Detecting outlying subspaces for high-dimensional data: the new task, algorithms and performance

[Abstract]: In this paper, we identify a new task for studying the outlying degree (OD) of high-dimensional data, i.e. finding the subspaces (subsets of features) in which the given points are outliers, which are called their outlying subspaces. Since the state-of-the-art outlier detection techniques fail to handle this new problem, we propose a novel detection algorithm, called High-Dimension Outlying subspace Detection (HighDOD), to detect the outlying subspaces of high-dimensional data efficiently. The intuitive idea of HighDOD is that we measure the OD of the point using the sum of distances between this point and its k nearest neighbors. Two heuristic pruning strategies are proposed to realize fast pruning in the subspace search and an efficient dynamic subspace search method with a sample-based learning process has been implemented. Experimental results show that HighDOD is efficient and outperforms other searching alternatives such as the naive top–down, bottom–up and random search methods, and the existing outlier detection methods cannot fulfill this new task effectively

Towards outlier detection for high-dimensional data streams using projected outlier analysis strategy

[Abstract]: Outlier detection is an important research problem in data mining that aims to discover useful abnormal and irregular patterns hidden in large data sets. Most existing outlier detection methods only deal with static data with relatively low dimensionality. Recently, outlier detection for high-dimensional stream data became a new emerging research problem. A key observation that motivates this research is that outliers in high-dimensional data are projected outliers, i.e., they are embedded in lower-dimensional subspaces. Detecting projected outliers from high-dimensional stream data is a very challenging task for several reasons. First, detecting projected outliers is difficult even for high-dimensional static data. The exhaustive search for the out-lying subspaces where projected outliers are embedded is a NP problem. Second, the algorithms for handling data streams are constrained to take only one pass to process the streaming data with the conditions of space limitation and time criticality. The currently existing methods for outlier detection are found to be ineffective for detecting projected outliers in high-dimensional data streams. In this thesis, we present a new technique, called the Stream Project Outlier deTector (SPOT), which attempts to detect projected outliers in high-dimensional data streams. SPOT employs an innovative window-based time model in capturing dynamic statistics from stream data, and a novel data structure containing a set of top sparse subspaces to detect projected outliers effectively. SPOT also employs a multi-objective genetic algorithm as an effective search method for finding the outlying subspaces where most projected outliers are embedded. The experimental results demonstrate that SPOT is efficient and effective in detecting projected outliers for high-dimensional data streams. The main contribution of this thesis is that it provides a backbone in tackling the challenging problem of outlier detection for high- dimensional data streams. SPOT can facilitate the discovery of useful abnormal patterns and can be potentially applied to a variety of high demand applications, such as for sensor network data monitoring, online transaction protection, etc

A Novel Subspace Outlier Detection Approach in High Dimensional Data Sets

Many real applications are required to detect outliers in high dimensional data sets. The major difficulty of mining outliers lies on the fact that outliers are often embedded in subspaces. No efficient methods are available in general for subspace-based outlier detection. Most existing subspacebased outlier detection methods identify outliers by searching for abnormal sparse density units in subspaces. In this paper, we present a novel approach for finding outliers in the ‘interesting’ subspaces. The interesting subspaces are strongly correlated with `good\u27 clusters. This approach aims to group the meaningful subspaces and then identify outliers in the projected subspaces. In doing so, an extension to the subspacebased clustering algorithm is proposed so as to find the ‘good’ subspaces, and then outliers are identified in the projected subspaces using some classical outlier detection techniques such as distance-based and density-based algorithms. Comprehensive case studies are conducted using various types of subspace clustering and outlier detection algorithms. The experimental results demonstrate that the proposed method can detect outliers effectively and efficiently in high dimensional data sets

Random Subspace Learning on Outlier Detection and Classification with Minimum Covariance Determinant Estimator

The questions brought by high dimensional data is interesting and challenging. Our study is targeting on the particular type of data in this situation that namely “large p, small n”. Since the dimensionality is massively larger than the number of observations in the data, any measurement of covariance and its inverse will be miserably affected. The definition of high dimension in statistics has been changed throughout decades. Modern datasets with over thousands of dimensions are demanding the ability to gain deeper understanding but hindered by the curse of dimensionality. We decide to review and explore further to negotiate with the curse and extend previous studies to pave a new way for estimating robustness then apply it to outlier detection and classification. We explored the random subspace learning and expand other classification and outlier detection algorithms to adapt its framework. Our proposed methods can handle both high-dimension low-sample size and traditional low-dimensional high-sample size datasets. Essentially, we avoid the computational bottleneck of techniques like Minimum Covariance Determinant (MCD) by computing the needed determinants and associated measures in much lower dimensional subspaces. Both theoretical and computational development of our approach reveal that it is computationally more efficient than the regularized methods in high-dimensional low-sample size, and often competes favorably with existing methods as far as the percentage of correct outlier detection are concerned

