Neuroengineering of Clustering Algorithms

Cluster analysis can be broadly divided into multivariate data visualization, clustering algorithms, and cluster validation. This dissertation contributes neural network-based techniques to perform all three unsupervised learning tasks. Particularly, the first paper provides a comprehensive review on adaptive resonance theory (ART) models for engineering applications and provides context for the four subsequent papers. These papers are devoted to enhancements of ART-based clustering algorithms from (a) a practical perspective by exploiting the visual assessment of cluster tendency (VAT) sorting algorithm as a preprocessor for ART offline training, thus mitigating ordering effects; and (b) an engineering perspective by designing a family of multi-criteria ART models: dual vigilance fuzzy ART and distributed dual vigilance fuzzy ART (both of which are capable of detecting complex cluster structures), merge ART (aggregates partitions and lessens ordering effects in online learning), and cluster validity index vigilance in fuzzy ART (features a robust vigilance parameter selection and alleviates ordering effects in offline learning). The sixth paper consists of enhancements to data visualization using self-organizing maps (SOMs) by depicting in the reduced dimension and topology-preserving SOM grid information-theoretic similarity measures between neighboring neurons. This visualization\u27s parameters are estimated using samples selected via a single-linkage procedure, thereby generating heatmaps that portray more homogeneous within-cluster similarities and crisper between-cluster boundaries. The seventh paper presents incremental cluster validity indices (iCVIs) realized by (a) incorporating existing formulations of online computations for clusters\u27 descriptors, or (b) modifying an existing ART-based model and incrementally updating local density counts between prototypes. Moreover, this last paper provides the first comprehensive comparison of iCVIs in the computational intelligence literature --Abstract, page iv

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

DCSI -- An improved measure of cluster separability based on separation and connectedness

Whether class labels in a given data set correspond to meaningful clusters is crucial for the evaluation of clustering algorithms using real-world data sets. This property can be quantified by separability measures. A review of the existing literature shows that neither classification-based complexity measures nor cluster validity indices (CVIs) adequately incorporate the central aspects of separability for density-based clustering: between-class separation and within-class connectedness. A newly developed measure (density cluster separability index, DCSI) aims to quantify these two characteristics and can also be used as a CVI. Extensive experiments on synthetic data indicate that DCSI correlates strongly with the performance of DBSCAN measured via the adjusted rand index (ARI) but lacks robustness when it comes to multi-class data sets with overlapping classes that are ill-suited for density-based hard clustering. Detailed evaluation on frequently used real-world data sets shows that DCSI can correctly identify touching or overlapping classes that do not form meaningful clusters

Multi-objective evolutionary algorithms for data clustering

In this work we investigate the use of Multi-Objective metaheuristics for the data-mining task of clustering. We �first investigate methods of evaluating the quality of clustering solutions, we then propose a new Multi-Objective clustering algorithm driven by multiple measures of cluster quality and then perform investigations into the performance of different Multi-Objective clustering algorithms. In the context of clustering, a robust measure for evaluating clustering solutions is an important component of an algorithm. These Cluster Quality Measures (CQMs) should rely solely on the structure of the clustering solution. A robust CQM should have three properties: it should be able to reward a \good" clustering solution; it should decrease in value monotonically as the solution quality deteriorates and, it should be able to evaluate clustering solutions with varying numbers of clusters. We review existing CQMs and present an experimental evaluation of their robustness. We find that measures based on connectivity are more robust than other measures for cluster evaluation. We then introduce a new Multi-Objective Clustering algorithm (MOCA). The use of Multi-Objective optimisation in clustering is desirable because it permits the incorporation of multiple measures of cluster quality. Since the definition of what constitutes a good clustering is far from clear, it is beneficial to develop algorithms that allow for multiple CQMs to be accommodated. The selection of the clustering quality measures to use as objectives for MOCA is informed by our previous work with internal evaluation measures. We explain the implementation details and perform experimental work to establish its worth. We compare MOCA with k-means and find some promising results. We�find that MOCA can generate a pool of clustering solutions that is more likely to contain the optimal clustering solution than the pool of solutions generated by k-means. We also perform an investigation into the performance of different implementations of MOEA algorithms for clustering. We�find that representations of clustering based around centroids and medoids produce more desirable clustering solutions and Pareto fronts. We also �find that mutation operators that greatly disrupt the clustering solutions lead to better exploration of the Pareto front whereas mutation operators that modify the clustering solutions in a more moderate way lead to higher quality clustering solutions. We then perform more specific investigations into the performance of mutation operators focussing on operators that promote clustering solution quality, exploration of the Pareto front and a hybrid combination. We use a number of techniques to assess the performance of the mutation operators as the algorithms execute. We confirm that a disruptive mutation operator leads to better exploration of the Pareto front and mutation operators that modify the clustering solutions lead to the discovery of higher quality clustering solutions. We find that our implementation of a hybrid mutation operator does not lead to a good improvement with respect to the other mutation operators but does show promise for future work

