We study anomaly detection for fast streaming temporal data with real time Type-I error, i.e., false alarm rate, controllability; and propose a computationally highly efficient online algorithm, which closely achieves a specified false alarm rate while maximizing the detection power. Regardless of whether the source is stationary or nonstationary, the proposed algorithm sequentially receives a time series and learns the nominal attributes-in the online setting-under possibly varying Markov statistics. Then, an anomaly is declared at a time instance, if the observations are statistically sufficiently deviant. Moreover, the proposed algorithm is remarkably versatile since it does not require parameter tuning to match the desired rates even in the case of strong nonstationarity. The presented study is the first to provide the online implementation of Neyman-Pearson (NP) characterization for the problem such that the NP optimality, i.e., maximum detection power at a specified false alarm rate, is nearly achieved in a truly online manner. In this regard, the proposed algorithm is highly novel and appropriate especially for the applications requiring sequential data processing at large scales/high rates due to its parameter-tuning free computational efficient design with the practical NP constraints under stationary or non-stationary source statistics.
We analyze an online learning algorithm that adaptively combines outputs of two constituent algorithms (or the experts) running in parallel to estimate an unknown desired signal. This online learning algorithm is shown to achieve and in some cases outperform the mean-square error (MSE) performance of the best constituent algorithm in the steady state. However, the MSE analysis of this algorithm in the literature uses approximations and relies on statistical models on the underlying signals. Hence, such an analysis may not be useful or valid for signals generated by various real-life systems that show high degrees of nonstationarity, limit cycles and that are even chaotic in many cases. In this brief, we produce results in an individual sequence manner. In particular, we relate the time-accumulated squared estimation error of this online algorithm at any time over any interval to the one of the optimal convex mixture of the constituent algorithms directly tuned to the underlying signal in a deterministic sense without any statistical assumptions. In this sense, our analysis provides the transient, steady-state, and tracking behavior of this algorithm in a strong sense without any approximations in the derivations or statistical assumptions on the underlying signals such that our results are guaranteed to hold. We illustrate the introduced results through examples.
Nonlinear kernel Support Vector Machines achieve better generalizations, yet their training and evaluation speeds are prohibitively slow for real-time object detection tasks where the number of data points in training and the number of hypotheses to be tested in evaluation are in the order of millions. To accelerate the training and particularly testing of such nonlinear kernel machines, we map the input data onto a low-dimensional spectral (Fourier) feature space using a cosine transform, design a kernel that approximates the classification objective in a supervised setting, and apply a fast linear classifier instead of the conventional radial basis functions. We present a data driven hypotheses generation technique and a LogistBoost feature selection. Our experimental results demonstrate the computational improvements 20 100x while maintaining a high classification accuracy in comparison to SVM linear and radial kernel basis function classifiers. IEEE International Conference on Advanced Video and Signal-based Surveillance (AVSS)This work may not be copied or reproduced in whole or in part for any commercial purpose. Permission to copy in whole or in part without payment of fee is granted for nonprofit educational and research purposes provided that all such whole or partial copies include the following: a notice that such copying is by permission of Mitsubishi Electric Research Laboratories, Inc.; an acknowledgment of the authors and individual contributions to the work; and all applicable portions of the copyright notice. Copying, reproduction, or republishing for any other purpose shall require a license with payment of fee to Mitsubishi Electric Research Laboratories, Inc. All rights reserved. AbstractNonlinear kernel Support Vector Machines achieve better generalizations, yet their training and evaluation speeds are prohibitively slow for real-time object detection tasks where the number of data points in training and the number of hypotheses to be tested in evaluation are in the order of millions. To accelerate the training and particularly testing of such nonlinear kernel machines, we map the input data onto a low-dimensional spectral (Fourier) feature space using a cosine transform, design a kernel that approximates the classification objective in a supervised setting, and apply a fast linear classifier instead of the conventional radial basis functions. We present a data driven hypotheses generation technique and a LogistBoost feature selection. Our experimental results demonstrate the computational improvements 20∼100× while maintaining a high classification accuracy in comparison to SVM linear and radial kernel basis function classifiers.
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