On clustering stability

JEL Classification: C100; C150; C380This work is dedicated to the evaluation of the stability of clustering solutions, namely the stability of crisp clusterings or partitions. We specifically refer to stability as the concordance of clusterings across several samples. In order to evaluate stability, we use a weighted cross-validation procedure, the result of which is summarized by simple and paired agreement indices values. To exclude the amount of agreement by chance of these values, we propose a new method – IADJUST – that resorts to simulated crossclassification tables. This contribution makes viable the correction of any index of agreement. Experiments on stability rely on 540 simulated data sets, design factors being the number of clusters, their balance and overlap. Six real data with a priori known clusters are also considered. The experiments conducted enable to illustrate the precision and pertinence of the IADJUST procedure and allow to know the distribution of indices under the hypothesis of agreement by chance. Therefore, we recommend the use of adjusted indices to be common practice when addressing stability. We then compare the stability of two clustering algorithms and conclude that Expectation-Maximization (EM) results are more stable when referring to unbalanced data sets than K means results. Finally, we explore the relationship between stability and external validity of a clustering solution. When all experimental scenarios’ results are considered there is a strong correlation between stability and external validity. However, within a specific experimental scenario (when a practical clustering task is considered), we find no relationship between stability and agreement with ground truth.Este trabalho é dedicado à avaliação da estabilidade de agrupamentos, nomeadamente de partições. Consideramos a estabilidade como sendo a concordância dos agrupamentos obtidos sobre diversas amostras. Para avaliar a estabilidade, usamos um procedimento de validação cruzada ponderada, cujo resultado é resumido pelos valores de índices de concordância simples e pareados. Para excluir, destes valores, a parcela de concordância por acaso, propomos um novo método - IADJUST - que recorre à simulação de tabelas cruzadas de classificação. Essa contribuição torna viável a correção de qualquer índice de concordância. A análise experimental da estabilidade baseia-se em 540 conjuntos de dados simulados, controlando os números de grupos, dimensões relativas e graus de sobreposição dos grupos. Também consideramos seis conjuntos de dados reais com classes a priori conhecidas. As experiências realizadas permitem ilustrar a precisão e pertinência do procedimento IADJUST e conhecer a distribuição dos índices sob a hipótese de concordância por acaso. Assim sendo, recomendamos a utilização de índices ajustados como prática comum ao abordar a estabilidade. Comparamos, então, a estabilidade de dois algoritmos de agrupamento e concluímos que as soluções do algoritmo Expectation Maximization são mais estáveis que as do K-médias em conjuntos de dados não balanceados. Finalmente, estudamos a relação entre a estabilidade e validade externa de um agrupamento. Agregando os resultados dos cenários experimentais obtemos uma forte correlação entre estabilidade e validade externa. No entanto, num cenário experimental particular (para uma tarefa prática de agrupamento), não encontramos relação entre estabilidade e a concordância com a verdadeira estrutura dos dados

Simulation experiments for similarity indexes between two hierarchical clusterings

Morlini and Zani (2012) have proposed a new dissimilarity indexfor comparing two hierarchical clusterings on the basis of thewhole dendrograms. They have presented and discussed its basicproperties and have shown that the index can be decomposed intocontributions pertaining to each stage of the hierarchies. Then,they have obtained a similarity index $S$ as the complement to oneof the suggested distance and have shown that its singlecomponents $S_k$ obtained at each stage $k$ of the hierarchies canbe related to the measure $B_k$ suggested by Fowlkes \& Mallows(1983) and to the Rand index $R_k$. In this paper, we reportresults of a series of simulation experiments aimed at comparingthe behavior of these new indexes with other well-establishedsimilarity measures, over different experimental conditions. Thefirst set of simulations is aimed at determining the behavior ofthe indexes when the clusterings being compared are unrelated. Thesecond set tries to investigate the robustness to different levelsof nois

Evaluation of Performance Measures for Classifiers Comparison

The selection of the best classification algorithm for a given dataset is a very widespread problem, occuring each time one has to choose a classifier to solve a real-world problem. It is also a complex task with many important methodological decisions to make. Among those, one of the most crucial is the choice of an appropriate measure in order to properly assess the classification performance and rank the algorithms. In this article, we focus on this specific task. We present the most popular measures and compare their behavior through discrimination plots. We then discuss their properties from a more theoretical perspective. It turns out several of them are equivalent for classifiers comparison purposes. Futhermore. they can also lead to interpretation problems. Among the numerous measures proposed over the years, it appears that the classical overall success rate and marginal rates are the more suitable for classifier comparison task

Comparing hard and overlapping clusterings

Similarity measures for comparing clusterings is an important component, e.g., of evaluating clustering algorithms, for consensus clustering, and for clustering stability assessment. These measures have been studied for over 40 years in the domain of exclusive hard clusterings (exhaustive and mutually exclusive object sets). In the past years, the literature has proposed measures to handle more general clusterings (e.g., fuzzy/probabilistic clusterings). This paper provides an overview of these new measures and discusses their drawbacks. We ultimately develop a corrected-for-chance measure (13AGRI) capable of comparing exclusive hard, fuzzy/probabilistic, non-exclusive hard, and possibilistic clusterings. We prove that 13AGRI and the adjusted Rand index (ARI, by Hubert and Arabie) are equivalent in the exclusive hard domain. The reported experiments show that only 13AGRI could provide both a fine-grained evaluation across clusterings with different numbers of clusters and a constant evaluation between random clusterings, showing all the four desirable properties considered here. We identified a high correlation between 13AGRI applied to fuzzy clusterings and ARI applied to hard exclusive clusterings over 14 real data sets from the UCI repository, which corroborates the validity of 13AGRI fuzzy clustering evaluation. 13AGRI also showed good results as a clustering stability statistic for solutions produced by the expectation maximization algorithm for Gaussian mixture

