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

We propose a framework for analyzing and comparing distributions, which we use to construct statistical tests to determine if two samples are drawn from different distributions. Our test statistic is the largest difference in expectations over functions in the unit ball of a reproducing kernel Hilbert space (RKHS), and is called the maximum mean discrepancy (MMD).We present two distribution free tests based on large deviation bounds for the MMD, and a third test based on the asymptotic distribution of this statistic. The MMD can be computed in quadratic time, although efficient linear time approximations are available. Our statistic is an instance of an integral probability metric, and various classical metrics on distributions are obtained when alternative function classes are used in place of an RKHS. We apply our two-sample tests to a variety of problems, including attribute matching for databases using the Hungarian marriage method, where they perform strongly. Excellent performance is also obtained when comparing distributions over graphs, for which these are the first such tests.

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A kernel two-sample test

A wide range of methods for analysis of airborne- and satellite-derived imagery continues to be proposed and assessed. In this paper, we review remote sensing implementations of support vector machines (SVMs), a promising machine learning methodology. This review is timely due to the exponentially increasing number of works published in recent years. SVMs are particularly appealing in the remote sensing field due to their ability to generalize well even with limited training samples, a common limitation for remote sensing applications. However, they also suffer from parameter assignment issues that can significantly affect obtained results. A summary of empirical results is provided for various applications of over one hundred published works (as of April, 2010). It is our hope that this survey will provide guidelines for future applications of SVMs and possible areas of algorithm enhancement.

https://www.aboutgis.com/Publications/Mountrakis_SVM_review_in_remote_sensing_ISPRS2010.pdf

Support vector machines in remote sensing: A review

This document describes version 0.4.0 of librosa: a Python pack- age for audio and music signal processing. At a high level, librosa provides implementations of a variety of common functions used throughout the field of music information retrieval. In this document, a brief overview of the library's functionality is provided, along with explanations of the design goals, software development practices, and notational conventions.

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librosa: Audio and Music Signal Analysis in Python

We propose two statistical tests to determine if two samples are from different distributions. Our test statistic is in both cases the distance between the means of the two samples mapped into a reproducing kernel Hilbert space (RKHS). The first test is based on a large deviation bound for the test statistic, while the second is based on the asymptotic distribution of this statistic. The test statistic can be computed in O(m2) time. We apply our approach to a variety of problems, including attribute matching for databases using the Hungarian marriage method, where our test performs strongly. We also demonstrate excellent performance when comparing distributions over graphs, for which no alternative tests currently exist.

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A Kernel Method for the Two-Sample-Problem

This book serves as an ideal starting point for newcomers and an excellent reference source for people already working in the field. Researchers and graduate students in signal processing, computer science, acoustics and music will primarily benefit from this text. It could be used as a textbook for advanced courses in music signal processing. Since it only requires a basic knowledge of signal processing, it is accessible to undergraduate students.

Signal Processing Methods for Music Transcription

A number of abrupt change detection methods have been proposed in the past, among which are efficient model-based techniques such as the Generalized Likelihood Ratio (GLR) test. We consider the case where no accurate nor tractable model can be found, using a model-free approach, called Kernel change detection (KCD). KCD compares two sets of descriptors extracted online from the signal at each time instant: The immediate past set and the immediate future set. Based on the soft margin single-class Support Vector Machine (SVM), we build a dissimilarity measure in feature space between those sets, without estimating densities as an intermediary step. This dissimilarity measure is shown to be asymptotically equivalent to the Fisher ratio in the Gaussian case. Implementation issues are addressed; in particular, the dissimilarity measure can be computed online in input space. Simulation results on both synthetic signals and real music signals show the efficiency of KCD.

An online kernel change detection algorithm

We present an efficient particle filtering method to perform optimal estimation in jump Markov (nonlinear) systems (JMSs). Such processes consist of a mixture of heterogeneous models and possess a natural hierarchical structure. We take advantage of these specificities in order to develop a generic filtering methodology for these models. The method relies on an original and nontrivial combination of techniques that have been presented recently in the filtering literature, namely, the auxiliary particle filter and the unscented transform. This algorithm is applied to the complex problem of time-varying autoregressive estimation with an unknown time-varying model order. More precisely, we develop an attractive and original probabilistic model that relies on a flexible pole representation that easily lends itself to interpretations. We show that this problem can be formulated as a JMS and that the associated filtering problem can be efficiently addressed using the generic methodology developed in this paper. Simulations demonstrate the performance of our method compared to standard particle filtering techniques.

Efficient particle filtering for jump Markov systems. Application to time-varying autoregressions

This paper presents a method aimed at recognizing environmental sounds for surveillance and security applications. We propose to apply one-class support vector machines (1-SVMs) together with a sophisticated dissimilarity measure in order to address audio classification, and more specifically, sound recognition. We illustrate the performance of this method on an audio database, which consists of 1015 sounds belonging to nine classes. The database used presents high intraclass diversity in temps of signal properties and some kind of interclass similarities. A large discrepancy in the number of items in each class implies nonuniform probability of sound appearances. The method proceeds as follows: first, the use of a set of state-of-the-art audio features is studied. Then, we introduce a set of novel features obtained by combining elementary features. Experiments conducted on a nine-class classification problem show the superiority of this novel sound recognition method. The best recognition accuracy (96.89%) is obtained when combining wavelet-based features, MFCCs, and individual temporal and frequency features. Our 1-SVM-based multiclass classification approach overperforms the conventional hidden Markov model-based system in the experiments conducted, the improvement in the error rate can reach 50%. Besides, we provide empirical results showing that the single-class SVM outperforms a combination of binary SVMs. Additional experiments demonstrate our method is robust to environmental noise.

Using One-Class SVMs and Wavelets for Audio Surveillance

This paper concerns the sequential estimation of a hidden state vector from noisy observations delivered by several sensors. Different from the standard framework, we assume here that the sensors may switch autonomously between different sensor states, that is, between different observation models. This includes sensor failure or sensor functioning conditions change. In our model, sensor states are represented by discrete latent variables, whose prior probabilities are Markovian. We propose a family of efficient particle filters, for both synchronous and asynchronous sensor observations as well as for important special cases. Moreover, we discuss connections with previous works. Lastly, we study thoroughly a wheel land vehicle positioning problem where the GPS information may be unreliable because of multipath/masking effects

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Manuel Davy

Papers

Signal Processing Methods for Music Transcription

An online kernel change detection algorithm

Efficient particle filtering for jump Markov systems. Application to time-varying autoregressions

Using One-Class SVMs and Wavelets for Audio Surveillance

Particle Filtering for Multisensor Data Fusion With Switching Observation Models: Application to Land Vehicle Positioning