Anomaly detection is an important problem that has been researched within diverse research areas and application domains. Many anomaly detection techniques have been specifically developed for certain application domains, while others are more generic. This survey tries to provide a structured and comprehensive overview of the research on anomaly detection. We have grouped existing techniques into different categories based on the underlying approach adopted by each technique. For each category we have identified key assumptions, which are used by the techniques to differentiate between normal and anomalous behavior. When applying a given technique to a particular domain, these assumptions can be used as guidelines to assess the effectiveness of the technique in that domain. For each category, we provide a basic anomaly detection technique, and then show how the different existing techniques in that category are variants of the basic technique. This template provides an easier and more succinct understanding of the techniques belonging to each category. Further, for each category, we identify the advantages and disadvantages of the techniques in that category. We also provide a discussion on the computational complexity of the techniques since it is an important issue in real application domains. We hope that this survey will provide a better understanding of the different directions in which research has been done on this topic, and how techniques developed in one area can be applied in domains for which they were not intended to begin with.

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Anomaly detection: A survey

Data Mining - Concepts and Techniques.

Over the past five years a new approach to privacy-preserving data analysis has born fruit [13, 18, 7, 19, 5, 37, 35, 8, 32]. This approach differs from much (but not all!) of the related literature in the statistics, databases, theory, and cryptography communities, in that a formal and ad omnia privacy guarantee is defined, and the data analysis techniques presented are rigorously proved to satisfy the guarantee. The key privacy guarantee that has emerged is differential privacy. Roughly speaking, this ensures that (almost, and quantifiably) no risk is incurred by joining a statistical database.

In this survey, we recall the definition of differential privacy and two basic techniques for achieving it. We then show some interesting applications of these techniques, presenting algorithms for three specific tasks and three general results on differentially private learning.

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Differential privacy: a survey of results

The k-anonymity privacy requirement for publishing microdata requires that each equivalence class (ie, a set of records that are indistinguishable from each other with respect to certain "identifying" attributes) contains at least k records Recently, several authors have recognized that k-anonymity cannot prevent attribute disclosure The notion of l-diversity has been proposed to address this; l-diversity requires that each equivalence class has at least l well-represented values for each sensitive attribute In this paper we show that l-diversity has a number of limitations In particular, it is neither necessary nor sufficient to prevent attribute disclosure We propose a novel privacy notion called t-closeness, which requires that the distribution of a sensitive attribute in any equivalence class is close to the distribution of the attribute in the overall table (ie, the distance between the two distributions should be no more than a threshold t) We choose to use the earth mover distance measure for our t-closeness requirement We discuss the rationale for t-closeness and illustrate its advantages through examples and experiments

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t-Closeness: Privacy Beyond k-Anonymity and l-Diversity

The book Knowledge Discovery in Databases, edited by Piatetsky-Shapiro and Frawley [PSF91], is an early collection of research papers on knowledge discovery from data. The book Advances in Knowledge Discovery and Data Mining, edited by Fayyad, Piatetsky-Shapiro, Smyth, and Uthurusamy [FPSSe96], is a collection of later research results on knowledge discovery and data mining. There have been many data mining books published in recent years, including Predictive Data Mining by Weiss and Indurkhya [WI98], Data Mining Solutions: Methods and Tools for Solving Real-World Problems by Westphal and Blaxton [WB98], Mastering Data Mining: The Art and Science of Customer Relationship Management by Berry and Linofi [BL99], Building Data Mining Applications for CRM by Berson, Smith, and Thearling [BST99], Data Mining: Practical Machine Learning Tools and Techniques by Witten and Frank [WF05], Principles of Data Mining (Adaptive Computation and Machine Learning) by Hand, Mannila, and Smyth [HMS01], The Elements of Statistical Learning by Hastie, Tibshirani, and Friedman [HTF01], Data Mining: Introductory and Advanced Topics by Dunham, and Data Mining: Multimedia, Soft Computing, and Bioinformatics by Mitra and Acharya [MA03]. There are also books containing collections of papers on particular aspects of knowledge discovery, such as Machine Learning and Data Mining: Methods and Applications edited by Michalski, Brakto, and Kubat [MBK98], and Relational Data Mining edited by Dzeroski and Lavrac [De01], as well as many tutorial notes on data mining in major database, data mining and machine learning conferences.

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Data Mining: Concepts and Techniques (2nd edition)

In \em monotone classification, the input is a set P of n points in d-dimensional space, where each point carries a label 0 or 1. A point p \em dominates another point q if the coordinate of p is at least that of q on every dimension. A \em monotone classifier is a function h mapping each d-dimensional point to $\0, 1\ $, subject to the condition that $h(p) \ge h(q)$ holds whenever p dominates q. The classifier h \em mis-classifies a point $p \in P$ if $h(p)$ is different from the label of p. The \em error of h is the number of points in P mis-classified by h. The objective is to find a monotone classifier with a small error. The problem is fundamental to numerous database applications in entity matching, record linkage, and duplicate detection. This paper studies two variants of the problem. In the first \em active version, all the labels are hidden in the beginning; an algorithm must pay a unit cost to \em probe (i.e., reveal) the label of a point in P. We prove that $Omega(n)$ probes are necessary to find an optimal classifier even in one-dimensional space ($d=1$). On the other hand, given an arbitrary $\eps > 0$, we show how to obtain (with high probability) a monotone classifier whose error is worse than the optimum by at most a $1 + \eps$ factor, while probing $\tO(w/\eps^2)$ labels, where w is the dominance width of P and $\tO(.)$ hides a polylogarithmic factor. For constant $\eps$, the probing cost matches an existing lower bound up to an $\tO(1)$ factor. In the second \em passive version, the point labels in P are explicitly given; the goal is to minimize CPU computation in finding an optimal classifier. We show that the problem can be settled in time polynomial to both d and n.

New Algorithms for Monotone Classification

Existing research onprivacy-preserving datapub- lishing focuses onrelational data:inthiscontext, theobjec- tiveistoenforce privacy-preserving paradigms, suchask- anonymity andf-diversity, while minimizing theinformation loss incurred intheanonymizing process (i.e. maximize datautility). However, existing techniques adoptanindexing- orclustering- basedapproach, andworkwellforfixed-schema data,with lowdimensionality. Nevertheless, certain applications require privacy-preserving publishing oftransaction data(orbasket data), whichinvolves hundreds oreventhousands ofdimensions, rendering existing methods unusable. We propose anovelanonymization methodforsparse high- dimensional data.We employa particular representation that captures thecorrelation intheunderlying data, andfacilitates theformation ofanonymized groupswithlowinformation loss. We propose anefficient anonymization algorithm basedonthis representation. We showexperimentally, using real-life datasets, thatourmethodclearly outperforms existing state-of-the-art in termsofbothdatautility andcomputational overhead.

HI gh-imensional Data

Maximizing Range Sum in Spatial Databases.

This paper formalizes cross-space active learning on a graph convolutional network (GCN). The objective is to attain the most accurate hypothesis available in any of the instance spaces generated by the GCN. Subject to the objective, the chal-lenge is to minimize the label cost , measured in the number of vertices whose labels are requested. Our study covers both budget algorithms which terminate after a designated number of label requests, and verifiable algorithms which terminate only after having found an accurate hypothesis. A new separation in label complexity between the two algorithm types is established. The separation is unique to GCNs.

Yufei Tao

Papers

New Algorithms for Monotone Classification

HI gh-imensional Data

Maximizing Range Sum in Spatial Databases.

Cross-Space Active Learning on Graph Convolutional Networks

Indexing, BDual Tree.