Revealing the Hierarchical Structure of Galactic Haloes with Novel Data Mining Algorithms

The research within this thesis is directed at developing, training, and testing unsupervised astrophysical clustering algorithms that extract meaningful structures from their input data. It is a well-studied consequence of the ΛCDM cosmological model of the Universe that these structures form hierarchically through the continual merging of smaller structures. As such, galaxies are expected to contain a myriad of substructure that act as fossil records of the galaxies themselves. As larger and more advanced surveys continue to be conducted, we are faced with the task of unearthing these galaxies and their substructures over a vast range of ever-more-complicated data sets. To tackle this issue, it is necessary to prepare ourselves with appropriate tools that can sift through these data sets and discover new structures. This is the goal that motivates the works within this thesis. First I developed Halo-OPTICS, a new algorithm designed to hierarchically classify astrophysical clusters within N-body particle simulations. I showed that it performs well against a current state-of-the-art code (e.g. VELOCIraptor) even though it uses comparatively less of the available information within the simulation data. Next I developed CluSTAR-ND and in doing so I made various algorithmic improvements upon its predecessor Halo-OPTICS. These upgrades dramatically improved CluSTAR-ND's computational footprint, its sensitivity to relevant clusters, and its capacity to operate over any size data set containing any number of dimensions. Finally, I developed CluSTARR-ND which boasts all the operational virtues of CluSTAR-ND while also providing an OPTICS-style representation of clustering structure and identifying clusters as statistically distinct overdensities of the input data. CluSTARR-ND therefore opens up the opportunity for adaptively providing a meaningful hierarchical astrophysical clustering of any n-point d-dimensional data set with an extremely modest computational demand