Detecting outlying subspaces for high-dimensional data: a heuristic search approach

[Abstract]: In this paper, we identify a new task for studying the out-lying degree of high-dimensional data, i.e. finding the sub-spaces (subset of features) in which given points are out-liers, and propose a novel detection algorithm, called High-D Outlying subspace Detection (HighDOD). We measure the outlying degree of the point using the sum of distances between this point and its k nearest neighbors. Heuristic pruning strategies are proposed to realize fast pruning in the subspace search and an efficient dynamic subspace search method with a sample-based learning process has been im- plemented. Experimental results show that HighDOD is efficient and outperforms other searching alternatives such as the naive top-down, bottom-up and random search methods. Points in these sparse subspaces are assumed to be the outliers. While knowing which data points are the outliers can be useful, in many applications, it is more important to identify the subspaces in which a given point is an outlier, which motivates the proposal of a new technique in this paper to handle this new task

Generalized and efficient outlier detection for spatial, temporal, and high-dimensional data mining

Knowledge Discovery in Databases (KDD) ist der Prozess, nicht-triviale Muster aus großen Datenbanken zu extrahieren, mit dem Ziel, dass diese bisher unbekannt, potentiell nützlich, statistisch fundiert und verständlich sind. Der Prozess umfasst mehrere Schritte wie die Selektion, Vorverarbeitung, Evaluierung und den Analyseschritt, der als Data-Mining bekannt ist. Eine der zentralen Aufgabenstellungen im Data-Mining ist die Ausreißererkennung, das Identifizieren von Beobachtungen, die ungewöhnlich sind und mit der Mehrzahl der Daten inkonsistent erscheinen. Solche seltene Beobachtungen können verschiedene Ursachen haben: Messfehler, ungewöhnlich starke (aber dennoch genuine) Abweichungen, beschädigte oder auch manipulierte Daten. In den letzten Jahren wurden zahlreiche Verfahren zur Erkennung von Ausreißern vorgeschlagen, die sich oft nur geringfügig zu unterscheiden scheinen, aber in den Publikationen experimental als ``klar besser'' dargestellt sind. Ein Schwerpunkt dieser Arbeit ist es, die unterschiedlichen Verfahren zusammenzuführen und in einem gemeinsamen Formalismus zu modularisieren. Damit wird einerseits die Analyse der Unterschiede vereinfacht, andererseits aber die Flexibilität der Verfahren erhöht, indem man Module hinzufügen oder ersetzen und damit die Methode an geänderte Anforderungen und Datentypen anpassen kann. Um die Vorteile der modularisierten Struktur zu zeigen, werden (i) zahlreiche bestehende Algorithmen in dem Schema formalisiert, (ii) neue Module hinzugefügt, um die Robustheit, Effizienz, statistische Aussagekraft und Nutzbarkeit der Bewertungsfunktionen zu verbessern, mit denen die existierenden Methoden kombiniert werden können, (iii) Module modifiziert, um bestehende und neue Algorithmen auf andere, oft komplexere, Datentypen anzuwenden wie geographisch annotierte Daten, Zeitreihen und hochdimensionale Räume, (iv) mehrere Methoden in ein Verfahren kombiniert, um bessere Ergebnisse zu erzielen, (v) die Skalierbarkeit auf große Datenmengen durch approximative oder exakte Indizierung verbessert. Ausgangspunkt der Arbeit ist der Algorithmus Local Outlier Factor (LOF). Er wird zunächst mit kleinen Erweiterungen modifiziert, um die Robustheit und die Nutzbarkeit der Bewertung zu verbessern. Diese Methoden werden anschließend in einem gemeinsamen Rahmen zur Erkennung lokaler Ausreißer formalisiert, um die entsprechenden Vorteile auch in anderen Algorithmen nutzen zu können. Durch Abstraktion von einem einzelnen Vektorraum zu allgemeinen Datentypen können auch räumliche und zeitliche Beziehungen analysiert werden. Die Verwendung von Unterraum- und Korrelations-basierten Nachbarschaften ermöglicht dann, einen neue Arten von Ausreißern in beliebig orientierten Projektionen zu erkennen. Verbesserungen bei den Bewertungsfunktionen erlauben es, die Bewertung mit der statistischen Intuition einer Wahrscheinlichkeit zu interpretieren und nicht nur eine Ausreißer-Rangfolge zu erstellen wie zuvor. Verbesserte Modelle generieren auch Erklärungen, warum ein Objekt als Ausreißer bewertet wurde. Anschließend werden für verschiedene Module Verbesserungen eingeführt, die unter anderem ermöglichen, die Algorithmen auf wesentlich größere Datensätze anzuwenden -- in annähernd linearer statt in quadratischer Zeit --, indem