Medoid Silhouette clustering with automatic cluster number selection

The evaluation of clustering results is difficult, highly dependent on the evaluated data set and the perspective of the beholder. There are many different clustering quality measures, which try to provide a general measure to validate clustering results. A very popular measure is the Silhouette. We discuss the efficient medoid-based variant of the Silhouette, perform a theoretical analysis of its properties, provide two fast versions for the direct optimization, and discuss the use to choose the optimal number of clusters. We combine ideas from the original Silhouette with the well-known PAM algorithm and its latest improvements FasterPAM. One of the versions guarantees equal results to the original variant and provides a run speedup of $O(k^2)$. In experiments on real data with 30000 samples and $k$=100, we observed a 10464$\times$ speedup compared to the original PAMMEDSIL algorithm. Additionally, we provide a variant to choose the optimal number of clusters directly.Comment: arXiv admin note: substantial text overlap with arXiv:2209.1255

Graph-Based Automatic Feature Selection for Multi-Class Classification via Mean Simplified Silhouette

This paper introduces a novel graph-based filter method for automatic feature selection (abbreviated as GB-AFS) for multi-class classification tasks. The method determines the minimum combination of features required to sustain prediction performance while maintaining complementary discriminating abilities between different classes. It does not require any user-defined parameters such as the number of features to select. The methodology employs the Jeffries-Matusita (JM) distance in conjunction with t-distributed Stochastic Neighbor Embedding (t-SNE) to generate a low-dimensional space reflecting how effectively each feature can differentiate between each pair of classes. The minimum number of features is selected using our newly developed Mean Simplified Silhouette (abbreviated as MSS) index, designed to evaluate the clustering results for the feature selection task. Experimental results on public data sets demonstrate the superior performance of the proposed GB-AFS over other filter-based techniques and automatic feature selection approaches. Moreover, the proposed algorithm maintained the accuracy achieved when utilizing all features, while using only $7\%$ to $30\%$ of the features. Consequently, this resulted in a reduction of the time needed for classifications, from $15\%$ to $70\%$.Comment: 8 pages, 4 figure

On the use of Silhouette for cost based clustering

Clustering plays a fundamental role in Machine Learning. With clustering we refer to the problem of finding coherent groups in a dataset of elements. There are several algorithms to perform clustering that have been proposed in the literature, considering different costs for the optimization problems they consider. In this thesis we study the problem of clustering when the cost function is the silhouette coefficient, an index traditionally used for the internal validation of the results

Meta-optimizations for Cluster Analysis

This dissertation thesis deals with advances in the automation of cluster analysis.This dissertation thesis deals with advances in the automation of cluster analysis

Deep generative modeling for single-cell transcriptomics.

Single-cell transcriptome measurements can reveal unexplored biological diversity, but they suffer from technical noise and bias that must be modeled to account for the resulting uncertainty in downstream analyses. Here we introduce single-cell variational inference (scVI), a ready-to-use scalable framework for the probabilistic representation and analysis of gene expression in single cells ( https://github.com/YosefLab/scVI ). scVI uses stochastic optimization and deep neural networks to aggregate information across similar cells and genes and to approximate the distributions that underlie observed expression values, while accounting for batch effects and limited sensitivity. We used scVI for a range of fundamental analysis tasks including batch correction, visualization, clustering, and differential expression, and achieved high accuracy for each task

Incremental Cluster Validity Indices for Online Learning of Hard Partitions: Extensions and Comparative Study

Validation is one of the most important aspects of clustering, particularly when the user is designing a trustworthy or explainable system. However, most clustering validation approaches require batch calculation. This is an important gap because of the value of clustering in real-time data streaming and other online learning applications. Therefore, interest has grown in providing online alternatives for validation. This paper extends the incremental cluster validity index (iCVI) family by presenting incremental versions of Calinski-Harabasz (iCH), Pakhira-Bandyopadhyay-Maulik (iPBM), WB index (iWB), Silhouette (iSIL), Negentropy Increment (iNI), Representative Cross Information Potential (irCIP), Representative Cross Entropy (irH), and Conn_Index (iConn_Index). This paper also provides a thorough comparative study of correct, under- and over-partitioning on the behavior of these iCVIs, the Partition Separation (PS) index as well as four recently introduced iCVIs: incremental Xie-Beni (iXB), incremental Davies-Bouldin (iDB), and incremental generalized Dunn\u27s indices 43 and 53 (iGD43 and iGD53). Experiments were carried out using a framework that was designed to be as agnostic as possible to the clustering algorithms. The results on synthetic benchmark data sets showed that while evidence of most under-partitioning cases could be inferred from the behaviors of the majority of these iCVIs, over-partitioning was found to be a more challenging problem, detected by fewer of them. Interestingly, over-partitioning, rather then under-partitioning, was more prominently detected on the real-world data experiments within this study. The expansion of iCVIs provides significant novel opportunities for assessing and interpreting the results of unsupervised lifelong learning in real-time, wherein samples cannot be reprocessed due to memory and/or application constraints

