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

A review on data stream classification

At this present time, the significance of data streams cannot be denied as many researchers have placed their focus on the research areas of databases, statistics, and computer science. In fact, data streams refer to some data points sequences that are found in order with the potential to be non-binding, which is generated from the process of generating information in a manner that is not stationary. As such the typical tasks of searching data have been linked to streams of data that are inclusive of clustering, classification, and repeated mining of pattern. This paper presents several data stream clustering approaches, which are based on density, besides attempting to comprehend the function of the related algorithms; both semi-supervised and active learning, along with reviews of a number of recent studies

The Spatial Clustering of Low Luminosity AGN

We present the first multi-parameter analysis of the narrow line AGN clustering properties. Estimates of the two-point correlation function (CF) based on SDSS DR2 data reveal that Seyferts are clearly less clustered than normal galaxies, while the clustering amplitude (r_0) of LINERs is consistent with that of the parent galaxy population. The similarities in the host properties (color and concentration index) of Seyferts and LINERs suggest that the difference in their r_0 is not driven by the morphology-density relation. We find that the luminosity of [O I] emission shows the strongest influence on AGN clustering, with low L([O I]) sources having the highest r_0. This trend is much stronger than the previously detected dependence on L([O III]), which we confirm. There is a strong correspondence between the clustering patterns of objects of given spectral type and their physical properties. LINERs, which exhibit high r_0, show the lowest luminosities and obscuration levels, and relatively low gas densities (n_e), suggesting that these objects harbor black holes that are relatively massive yet weakly active or inefficient in their accretion, probably due to the insufficiency of their fuel supply. Seyferts, which have low r_0, are luminous and show large n_e, suggesting that their black holes are less massive but accrete quickly and efficiently enough to clearly dominate the ionization. The low r_0 of the H II galaxies can be understood as a consequence of both the morphology-density and star formation rate-density relations, however, their spectral properties suggest that their centers hide amidst large amounts of obscuring material black holes of generally low mass whose activity remains relatively feeble. Our own Milky Way may be a typical such case.[abridged]Comment: 27 pages, color figures, some are severely degraded in resolution, emulateapj. See http://www.physics.drexel.edu/~constant/work/agnclustering.ps for high resolution version. Accepted to Ap

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

Partitional Clustering - An Iterative Algorithm

Cluster analysis is the term applied to a group of analyses that seek to divide a set of objects into a number of homogeneous groups or clusters, when there no a priori information about the group structure of the data. Clustering is an active research topic in data mining and different methods have been proposed in the literature. Most of these methods are based on the use of a distance measure defined either on numerical attributes or on categorical attributes. There are three basic categories of clustering methods: partitional methods, hierarchical methods and density-based methods. This paper proposes an iterative algorithm for partitional clustering

The clustering properties of radio-selected AGN and star-forming galaxies up to redshifts z~3

We present the clustering properties of a complete sample of 968 radio sources detected at 1.4 GHz by the VLA-COSMOS survey with radio fluxes brighter than 0.15 mJy. 92% have redshift determinations from the Laigle et al. (2016) catalogue. Based on their radio-luminosity, these objects have been divided into two populations of 644 AGN and 247 star-forming galaxies. By fixing the slope of the auto-correlation function to gamma=2, we find r_0=11.7^{+1.0}_{-1.1} Mpc for the clustering length of the whole sample, while r_0=11.2^{+2.5}_{-3.3} Mpc and r_0=7.8^{+1.6}_{-2.1} Mpc (r_0=6.8^{+1.4}_{-1.8} Mpc if we restrict our analysis to z<0.9) are respectively obtained for AGN and star-forming galaxies. These values correspond to minimum masses for dark matter haloes of M_min=10^[13.6^{+0.3}_{-0.6}] M_sun for radio-selected AGN and M_min=10^[13.1^{+0.4}_{-1.6}] M_sun for radio-emitting star-forming galaxies (M_min=10^[12.7^{+0.7}_{-2.2}] M_sun for z<0.9). Comparisons with previous works imply an independence of the clustering properties of the AGN population with respect to both radio luminosity and redshift. We also investigate the relationship between dark and luminous matter in both populations. We obtain /M_halo/M_halo<~10^{-2.4} in the case of star-forming galaxies. Furthermore, if we restrict to z<~0.9 star-forming galaxies, we derive /M_halo<~10^{-2.1}, result which clearly indicates the cosmic process of stellar build-up as one moves towards the more local universe. Comparisons between the observed space density of radio-selected AGN and that of dark matter haloes shows that about one in two haloes is associated with a black hole in its radio-active phase. This suggests that the radio-active phase is a recurrent phenomenon.Comment: 11 pages, 7 figures, minor changes to match published version on MNRA

Estimating number of speakers via density-based clustering and classification decision

It is crucial to robustly estimate the number of speakers (NoS) from the recorded audio mixtures in a reverberant environment. Some popular time-frequency (TF) methods approach this NoS estimation problem by assuming that only one of the speech components is active at each TF slot. However, this condition is violated in many scenarios where the speeches are convolved with long length of room impulse response coefficients, which causes degenerated performance of NoS estimation. To tackle this problem, a density-based clustering strategy is proposed to estimate NoS based on a local dominance assumption of speeches. Our method consists of several steps from clustering to classification of speakers with the consideration of robustness. First, the leading eigenvectors are extracted from the local covariance matrices of mixture TF components and ranked by the combination of local density and minimum distance to other leading eigenvectors with higher density. Second, a gap-based method is employed to determine the cluster centers from the ranked leading eigenvectors at each frequency bin. Third, a criterion based on averaged volume of cluster centers is proposed to select reliable clustering results at some frequency bins for the classification decision of NoS. The experiment results demonstrate that the proposed algorithm is superior to the existing methods in various reverberation cases with noise-free condition or noise condition