Density-based algorithms for active and anytime clustering

Data intensive applications like biology, medicine, and neuroscience require effective and efficient data mining technologies. Advanced data acquisition methods produce a constantly increasing volume and complexity. As a consequence, the need of new data mining technologies to deal with complex data has emerged during the last decades. In this thesis, we focus on the data mining task of clustering in which objects are separated in different groups (clusters) such that objects inside a cluster are more similar than objects in different clusters. Particularly, we consider density-based clustering algorithms and their applications in biomedicine. The core idea of the density-based clustering algorithm DBSCAN is that each object within a cluster must have a certain number of other objects inside its neighborhood. Compared with other clustering algorithms, DBSCAN has many attractive benefits, e.g., it can detect clusters with arbitrary shape and is robust to outliers, etc. Thus, DBSCAN has attracted a lot of research interest during the last decades with many extensions and applications. In the first part of this thesis, we aim at developing new algorithms based on the DBSCAN paradigm to deal with the new challenges of complex data, particularly expensive distance measures and incomplete availability of the distance matrix. Like many other clustering algorithms, DBSCAN suffers from poor performance when facing expensive distance measures for complex data. To tackle this problem, we propose a new algorithm based on the DBSCAN paradigm, called Anytime Density-based Clustering (A-DBSCAN), that works in an anytime scheme: in contrast to the original batch scheme of DBSCAN, the algorithm A-DBSCAN first produces a quick approximation of the clustering result and then continuously refines the result during the further run. Experts can interrupt the algorithm, examine the results, and choose between (1) stopping the algorithm at any time whenever they are satisfied with the result to save runtime and (2) continuing the algorithm to achieve better results. Such kind of anytime scheme has been proven in the literature as a very useful technique when dealing with time consuming problems. We also introduced an extended version of A-DBSCAN called A-DBSCAN-XS which is more efficient and effective than A-DBSCAN when dealing with expensive distance measures. Since DBSCAN relies on the cardinality of the neighborhood of objects, it requires the full distance matrix to perform. For complex data, these distances are usually expensive, time consuming or even impossible to acquire due to high cost, high time complexity, noisy and missing data, etc. Motivated by these potential difficulties of acquiring the distances among objects, we propose another approach for DBSCAN, called Active Density-based Clustering (Act-DBSCAN). Given a budget limitation B, Act-DBSCAN is only allowed to use up to B pairwise distances ideally to produce the same result as if it has the entire distance matrix at hand. The general idea of Act-DBSCAN is that it actively selects the most promising pairs of objects to calculate the distances between them and tries to approximate as much as possible the desired clustering result with each distance calculation. This scheme provides an efficient way to reduce the total cost needed to perform the clustering. Thus it limits the potential weakness of DBSCAN when dealing with the distance sparseness problem of complex data. As a fundamental data clustering algorithm, density-based clustering has many applications in diverse fields. In the second part of this thesis, we focus on an application of density-based clustering in neuroscience: the segmentation of the white matter fiber tracts in human brain acquired from Diffusion Tensor Imaging (DTI). We propose a model to evaluate the similarity between two fibers as a combination of structural similarity and connectivity-related similarity of fiber tracts. Various distance measure techniques from fields like time-sequence mining are adapted to calculate the structural similarity of fibers. Density-based clustering is used as the segmentation algorithm. We show how A-DBSCAN and A-DBSCAN-XS are used as novel solutions for the segmentation of massive fiber datasets and provide unique features to assist experts during the fiber segmentation process.Datenintensive Anwendungen wie Biologie, Medizin und Neurowissenschaften erfordern effektive und effiziente Data-Mining-Technologien. Erweiterte Methoden der Datenerfassung erzeugen stetig wachsende Datenmengen und Komplexit\"at. In den letzten Jahrzehnten hat sich daher ein