EVALUATION OF THE CLUSTERING PERFORMANCE OF AFFINITY PROPAGATION ALGORITHM CONSIDERING THE INFLUENCE OF PREFERENCE PARAMETER AND DAMPING FACTOR

The identification of significant underlying data patterns such as image composition and spatial arrangements is fundamental in remote sensing tasks. Therefore, the development of an effective approach for information extraction is crucial to achieve this goal. Affinity propagation (AP) algorithm is a novel powerful technique with the ability of handling with unusual data, containing both categorical and numerical attributes. However, AP has some limitations related to the choice of initial preference parameter, occurrence of oscillations and processing of large data sets. This paper evaluates the clustering performance of AP algorithm taking into account the influence of preference parameter and damping factor. The study was conducted considering the AP algorithm, the adaptive AP and partition AP. According to the experiments, the choice of preference and damping greatly influences on the quality and the final number of clusters

An Improved Differential Evolution Algorithm for Data Stream Clustering

A Few algorithms were actualized by the analysts for performing clustering of data streams. Most of these algorithms require that the number of clusters (K) has to be fixed by the customer based on input data and it can be kept settled all through the clustering process. Stream clustering has faced few difficulties in picking up K. In this paper, we propose an efficient approach for data stream clustering by embracing an Improved Differential Evolution (IDE) algorithm. The IDE algorithm is one of the quick, powerful and productive global optimization approach for programmed clustering. In our proposed approach, we additionally apply an entropy based method for distinguishing the concept drift in the data stream and in this way updating the clustering procedure online. We demonstrated that our proposed method is contrasted with Genetic Algorithm and identified as proficient optimization algorithm. The performance of our proposed technique is assessed and cr eates the accuracy of 92.29%, the precision is 86.96%, recall is 90.30% and F-measure estimate is 88.60%

Comparison of Clustering Algorithms for Learning Analytics with Educational Datasets

Learning Analytics is becoming a key tool for the analysis and improvement of digital education processes, and its potential benefit grows with the size of the student cohorts generating data. In the context of Open Education, the potentially massive student cohorts and the global audience represent a great opportunity for significant analyses and breakthroughs in the field of learning analytics. However, these potentially huge datasets require proper analysis techniques, and different algorithms, tools and approaches may perform better in this specific context. In this work, we compare different clustering algorithms using an educational dataset. We start by identifying the most relevant algorithms in Learning Analytics and benchmark them to determine, according to internal validation and stability measurements, which algorithms perform better. We analyzed seven algorithms, and determined that K-means and PAM were the best performers among partition algorithms, and DIANA was the best performer among hierarchical algorithms