ConNEcT:A Novel Network Approach for Investigating the Co-occurrence of Binary Psychopathological Symptoms Over Time

Network analysis is an increasingly popular approach to study mental disorders in all their complexity. Multiple methods have been developed to extract networks from cross-sectional data, with these data being either continuous or binary. However, when it comes to time series data, most efforts have focused on continuous data. We therefore propose ConNEcT, a network approach for binary symptom data across time. ConNEcT allows to visualize and study the prevalence of different symptoms as well as their co-occurrence, measured by means of a contingency measure in one single network picture. ConNEcT can be complemented with a significance test that accounts for the serial dependence in the data. To illustrate the usefulness of ConNEcT, we re-analyze data from a study in which patients diagnosed with major depressive disorder weekly reported the absence or presence of eight depression symptoms. We first extract ConNEcTs for all patients that provided data during at least 104 weeks, revealing strong inter-individual differences in which symptom pairs co-occur significantly. Second, to gain insight into these differences, we apply Hierarchical Classes Analysis on the co-occurrence patterns of all patients, showing that they can be grouped into meaningful clusters. Core depression symptoms (i.e., depressed mood and/or diminished interest), cognitive problems and loss of energy seem to co-occur universally, but preoccupation with death, psychomotor problems or eating problems only co-occur with other symptoms for specific patient subgroups

Evaluation of clustering results and novel cluster algorithms

Cluster analysis is frequently performed in many application fields to find groups in data. For example, in medicine, researchers have used gene expression data to cluster patients suffering from a particular disease (e.g., breast cancer), in order to detect new disease subtypes. Many cluster algorithms and methods for cluster validation, i.e., methods for evaluating the quality of cluster analysis results, have been proposed in the literature. However, open questions about the evaluation of both clustering results and novel cluster algorithms remain. It has rarely been discussed whether a) interesting clustering results or b) promising performance evaluations of newly presented cluster algorithms might be over-optimistic, in the sense that these good results cannot be replicated on new data or in other settings. Such questions are relevant in light of the so-called "replication crisis"; in various research disciplines such as medicine, biology, psychology, and economics, many results have turned out to be non-replicable, casting doubt on the trustworthiness and reliability of scientific findings. This crisis has led to increasing popularity of "metascience". Metascientific studies analyze problems that have contributed to the replication crisis (e.g., questionable research practices), and propose and evaluate possible solutions. So far, metascientific studies have mainly focused on issues related to significance testing. In contrast, this dissertation addresses the reliability of a) clustering results in applied research and b) results concerning newly presented cluster algorithms in the methodological literature. Different aspects of this topic are discussed in three Contributions. The first Contribution presents a framework for validating clustering results on validation data. Using validation data is vital to examine the replicability and generalizability of results. While applied researchers sometimes use validation data to check their clustering results, our article is the first to review the different approaches in the literature and to structure them in a systematic manner. We demonstrate that many classical cluster validation techniques, such as internal and external validation, can be combined with validation data. Our framework provides guidance to applied researchers who wish to evaluate their own clustering results or the results of other teams on new data. The second Contribution applies the framework from Contribution 1 to quantify over-optimistic bias in the context of a specific application field, namely unsupervised microbiome research. We analyze over-optimism effects which result from the multiplicity of analysis strategies for cluster analysis and network learning. The plethora of possible analysis strategies poses a challenge for researchers who are often uncertain about which method to use. Researchers might be tempted to try different methods on their dataset and look for the method yielding the "best" result. If only the "best" result is selectively reported, this may cause "overfitting" of the method to the dataset and the result might not be replicable on validation data. We quantify such over-optimism effects for four illustrative types of unsupervised research tasks (clustering of bacterial genera, hub detection in microbial association networks, differential network analysis, and clustering of samples). Contributions 1 and 2 consider the evaluation of clustering results and thus adopt a metascientific perspective on applied research. In contrast, the third Contribution is a metascientific study about methodological research on the development of new cluster algorithms. This Contribution analyzes the over-optimistic evaluation and reporting of novel cluster algorithms. As an illustrative example, we consider the recently proposed cluster algorithm "Rock"; initially deemed promising, it later turned out to be not generally better than its competitors. We demonstrate how Rock can nevertheless appear to outperform competitors via optimization of the evaluation design, namely the used data types, data characteristics, the algorithm’s parameters, and the choice of competing algorithms. The study is a cautionary tale that illustrates how easy it can be for researchers to claim apparent "superiority" of a new cluster algorithm. This, in turn, stresses the importance of strategies for avoiding the problems of over-optimism, such as neutral benchmark studies