Bedarf an neuen Data-Mining-Technologien f\"ur komplexe Daten ergeben. In dieser Arbeit konzentrieren wir uns auf die Data-Mining-Aufgabe des Clusterings, in der Objekte in verschiedenen Gruppen (Cluster) getrennt werden, so dass Objekte in einem Cluster untereinander viel \"ahnlicher sind als Objekte in verschiedenen Clustern. Insbesondere betrachten wir dichtebasierte Clustering-Algorithmen und ihre Anwendungen in der Biomedizin. Der Kerngedanke des dichtebasierten Clustering-Algorithmus DBSCAN ist, dass jedes Objekt in einem Cluster eine bestimmte Anzahl von anderen Objekten in seiner Nachbarschaft haben muss. Im Vergleich mit anderen Clustering-Algorithmen hat DBSCAN viele attraktive Vorteile, zum Beispiel kann es Cluster mit beliebiger Form erkennen und ist robust gegen\"uber Ausrei{\ss}ern. So hat DBSCAN in den letzten Jahrzehnten gro{\ss}es Forschungsinteresse mit vielen Erweiterungen und Anwendungen auf sich gezogen. Im ersten Teil dieser Arbeit wollen wir auf die Entwicklung neuer Algorithmen eingehen, die auf dem DBSCAN Paradigma basieren, um mit den neuen Herausforderungen der komplexen Daten, insbesondere teurer Abstandsma{\ss}e und unvollst\"andiger Verf\"ugbarkeit der Distanzmatrix umzugehen. Wie viele andere Clustering-Algorithmen leidet DBSCAN an schlechter Per- formanz, wenn es teuren Abstandsma{\ss}en f\"ur komplexe Daten gegen\"uber steht. Um dieses Problem zu l\"osen, schlagen wir einen neuen Algorithmus vor, der auf dem DBSCAN Paradigma basiert, genannt Anytime Density-based Clustering (A-DBSCAN), der mit einem Anytime Schema funktioniert. Im Gegensatz zu dem urspr\"unglichen Schema DBSCAN, erzeugt der Algorithmus A-DBSCAN zuerst eine schnelle Ann\"aherung des Clusterings-Ergebnisses und verfeinert dann kontinuierlich das Ergebnis im weiteren Verlauf. Experten k\"onnen den Algorithmus unterbrechen, die Ergebnisse pr\"ufen und w\"ahlen zwischen (1) Anhalten des Algorithmus zu jeder Zeit, wann immer sie mit dem Ergebnis zufrieden sind, um Laufzeit sparen und (2) Fortsetzen des Algorithmus, um bessere Ergebnisse zu erzielen. Eine solche Art eines "Anytime Schemas" ist in der Literatur als eine sehr n\"utzliche Technik erprobt, wenn zeitaufwendige Problemen anfallen. Wir stellen auch eine erweiterte Version von A-DBSCAN als A-DBSCAN-XS vor, die effizienter und effektiver als A-DBSCAN beim Umgang mit teuren Abstandsma{\ss}en ist. Da DBSCAN auf der Kardinalit\"at der Nachbarschaftsobjekte beruht, ist es notwendig, die volle Distanzmatrix auszurechen. F\"ur komplexe Daten sind diese Distanzen in der Regel teuer, zeitaufwendig oder sogar unm\"oglich zu errechnen, aufgrund der hohen Kosten, einer hohen Zeitkomplexit\"at oder verrauschten und fehlende Daten. Motiviert durch diese m\"oglichen Schwierigkeiten der Berechnung von Entfernungen zwischen Objekten, schlagen wir einen anderen Ansatz f\"ur DBSCAN vor, namentlich Active Density-based Clustering (Act-DBSCAN). Bei einer Budgetbegrenzung B, darf Act-DBSCAN nur bis zu B ideale paarweise Distanzen verwenden, um das gleiche Ergebnis zu produzieren, wie wenn es die gesamte Distanzmatrix zur Hand h\"atte. Die allgemeine Idee von Act-DBSCAN ist, dass es aktiv die erfolgversprechendsten Paare von Objekten w\"ahlt, um die Abst\"ande zwischen ihnen zu berechnen, und versucht, sich so viel wie m\"oglich dem gew\"unschten Clustering mit jeder Abstandsberechnung zu n\"ahern. Dieses Schema bietet eine effiziente M\"oglichkeit, die Gesamtkosten der Durchf\"uhrung des Clusterings zu reduzieren. So schr\"ankt sie die potenzielle Schw\"ache des DBSCAN beim Umgang mit dem Distance Sparseness Problem von komplexen Daten ein. Als fundamentaler Clustering-Algorithmus, hat dichte-basiertes Clustering viele Anwendungen in den unterschiedlichen Bereichen. Im zweiten Teil dieser Arbeit konzentrieren wir uns auf eine Anwendung des dichte-basierten Clusterings in den Neurowissenschaften: Die Segmentierung der wei{\ss}en Substanz bei Faserbahnen im menschlichen Gehirn, die vom Diffusion Tensor Imaging (DTI) erfasst werden. Wir schlagen ein Modell vor, um die \"Ahnlichkeit zwischen zwei Fasern als einer Kombination von struktureller und konnektivit\"atsbezogener \"Ahnlichkeit von Faserbahnen zu beurteilen. Verschiedene Abstandsma{\ss}e aus Bereichen wie dem Time-Sequence Mining werden angepasst, um die strukturelle \"Ahnlichkeit von Fasern zu berechnen. Dichte-basiertes Clustering wird als Segmentierungsalgorithmus verwendet. Wir zeigen, wie A-DBSCAN und A-DBSCAN-XS als neuartige L\"osungen f\"ur die Segmentierung von sehr gro{\ss}en Faserdatens\"atzen verwendet werden, und bieten innovative Funktionen, um Experten w\"ahrend des Fasersegmentierungsprozesses zu unterst\"utzen

