One‐class tensor machine with randomized projection for large‐scale anomaly detection in high‐dimensional and noisy data

Abstract

The modern industrial sector generates enormous amounts of high-dimensional heterogeneous data daily.However, mostly the vectored data (rank-one tensor) have been considered for anomaly detection, whereas the data in real-life is high dimensional. The expressive power of methods based on vector data is restrictive as they may destroy the structural information embedded in data and lead to the curse-of-dimensionality and overfitting. In this paper, we present a novel anomaly detection approach for large-scale tensor data. We first present novel one-class support tensor machines (OCSTM) with bounded loss function. We further extend it by leveraging the randomness to design a scalable approach that can also be used for large-scale anomaly detection. To solve the corresponding optimization of the objective function, we utilize half-quadratic optimization followed by solving it like a traditional OCSTM optimization at each iteration. We demonstrate the proposed randomized OCSTM with bounded hinge loss through experiments on 14 benchmark data sets. Experimental results demonstrate the effectiveness of the proposed approach against anomalies and a significant reduction in the computational complexity.

An improved stochastic gradient descent algorithm based on Rényi differential privacy

“…The denoise methods such as Wavelet Transform, 27 Trend filtering, 27 and Laplace Smooth 28 and the method proposed by Razzak et al 29 are commonly used in practice. In Algorithm 3 line 11, we use Laplace Smooth method to design a postprocessing algorithm for denoising noise gradients matrix.…”