1,799 research outputs found
A Survey on Soft Subspace Clustering
Subspace clustering (SC) is a promising clustering technology to identify
clusters based on their associations with subspaces in high dimensional spaces.
SC can be classified into hard subspace clustering (HSC) and soft subspace
clustering (SSC). While HSC algorithms have been extensively studied and well
accepted by the scientific community, SSC algorithms are relatively new but
gaining more attention in recent years due to better adaptability. In the
paper, a comprehensive survey on existing SSC algorithms and the recent
development are presented. The SSC algorithms are classified systematically
into three main categories, namely, conventional SSC (CSSC), independent SSC
(ISSC) and extended SSC (XSSC). The characteristics of these algorithms are
highlighted and the potential future development of SSC is also discussed.Comment: This paper has been published in Information Sciences Journal in 201
Stable Feature Selection for Biomarker Discovery
Feature selection techniques have been used as the workhorse in biomarker
discovery applications for a long time. Surprisingly, the stability of feature
selection with respect to sampling variations has long been under-considered.
It is only until recently that this issue has received more and more attention.
In this article, we review existing stable feature selection methods for
biomarker discovery using a generic hierarchal framework. We have two
objectives: (1) providing an overview on this new yet fast growing topic for a
convenient reference; (2) categorizing existing methods under an expandable
framework for future research and development
Tree-guided group lasso for multi-response regression with structured sparsity, with an application to eQTL mapping
We consider the problem of estimating a sparse multi-response regression
function, with an application to expression quantitative trait locus (eQTL)
mapping, where the goal is to discover genetic variations that influence
gene-expression levels. In particular, we investigate a shrinkage technique
capable of capturing a given hierarchical structure over the responses, such as
a hierarchical clustering tree with leaf nodes for responses and internal nodes
for clusters of related responses at multiple granularity, and we seek to
leverage this structure to recover covariates relevant to each
hierarchically-defined cluster of responses. We propose a tree-guided group
lasso, or tree lasso, for estimating such structured sparsity under
multi-response regression by employing a novel penalty function constructed
from the tree. We describe a systematic weighting scheme for the overlapping
groups in the tree-penalty such that each regression coefficient is penalized
in a balanced manner despite the inhomogeneous multiplicity of group
memberships of the regression coefficients due to overlaps among groups. For
efficient optimization, we employ a smoothing proximal gradient method that was
originally developed for a general class of structured-sparsity-inducing
penalties. Using simulated and yeast data sets, we demonstrate that our method
shows a superior performance in terms of both prediction errors and recovery of
true sparsity patterns, compared to other methods for learning a
multivariate-response regression.Comment: Published in at http://dx.doi.org/10.1214/12-AOAS549 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Correlation Clustering
Knowledge Discovery in Databases (KDD) is the non-trivial process of identifying valid, novel, potentially useful, and ultimately understandable patterns in data. The core step of the KDD process is the application of a Data Mining algorithm in order to produce a particular enumeration of patterns and relationships in large databases. Clustering is one of the major data mining techniques and aims at grouping the data objects into meaningful classes (clusters) such that the similarity of objects within clusters is maximized, and the similarity of objects from different clusters is minimized. This can serve to group customers with similar interests, or to group genes with related functionalities.
Currently, a challenge for clustering-techniques are especially high dimensional feature-spaces. Due to modern facilities of data collection, real data sets usually contain many features. These features are often noisy or exhibit correlations among each other. However, since these effects in different parts of the data set are differently relevant, irrelevant features cannot be discarded in advance. The selection of relevant features must therefore be integrated into the data mining technique.
Since about 10 years, specialized clustering approaches have been developed to cope with problems in high dimensional data better than classic clustering approaches. Often, however, the different problems of very different nature are not distinguished from one another. A main objective of this thesis is therefore a systematic classification of the diverse approaches developed in recent years according to their task definition, their basic strategy, and their algorithmic approach. We discern as main categories the search for clusters (i) w.r.t. closeness of objects in axis-parallel subspaces, (ii) w.r.t. common behavior (patterns) of objects in axis-parallel subspaces, and (iii) w.r.t. closeness of objects in arbitrarily oriented subspaces (so called correlation cluster).