man approximative Nachbarschaften bei geringem Verlust an Präzision und Effektivität erlaubt. Des weiteren wird gezeigt, wie mehrere solcher Algorithmen mit unterschiedlichen Intuitionen gleichzeitig benutzt und die Ergebnisse in einer Methode kombiniert werden können, die dadurch unterschiedliche Arten von Ausreißern erkennen kann. Schließlich werden für reale Datensätze neue Ausreißeralgorithmen konstruiert, die auf das spezifische Problem angepasst sind. Diese neuen Methoden erlauben es, so aufschlussreiche Ergebnisse zu erhalten, die mit den bestehenden Methoden nicht erreicht werden konnten. Da sie aus den Bausteinen der modularen Struktur entwickelt wurden, ist ein direkter Bezug zu den früheren Ansätzen gegeben. Durch Verwendung der Indexstrukturen können die Algorithmen selbst auf großen Datensätzen effizient ausgeführt werden.Knowledge Discovery in Databases (KDD) is the process of extracting non-trivial patterns in large data bases, with the focus of extracting novel, potentially useful, statistically valid and understandable patterns. The process involves multiple phases including selection, preprocessing, evaluation and the analysis step which is known as Data Mining. One of the key techniques of Data Mining is outlier detection, that is the identification of observations that are unusual and seemingly inconsistent with the majority of the data set. Such rare observations can have various reasons: they can be measurement errors, unusually extreme (but valid) measurements, data corruption or even manipulated data. Over the previous years, various outlier detection algorithms have been proposed that often appear to be only slightly different than previous but ``clearly outperform'' the others in the experiments. A key focus of this thesis is to unify and modularize the various approaches into a common formalism to make the analysis of the actual differences easier, but at the same time increase the flexibility of the approaches by allowing the addition and replacement of modules to adapt the methods to different requirements and data types. To show the benefits of the modularized structure, (i) several existing algorithms are formalized within the new framework (ii) new modules are added that improve the robustness, efficiency, statistical validity and score usability and that can be combined with existing methods (iii) modules are modified to allow existing and new algorithms to run on other, often more complex data types including spatial, temporal and high-dimensional data spaces (iv) the combination of multiple algorithm instances into an ensemble method is discussed (v) the scalability to large data sets is improved using approximate as well as exact indexing. The starting point is the Local Outlier Factor (LOF) algorithm, which is extended with slight modifications to increase robustness and the usability of the produced scores. In order to get the same benefits for other methods, these methods are abstracted to a general framework for local outlier detection. By abstracting from a single vector space, other data types that involve spatial and temporal relationships can be analyzed. The use of subspace and correlation neighborhoods allows the algorithms to detect new kinds of outliers in arbitrarily oriented subspaces. Improvements in the score normalization bring back a statistic intuition of probabilities to the outlier scores that previously were only useful for ranking objects, while improved models also offer explanations of why an object was considered to be an outlier. Subsequently, for different modules found in the framework improved modules are presented that for example allow to run the same algorithms on significantly larger data sets -- in approximately linear complexity instead of quadratic complexity -- by accepting approximated neighborhoods at little loss in precision and effectiveness. Additionally, multiple algorithms with different intuitions can be run at the same time, and the results combined into an ensemble method that is able to detect outliers of different types. Finally, new outlier detection methods are constructed; customized for the specific problems of these real data sets. The new methods allow to obtain insightful results that could not be obtained with the existing methods. Since being constructed from the same building blocks, there however exists a strong and explicit connection to the previous approaches, and by using the indexing strategies introduced earlier, the algorithms can be executed efficiently even on large data sets