Multi-View Multiple Clusterings using Deep Matrix Factorization

Multi-view clustering aims at integrating complementary information from multiple heterogeneous views to improve clustering results. Existing multi-view clustering solutions can only output a single clustering of the data. Due to their multiplicity, multi-view data, can have different groupings that are reasonable and interesting from different perspectives. However, how to find multiple, meaningful, and diverse clustering results from multi-view data is still a rarely studied and challenging topic in multi-view clustering and multiple clusterings. In this paper, we introduce a deep matrix factorization based solution (DMClusts) to discover multiple clusterings. DMClusts gradually factorizes multi-view data matrices into representational subspaces layer-by-layer and generates one clustering in each layer. To enforce the diversity between generated clusterings, it minimizes a new redundancy quantification term derived from the proximity between samples in these subspaces. We further introduce an iterative optimization procedure to simultaneously seek multiple clusterings with quality and diversity. Experimental results on benchmark datasets confirm that DMClusts outperforms state-of-the-art multiple clustering solutions

Discovering multi–level structures in bio-molecular data through the Bernstein inequality

Background: The unsupervised discovery of structures (i.e. clusterings) underlying data is a central issue in several branches of bioinformatics. Methods based on the concept of stability have been recently proposed to assess the reliability of a clustering procedure and to estimate the ”optimal ” number of clusters in bio-molecular data. A major problem with stability-based methods is the detection of multi-level structures (e.g. hierarchical functional classes of genes), and the assessment of their statistical significance. In this context, a chi-square based statistical test of hypothesis has been proposed; however, to assure the correctness of this technique some assumptions about the distribution of the data are needed. Results: To assess the statistical significance and to discover multi-level structures in bio-molecular data, a new method based on Bernstein’s inequality is proposed. This approach makes no assumptions about the distribution of the data, thus assuring a reliable application to a large range of bioinformatics problems. Results with synthetic and DNA microarray data show the effectiveness of the proposed method. Conclusions: The Bernstein test, due to its loose assumptions, is more sensitive than the chi-square test to the detection of multiple structures simultaneously present in the data. Nevertheless it is less selective, that is subject to more false positives, but adding independence assumptions, a more selective variant of the Bernstein inequality-based test is also presented. The proposed methods can be applied to discover multiple structures and to assess their significance in different types of bio-molecular data

An Analytical Performance Evaluation on Multiview Clustering Approaches

The concept of machine learning encompasses a wide variety of different approaches, one of which is called clustering. The data points are grouped together in this approach to the problem. Using a clustering method, it is feasible, given a collection of data points, to classify each data point as belonging to a specific group. This can be done if the algorithm is given the collection of data points. In theory, data points that constitute the same group ought to have attributes and characteristics that are equivalent to one another, however data points that belong to other groups ought to have properties and characteristics that are very different from one another. The generation of multiview data is made possible by recent developments in information collecting technologies. The data were collected from à variety of sources and were analysed using a variety of perspectives. The data in question are what are known as multiview data. On a single view, the conventional clustering algorithms are applied. In spite of this, real-world data are complicated and can be clustered in a variety of different ways, depending on how the data are interpreted. In practise, the real-world data are messy. In recent years, Multiview Clustering, often known as MVC, has garnered an increasing amount of attention due to its goal of utilising complimentary and consensus information derived from different points of view. On the other hand, the vast majority of the systems that are currently available only enable the single-clustering scenario, whereby only makes utilization of a single cluster to split the data. This is the case since there is only one cluster accessible. In light of this, it is absolutely necessary to carry out investigation on the multiview data format. The study work is centred on multiview clustering and how well it performs compared to these other strategies

