One-Class Support Measure Machines for Group Anomaly Detection

By Krikamol Muandet, Bernhard Schölkopf. 2013

87 citations recorded by the source corpus.

We propose one-class support measure machines (OCSMMs) for group anomaly detection which aims at recognizing anomalous aggregate behaviors of data points. The OCSMMs generalize well-known one-class support vector machines (OCSVMs) to a space of probability measures. By formulating the problem as quantile estimation on distributions, we can establish an interesting connection to the OCSVMs and variable kernel density estimators (VKDEs) over the input space on which the distributions are defined, bridging the gap between large-margin methods and kernel density estimators. In particular, we show that various types of VKDEs can be considered as solutions to a class of regularization problems studied in this paper. Experiments on Sloan Digital Sky Survey dataset and High Energy Particle Physics dataset demonstrate the benefits of the proposed framework in real-world applications.

Subfields: Anomaly & Outlier Detection, Statistical Learning Theory

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Citations in the corpus

Kernel Mean Embedding of Distributions: A Review and Beyonds (2016, methodology): “A slightly different interpretation is to look at this problem as a learning problem on probability distributions (Muandet et al. 2012, Muandet and Schölkopf 2013, Szabó et al. 2015).”
Non-Linear Regression for Bag-of-Words Data via Gaussian Process Latent Variable Set Model (2015, background): “The one-class support measure machine is a group anomaly detection method that finds anomalous aggregated behaviors of objects (Muandet and Schölkopf 2013).”
Kernel Mean Shrinkage Estimators (2014, methodology): “To this end, we conduct experiments on natural scene categorization using support measure machine (SMM) (Muandet et al., 2012) and group anomaly detection on a high-energy physics dataset using one-class SMM (OCSMM) (Muandet and Sch¨olkopf, 2013).”
Kernel Mean Estimation and Stein's Effect (2013, positive): “We consider three benchmark applications: density estimation via kernel mean matching [20], kernel PCA using shrinkage mean and covariance operator [2], and discriminative learning on distributions [25, 26].”
Support Measure Data Description A One-Class Classifier for Group Anomaly Detection (2017, methodology): “For similar experiments with generative models vs the OCSMM classier in a the same task we refer [19].”
CSI: A Hybrid Deep Model for Fake News Detection (2017, methodology): “[30] took a similar approach by combining kernel embedding with an SVM classier.”
A Unifying Review of Deep and Shallow Anomaly Detection (2020, background): “Many variants of kernel one-class classification have been proposed and studied over the years, such as hierarchical formulations for nested density level set estimation [314], [315], multisphere SVDD [316], multiple kernel learning for OC-SVM [317], [318], OC-SVM for group AD [197], boosting via L1”
Support Measure Data Description for group anomaly detection (2015, methodology): “Experimental evaluation, using those datasets, shows that SMDD model M1 is better than SMDD models M2 and M3, and performs similarly to OCSMM.”