Computational analysis of gene expression data

Gene expression is central to the function of living cells. While advances in sequencing and expression measurement technology over the past decade has greatly facilitated the further understanding of the genome and its functions, the characterisation of functional groups of genes remains one of the most important problems in modern biology. Technological advancements have resulted in massive information output, with the priority objective shifting to development of data analysis methods. As such, a large number of clustering approaches have been proposed for the analysis of gene expression data obtained from microarray experiments, and consequently, confusion regarding the best approach to take. Common techniques applied are not necessarily the most applicable for the analysis of patterns in microarray data. This confusion is clarified through provision of a framework for the analysis of clustering technique and investigation of how well they apply to gene expression data. To this end, the properties of microarray data itself are examined, followed by an examination of the properties of clustering techniques and how well they apply to gene expression. Clearly, each technique will find patterns even if the structures are not meaningful in a biological context and these structures are not usually the same for different algorithms. Also, these algorithms are inherently biased as properties of clusters reflect built in clustering criteria. From these considerations, it is clear that cluster validation is critical for algorithm development and verification of results, usually based on a manual, lengthy and subjective exploration process. Consequently, it is key to the interpretation of the gene expression data. We carry out a critical analysis of current methods used to evaluate clustering results. Clusters obtained from real and synthetic datasets are compared between algorithms. To understand the properties of complex gene expression datasets, graphical representations can be used. Intuitively, the data can be represented in terms of a bipartite graph, with weighted edges between gene-sample node couples corresponding to significant expression measurements of interest. In this research, this method of representation is extensively studied and methods are used, in combination with probabilistic models, to develop new clustering techniques for analysis of gene expression data in this mode of representation. Performance of these techniques can be influenced both by the search algorithm, and, by the graph weighting scheme and both merit vigorous investigation. A novel edge-weighting scheme, based on empirical evidence, is presented. The scheme is tested using several benchmark datasets at various levels of granularity, and comparisons are provided with current a popular data analysis method used in the Bioinformatics community. The analysis shows that the new empirical based scheme developed out-performs current edge-weighting methods by accounting for the subtleties in the data through a data-dependent threshold analysis, and selecting ‘interesting’ gene-sample couples based on relative values. The graphical theme of gene expression analysis is further developed by construction of a one-mode gene expression network which specifically focuses on local interactions among genes. Classical network theory is used to identify and examine organisational properties in the resulting graphs. A new algorithm, GraphCreate, is presented which finds functional modules in the one-mode graph, i.e. sets of genes which are coherently expressed over subsets of samples, and a scoring scheme developed (using bi-partite graph properties as a basis) to weight these modules. Use of this representation is used to extensively study published gene expression datasets and to identify functional modules of genes with GraphCreate. This work is important as it advances research in the area of transcriptome analyiii sis, beyond simply finding groups of coherently expressed genes, by developing a general framework to understand how and when gene sets are interacting

Multilevel mixed-type data analysis for validating partitions of scrapie isolates

