret. We describe motivating real-world scenarios that necessitate reconfigurability and high interpretability of clusters and outline the problem of generating clusterings with interpretable and reconfigurable cluster models. We develop two clustering algorithms toward the outlined goal of building interpretable and reconfigurable cluster models. They generate clusters with associated rules that are composed of conditions on word occurrences or nonoccurrences. The proposed approaches vary in the complexity of the format of the rules; RGC employs disjunctions and conjunctions in rule generation whereas RGC-D rules are simple disjunctions of conditions signifying presence of various words. In both the cases, each cluster is comprised of precisely the set of documents that satisfy the corresponding rule. Rules of the latter kind are easy to interpret, whereas the former leads to more accurate clustering. We show that our approaches outperform the unsupervised decision tree approach for rule-generating clustering and also an approach we provide for generating interpretable models for general clusterings, both by significant margins. We empirically show that the purity and f-measure losses to achieve interpretability can be as little as 3 and 5%, respectively using the algorithms presented herein.

Accelerating Large Scale Centroid-based Clustering with Locality Sensitive Hashing

Most traditional data mining algorithms struggle to cope with the sheer scale of data efficiently. In this paper, we propose a general framework to accelerate existing clustering algorithms to cluster large-scale datasets which contain large numbers of attributes, items, and clusters. Our framework makes use of locality sensitive hashing (LSH) to significantly reduce the cluster search space. We also theoretically prove that our framework has a guaranteed error bound in terms of the clustering quality. This framework can be applied to a set of centroid-based clustering algorithms that assign an object to the most similar cluster, and we adopt the popular K-Modes categorical clustering algorithm to present how the framework can be applied. We validated our framework with five synthetic datasets and a real world Yahoo! Answers dataset. The experimental results demonstrate that our framework is able to speed up the existing clustering algorithm between factors of 2 and 6, while maintaining comparable cluster purity.

Contributos para a eficácia do clustering usando o tagging social

Nos últimos anos temos vindo a assistir a uma mudança na forma como a informação é disponibilizada online. O surgimento da web para todos possibilitou a fácil edição, disponibilização e partilha da informação gerando um considerável aumento da mesma. Rapidamente surgiram sistemas que permitem a coleção e partilha dessa informação, que para além de possibilitarem a coleção dos recursos também permitem que os utilizadores a descrevam utilizando tags ou comentários. A organização automática dessa informação é um dos maiores desafios no contexto da web atual. Apesar de existirem vários algoritmos de clustering, o compromisso entre a eficácia (formação de grupos que fazem sentido) e a eficiência (execução em tempo aceitável) é difícil de encontrar. Neste sentido, esta investigação tem por problemática aferir se um sistema de agrupamento automático de documentos, melhora a sua eficácia quando se integra um sistema de classificação social. Analisámos e discutimos dois métodos baseados no algoritmo k-means para o clustering de documentos e que possibilitam a integração do tagging social nesse processo. O primeiro permite a integração das tags diretamente no Vector Space Model e o segundo propõe a integração das tags para a seleção das sementes iniciais. O primeiro método permite que as tags sejam pesadas em função da sua ocorrência no documento através do parâmetro Social Slider. Este método foi criado tendo por base um modelo de predição que sugere que, quando se utiliza a similaridade dos cossenos, documentos que partilham tags ficam mais próximos enquanto que, no caso de não partilharem, ficam mais distantes. O segundo método deu origem a um algoritmo que denominamos k-C. Este para além de permitir a seleção inicial das sementes através de uma rede de tags também altera a forma como os novos centróides em cada iteração são calculados. A alteração ao cálculo dos centróides teve em consideração uma reflexão sobre a utilização da distância euclidiana e similaridade dos cossenos no algoritmo de clustering k-means. No contexto da avaliação dos algoritmos foram propostos dois algoritmos, o algoritmo da “Ground truth automática” e o algoritmo MCI. O primeiro permite a deteção da estrutura dos dados, caso seja desconhecida, e o segundo é uma medida de avaliação interna baseada na similaridade dos cossenos entre o documento mais próximo de cada documento. A análise de resultados preliminares sugere que a utilização do primeiro método de integração das tags no VSM tem mais impacto no algoritmo k-means do que no algoritmo k-C. Além disso, os resultados obtidos evidenciam que não existe correlação entre a escolha do parâmetro SS e a qualidade dos clusters. Neste sentido, os restantes testes foram conduzidos utilizando apenas o algoritmo k-C (sem integração de tags no VSM), sendo que os resultados obtidos indicam que a utilização deste algoritmo tende a gerar clusters mais eficazes.