For the third category, the remaining parts of the thesis describe novel approaches. A first approach is the adaptation of density-based clustering to the problem of correlation clustering. The starting point here is the first density-based approach in this field, the algorithm 4C. Subsequently, enhancements and variations of this approach are discussed allowing for a more robust, more efficient, or more effective behavior or even find hierarchies of correlation clusters and the corresponding subspaces. The density-based approach to correlation clustering, however, is fundamentally unable to solve some issues since an analysis of local neighborhoods is required. This is a problem in high dimensional data. Therefore, a novel method is proposed tackling the correlation clustering problem in a global approach. Finally, a method is proposed to derive models for correlation clusters to allow for an interpretation of the clusters and facilitate more thorough analysis in the corresponding domain science. Finally, possible applications of these models are proposed and discussed.Knowledge Discovery in Databases (KDD) ist der Prozess der automatischen Extraktion von Wissen aus groĂen Datenmengen, das gĂŒltig, bisher unbekannt und potentiell nĂŒtzlich fĂŒr eine gegebene Anwendung ist. Der zentrale Schritt des KDD-Prozesses ist das Anwenden von Data Mining-Techniken,
um nĂŒtzliche Beziehungen und ZusammenhĂ€nge in einer aufbereiteten Datenmenge aufzudecken. Eine der wichtigsten Techniken des Data Mining ist die Cluster-Analyse (Clustering). Dabei sollen die Objekte einer Datenbank in Gruppen (Cluster) partitioniert werden, so dass Objekte eines Clusters möglichst Ă€hnlich und Objekte verschiedener Cluster möglichst unĂ€hnlich zu einander sind. Hier können beispielsweise Gruppen von Kunden identifiziert werden, die Ă€hnliche Interessen haben, oder Gruppen von Genen, die Ă€hnliche FunktionalitĂ€ten besitzen.
Eine aktuelle Herausforderung fĂŒr Clustering-Verfahren stellen hochdimensionale Feature-RĂ€ume dar. Reale DatensĂ€tze beinhalten dank moderner Verfahren zur Datenerhebung hĂ€ufig sehr viele Merkmale (Features). Teile dieser Merkmale unterliegen oft Rauschen oder AbhĂ€ngigkeiten und können meist nicht im Vorfeld ausgesiebt werden, da diese Effekte in Teilen der Datenbank jeweils unterschiedlich ausgeprĂ€gt sind. Daher muss die Wahl der Features mit dem Data-Mining-Verfahren verknĂŒpft werden.
Seit etwa 10 Jahren werden vermehrt spezialisierte Clustering-Verfahren entwickelt, die mit den in hochdimensionalen Feature-RÀumen auftretenden Problemen besser umgehen können als klassische Clustering-Verfahren. Hierbei wird aber oftmals nicht zwischen den ihrer Natur nach im Einzelnen sehr unterschiedlichen Problemen unterschieden. Ein Hauptanliegen der Dissertation ist daher eine systematische Einordnung der in den letzten Jahren entwickelten sehr diversen AnsÀtze nach den Gesichtspunkten ihrer jeweiligen Problemauffassung, ihrer grundlegenden Lösungsstrategie und ihrer algorithmischen Vorgehensweise. Als Hauptkategorien unterscheiden wir hierbei die Suche nach Clustern (1.) hinsichtlich der NÀhe von Cluster-Objekten in
achsenparallelen UnterrÀumen, (2.) hinsichtlich gemeinsamer Verhaltensweisen (Mustern) von Cluster-Objekten in achsenparallelen UnterrÀumen und (3.) hinsichtlich der NÀhe von Cluster-Objekten in beliebig orientierten UnterrÀumen (sogenannte Korrelations-Cluster).
FĂŒr die dritte Kategorie sollen in den weiteren Teilen der Dissertation innovative LösungsansĂ€tze entwickelt werden. Ein erster Lösungsansatz basiert auf einer Erweiterung des dichte-basierten Clustering auf die Problemstellung des Korrelations-Clustering. Den Ausgangspunkt bildet der erste dichtebasierte Ansatz in diesem Bereich, der Algorithmus 4C. AnschlieĂend werden Erweiterungen und Variationen dieses Ansatzes diskutiert, die robusteres, effizienteres oder effektiveres Verhalten aufweisen oder sogar Hierarchien
von Korrelations-Clustern und den entsprechenden UnterrĂ€umen finden. Die dichtebasierten Korrelations-Cluster-Verfahren können allerdings einige Probleme grundsĂ€tzlich nicht lösen, da sie auf der Analyse lokaler Nachbarschaften beruhen. Dies ist in hochdimensionalen Feature-RĂ€umen problematisch. Daher wird eine weitere Neuentwicklung vorgestellt, die das Korrelations-Cluster-Problem mit einer globalen Methode angeht. SchlieĂlich wird eine Methode vorgestellt, die Cluster-Modelle fĂŒr Korrelationscluster ableitet, so dass die gefundenen Cluster interpretiert werden können und tiefergehende Untersuchungen in der jeweiligen Fachdisziplin zielgerichtet möglich sind. Mögliche Anwendungen dieser Modelle werden abschlieĂend vorgestellt und untersucht
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