New internal and external validation indices for clustering in Big Data

Esta tesis, presentada como un compendio de artículos de investigación, analiza el concepto de índices de validación de clustering y aporta nuevas medidas de bondad para conjuntos de datos que podrían considerarse Big Data debido a su volumen. Además, estas medidas han sido aplicadas en proyectos reales y se propone su aplicación futura para mejorar algoritmos de clustering. El clustering es una de las técnicas de aprendizaje automático no supervisado más usada. Esta técnica nos permite agrupar datos en clusters de manera que, aquellos datos que pertenezcan al mismo cluster tienen características o atributos con valores similares, y a su vez esos datos son disimilares respecto a aquellos que pertenecen a los otros clusters. La similitud de los datos viene dada normalmente por la cercanía en el espacio, teniendo en cuenta una función de distancia. En la literatura existen los llamados índices de validación de clustering, los cuales podríamos definir como medidas para cuantificar la calidad de un resultado de clustering. Estos índices se dividen en dos tipos: índices de validación internos, que miden la calidad del clustering en base a los atributos con los que se han construido los clusters; e índices de validación externos, que son aquellos que cuantifican la calidad del clustering a partir de atributos que no han intervenido en la construcción de los clusters, y que normalmente son de tipo nominal o etiquetas. En esta memoria se proponen dos índices de validación internos para clustering basados en otros índices existentes en la literatura, que nos permiten trabajar con grandes cantidades de datos, ofreciéndonos los resultados en un tiempo razonable. Los índices propuestos han sido testeados en datasets sintéticos y comparados con otros índices de la literatura. Las conclusiones de este trabajo indican que estos índices ofrecen resultados muy prometedores frente a sus competidores. Por otro lado, se ha diseñado un nuevo índice de validación externo de clustering basado en el test estadístico chi cuadrado. Este índice permite medir la calidad del clustering basando el resultado en cómo han quedado distribuidos los clusters respecto a una etiqueta dada en la distribución. Los resultados de este índice muestran una mejora significativa frente a otros índices externos de la literatura y en datasets de diferentes dimensiones y características. Además, estos índices propuestos han sido aplicados en tres proyectos con datos reales cuyas publicaciones están incluidas en esta tesis doctoral. Para el primer proyecto se ha desarrollado una metodología para analizar el consumo eléctrico de los edificios de una smart city. Para ello, se ha realizado un análisis de clustering óptimo aplicando los índices internos mencionados anteriormente. En el segundo proyecto se ha trabajado tanto los índices internos como con los externos para realizar un análisis comparativo del mercado laboral español en dos periodos económicos distintos. Este análisis se realizó usando datos del Ministerio de Trabajo, Migraciones y Seguridad Social, y los resultados podrían tenerse en cuenta para ayudar a la toma de decisión en mejoras de políticas de empleo. En el tercer proyecto se ha trabajado con datos de los clientes de una compañía eléctrica para caracterizar los tipos de consumidores que existen. En este estudio se han analizado los patrones de consumo para que las compañías eléctricas puedan ofertar nuevas tarifas a los consumidores, y éstos puedan adaptarse a estas tarifas con el objetivo de optimizar la generación de energía eliminando los picos de consumo que existen la actualidad.This thesis, presented as a compendium of research articles, analyses the concept of clustering validation indices and provides new measures of goodness for datasets that could be considered Big Data. In addition, these measures have been applied in real projects and their future application is proposed for the improvement of clustering algorithms. Clustering is one of the most popular unsupervised machine learning techniques. This technique allows us to group data into clusters so that the instances that belong to the same cluster have characteristics or attributes with similar values, and are dissimilar to those that belong to the other clusters. The similarity of the data is normally given by the proximity in space, which is measured using a distance function. In the literature, there are so-called clustering validation indices, which can be defined as measures for the quantification of the quality of a clustering result. These indices are divided into two types: internal validation indices, which measure the quality of clustering based on the attributes with which the clusters have been built; and external validation indices, which are those that quantify the quality of clustering from attributes that have not intervened in the construction of the clusters, and that are normally of nominal type or labels. In this doctoral thesis, two internal validation indices are proposed for clustering based on other indices existing in the literature, which enable large amounts of data to be handled, and provide the results in a reasonable time. The proposed indices have been tested with synthetic datasets and compared with other indices in the literature. The conclusions of this work indicate that these indices offer very promising results in comparison with their competitors. On the other hand, a new external clustering validation index based on the chi-squared statistical test has been designed. This index enables the quality of the clustering to be measured by basing the result on how the clusters have been distributed with respect to a given label in the distribution. The results of this index show a significant improvement compared to other external indices in the literature when used with datasets of different dimensions and characteristics. In addition, these proposed indices have been applied in three projects with real data whose corresponding publications are included in this doctoral thesis. For the first project, a methodology has been developed to analyse the electrical consumption of buildings in a smart city. For this study, an optimal clustering analysis has been carried out by applying the aforementioned internal indices. In the second project, both internal and external indices have been applied in order to perform a comparative analysis of the Spanish labour market in two different economic periods. This analysis was carried out using data from the Ministry of Labour, Migration, and Social Security, and the results could be taken into account to help decision-making for the improvement of employment policies. In the third project, data from the customers of an electric company has been employed to characterise the different types of existing consumers. In this study, consumption patterns have been analysed so that electricity companies can offer new rates to consumers. Conclusions show that consumers could adapt their usage to these rates and hence the generation of energy could be optimised by eliminating the consumption peaks that currently exist