Outlier Detection with Globally Optimal Exemplar-Based GMM

Abstract

Outlier detection has recently become an important problem in many data mining applications. In this paper, a novel unsupervised algorithm for outlier detection is proposed. First we apply a provably globally optimal Expectation Maximization (EM) algorithm to fit a Gaussian Mixture Model (GMM) to a given data set. In our approach, a Gaussian is centered at each data point, and hence, the estimated mixture proportions can be interpreted as probabilities of being a cluster center for all data points. The outlier factor at each data point is then defined as a weighted sum of the mixture proportions with weights representing the similarities to other data points. The proposed outlier factor is thus based on global properties of the data set. This is in contrast to most existing approaches to outlier detection, which are strictly local. Our experiments performed on several simulated and real life data sets demonstrate superior performance of the proposed approach. Moreover, we also demonstrate the ability to detect unusual shapes.

Outlier Detection Based on Local Kernel Regression for Instance Selection

“…K (x m , x n ) = exp(∥x m − x n ∥ 2 /h), and the parameter h and the ridge parameter γ were set at 100 and 0.1, respectively. To measure the performance of each algorithm, we utilized the Detection rate (True positive rate), the False alarm rate (False positive rate) from the work 17 , and the ROC curves, which are defined as follows:…”

“…Along this line, He et al 16 proposed FindCBLOF to determine the Cluster-Based Local Outlier Factor (CBLOF) for each data point. Yang et al 17 had introduced a globally optimal exemplarbased GMM to detect the outliers, in which a Gaussian is centered at each point. The outlier factor at each point is calculated by the weighted sum of the mixture proportion with the weights representing the similarities to the other points.…”

Generative Adversarial Active Learning for Unsupervised Outlier Detection

“…The most straightforward outlier detection method, modelbased method, is to create a model for all samples, and then predict outliers as those having large deviations from the established profiles. For example, the Gaussian mixture model (GMM) [11] fits the whole dataset to a mixed Gaussian distribution and evaluates the parameters through the Expectation-Maximization [29] or a deep estimation network [12]. However, GMM needs to predetermine the appropriate cluster type and number, which are crucial and extremely difficult.…”

“…We compare MO-GAAL with nine representative outlier detection algorithms. They can be divided into seven categories: (i) two density-based methods, LOF [18] and KDEOS [38]; (ii) two density estimators, GMM [11] and Parzen [17]; (iii) a typical distance-based approach, kNN [37]; (iv) an angle-based model, FastABOD [38]; (v) a clusterbased model, k-means; (vi) a popular one-class classification model, OC-SVM [35] and (vii) the Active-Outlier detection model, AO [24]. In addition, AGPO and SO-GAAL are also compared on real-world datasets to demonstrate the necessity of using multiple generators with different objectives.…”

“…The most straightforward way is to create a model for all samples, and then compute the outlier scores based on the deviations from the established normal profiles. Specific methods include the statistical-based models [11], [12], regression-based models [13], cluster-based models [14], and reconstruction-based models [15], [16], which make different assumptions about the generating mechanism of Xiangnan He is the corresponding author. normal data.…”