The dissertation arises from a joint study with the Department of Food Safety and Veterinary Public Health of the Istituto Superiore di Sanità. The aim is to investigate and validate the existence of distinct strains of the scrapie disease taking into account the availability of a priori benchmark partition formulated by researchers. Scrapie of small ruminants is caused by prions, which are unconventional infectious agents of proteinaceous nature a ecting humans and animals. Due to the absence of nucleic acids, which precludes direct analysis of strain variation by molecular methods, the presence of di erent sheep scrapie strains is usually investigated by bioassay in laboratory rodents. Data are collected by an experimental study on scrapie conducted at the Istituto Superiore di Sanità by experimental transmission of scrapie isolates to bank voles. We aim to discuss the validation of a given partition in a statistical classification framework using a multi-step procedure. Firstly, we use unsupervised classification to see how alternative clustering results match researchers’ understanding of the heterogeneity of the isolates. We discuss whether and how clustering results can be eventually exploited to extend the preliminary partition elicited by researchers. Then we motivate the subsequent partition validation based on the predictive performance of several supervised classifiers. Our data-driven approach contains two main methodological original contributions. We advocate the use of partition validation measures to investigate a given benchmark partition: firstly we discuss the issue of how the data can be used to evaluate a preliminary benchmark partition and eventually modify it with statistical results to find a conclusive partition that could be used as a “gold standard” in future studies. Moreover, collected data have a multilevel structure and for each lower-level unit, mixed-type data are available. Each step in the procedure is then adapted to deal with multilevel mixed-type data. We extend distance-based clustering algorithms to deal with multilevel mixed-type data. Whereas in supervised classification we propose a two-step approach to classify the higher-level units starting from the lower-level observations. In this framework, we also need to define an ad-hoc cross validation algorithm

Facing-up Challenges of Multiobjective Clustering Based on Evolutionary Algorithms: Representations, Scalability and Retrieval Solutions

Aquesta tesi es centra en algorismes de clustering multiobjectiu, que estan basats en optimitzar varis objectius simultàniament obtenint una col•lecció de solucions potencials amb diferents compromisos entre objectius. El propòsit d'aquesta tesi consisteix en dissenyar i implementar un nou algorisme de clustering multiobjectiu basat en algorismes evolutius per afrontar tres reptes actuals relacionats amb aquest tipus de tècniques. El primer repte es centra en definir adequadament l'àrea de possibles solucions que s'explora per obtenir la millor solució i que depèn de la representació del coneixement. El segon repte consisteix en escalar el sistema dividint el conjunt de dades original en varis subconjunts per treballar amb menys dades en el procés de clustering. El tercer repte es basa en recuperar la solució més adequada tenint en compte la qualitat i la forma dels clusters a partir de la regió més interessant de la col•lecció de solucions ofertes per l’algorisme.Esta tesis se centra en los algoritmos de clustering multiobjetivo, que están basados en optimizar varios objetivos simultáneamente obteniendo una colección de soluciones potenciales con diferentes compromisos entre objetivos. El propósito de esta tesis consiste en diseñar e implementar un nuevo algoritmo de clustering multiobjetivo basado en algoritmos evolutivos para afrontar tres retos actuales relacionados con este tipo de técnicas. El primer reto se centra en definir adecuadamente el área de posibles soluciones explorada para obtener la mejor solución y que depende de la representación del conocimiento. El segundo reto consiste en escalar el sistema dividiendo el conjunto de datos original en varios subconjuntos para trabajar con menos datos en el proceso de clustering El tercer reto se basa en recuperar la solución más adecuada según la calidad y la forma de los clusters a partir de la región más interesante de la colección de soluciones ofrecidas por el algoritmo.This thesis is focused on multiobjective clustering algorithms, which are based on optimizing several objectives simultaneously obtaining a collection of potential solutions with different trade¬offs among objectives. The goal of the thesis is to design and implement a new multiobjective clustering technique based on evolutionary algorithms for facing up three current challenges related to these techniques. The first challenge is focused on successfully defining the area of possible solutions that is explored in order to find the best solution, and this depends on the knowledge representation. The second challenge tries to scale-up the system splitting the original data set into several data subsets in order to work with less data in the clustering process. The third challenge is addressed to the retrieval of the most suitable solution according to the quality and shape of the clusters from the most interesting region of the collection of solutions returned by the algorithm