Advances in correlation clustering

The task of clustering is to partition a given dataset in such a way that objects within a cluster are similar to each other while being dissimilar to objects from other clusters. One challenge to this task arises when dealing with datasets where the objects are characterized by an increased number of features. Objects within a cluster may exhibit correlations among a subset of features. In order to detect such clusters, within the past two decades significant contributions have been made which yielded a wealth of literature presenting algorithms for detecting clusters in arbitrarily oriented subspaces. Each of them approaches the correlation clustering task differently, by relying on different underlying models and techniques. Building on the current progress made, this work addresses the following aspects: First, it is dedicated to the research question of how to actually measure and therefore evaluate the quality of a correlation clustering. As an initial endeavor, it is investigated how far objectives for internal evaluation criteria can be derived from existing correlation clustering algorithms. The results from this approach, however, exhibited limitations rendering the derived internal evaluation measures not suitable. As a consequence endeavors have been made to identify commonalities among correlation clustering algorithms leading to a cost function that is introduced as an internal evaluation measure. Experiments illustrate its capability to assess clusterings based on aspects that are inherent to all correlation clustering algorithms studied so far. Second, among the existing correlation clustering algorithms, one takes a unique approach. Clusters are detected in a space spanned by the parameters of a given function, known as Hough space. The detection itself is achieved by finding so-called regions of interest (ROI) in Hough space. While the de- tection of ROIs in the existing algorithm performs well in most cases, there are conditions under which the runtime deteriorates, especially in data sets with high amounts of noise. In this work, two different novel strategies are proposed for ROI detection in Hough space, where it is elaborated on their individual strengths and weaknesses. Besides the aspect of ROI detection, endeavors are made to go beyond linearity by proposing approaches for detecting quadratic and periodic correlated clusters using Hough transform. Third, while there exist different views, like local and global correlated clusters, explorations are made in this work with the question in mind, in how far both views can be unified under a single concept. Finally, approaches are proposed and investigated that enhance the resilience of correlation clustering methods against outliers.Die Aufgabe von Clustering besteht darin einen gegebenen Datensatz so zu partitionieren dass Objekte innerhalb eines Clusters ähnlich zueinander sind, während diese unähnlich zu Objekten aus anderen Clustern sind. Eine Herausforderung bei dieser Aufgabe kommt auf, wenn man mit Daten umgeht, die sich durch eine erhöhte Anzahl an Merkmalen auszeichnen. Objekte innerhalb eines Clusters können Korrelationen zwischen Teilmengen von Merkmalen aufweisen. Um solche Cluster erkennen zu können, wurden innerhalb der vergangenen zwei Dekaden signifikante Beiträge geleistet. Darin werden Algorithmen vorgestellt, mit denen Cluster in beliebig ausgerichteten Unterräumen erkannt werden können. Jedes der Verfahren verfolgt zur Lösung der Correlation Clustering Aufgabenstellung unterschiedliche Ansätze indem sie sich auf unterschiedliche zugrunde liegende Modelle und Techniken stützen. Aufbauend auf die bislang gemachten Fortschritte, adressiert diese Arbeit die folgenden Aspekte: Zunächst wurde sich der Forschungsfrage gewidmet wie die Güte eines Correlation Clustering Ergebnisses bestimmt werden kann. In einer ersten Bestrebung wurde ermittelt in wie fern Ziele für interne Evaluationskriterien von bereits bestehenden Correlation Clustering Algorithmen abgeleitet werden können. Die Ergebnisse von dieser Vorgehensweise offenbarten Limitationen die einen Einsatz als interne Evaluations- maße ungeeignet erschienen ließen. Als Konsequenz wurden Bestrebungen unternommen Gemeinsamkeiten zwischen Correlation Clustering Algorithmen zu identifizieren, welche zu einer Kostenfunktion führten die als ein internes Evaluationsmaß eingeführt wurde. Die Experimente illustrieren die Fähigkeit, Clusterings auf Basis von Aspekten die inherent in allen bislang studierten Correlation Clustering Algorithmen vorliegen zu bewerten. Als einen zweiten Punkt nimmt ein Correlation Clustering Verfahren unter den bislang existierenden Methoden eine Sonderstellung ein. Die Cluster werden in einem Raum erkannt welches von den parmetern einer gegebenen Funktion aufgespannt werden welches als Hough Raum bekannt ist. Die Erkennung selbst wird durch das Finden von sogenannten "Regions of Interest" (ROI) im Hough Raum erreicht. Während die Erkennung von ROIs in dem bestehenden Verfahren in den meisten Fällen gut verläuft, gibt es Bedingungen, unter welchen die Laufzeit sich verschlechtert, insbesondere bei Datensätzen mit großen Mengen von Rauschen. In dieser Arbeit werden zwei verschiedene neue Strategien für die ROI Erkennung im Hough Raum vorgeschlagen, wobei auf die individuellen Stärken und Schwächen eingegangen wird. Neben dem Aspekt der ROI Erkennung sind Forschungen unternommen worden um über die Linearität der Correlation Cluster hinaus zu gehen, indem Verfahren entwickelt wurden, mit denen quadratisch- und periodisch korrelierte Cluster mittels Hough Transform erkannt werden können. Der dritte Aspekt dieser Arbeit widmet sich den sogenannten "views". Während es verschiedene views gibt wie z.B. bei lokal oder global korrelierten Clustern, wurden Forschungen unternommen mit der Fragestellung, in wie fern beide Ansichten unter einem einzigen gemeinsamen Konzept vereinigt werden können. Zuletzt sind Ansätze vorgeschlagen und untersucht worden welche die Resilienz von Correlation Clustering Methoden hinsichtlich Ausreißer erhöhen