## 2 Related Works
In general, there were several key problems in existing studies about video mining using topic model: (1) model parameters increment leads to the increments of the model learning time, and then traditional off-line inference algorithm is not suitable for video monitoring system; (2) anomaly detection in a whole scene rather than in each region reduces the sensitivity of the anomaly detection. To address the problem of motion region, [PERSON] et al. [29] proposed a belief based on correlated topic model (BCTM) for the semantic region analysis of pedestrian motion patterns in the crowded scenes. [PERSON] proposed regional LDA model (rLDA) [30], which not only can model activities in a complicated scene, but also realize a high sensitivity detection and the localization of motion topic (especially the abnormal event) by extracting spatial information ignored by LDA. Nonetheless, the inference algorithm of above studies still used the collapsed Gibbs sampling, which needs to scan the whole samples at each iteration. For huge data sets and data streams such as video, this way adopted by Gibbs sampling leads to high memory overhead, slow running speed, and judging convergence difficultly. Classic approaches of inference algorithm in LDA are Gibbs sampling (GS) [31] and variational Bayesian (VB) batch inference [5]. In order to solve the problem of computational complexity, collapsed Gibbs sampling (CGS) [6] and collapsed VB batch inference (CVB) [32] were proposed. Nevertheless, for the purpose of LDA applied to video mining, we need to make the inference algorithm adapt to the characteristics of video streaming data set, it is better to a realize real-time and online processing quickly and efficiently. For text database which is huge or in the form of data stream, there have been developments of online LDA inference algorithm with less memory, faster running, and convergence speed. [PERSON] proposed the stochastic gradient optimization algorithm (online LDA) [33], which repeatedly subsamples a small set of documents from the collection and then updates the topics from an analysis of the subsample. Since online LDA does not need to scan the entire samples for updating topic parameter matrix at each iteration, the updating of topic parameters is more frequently. The algorithm not only takes up less memory, faster running, and convergence speed, but also realizes online inference in real time for huge data sets or data stream. Nonetheless, the algorithm complexity linearly increased with the number of topics. Therefore, it is not suitable for large collection with many topics. On the basis of online LDA algorithm, [PERSON] proposed hybrid stochastic variational Gibbs sampling (HSVG) [34]. This algorithm introduced the second source of stochasticity by MCMC sampling, and taken advantage of sparse computation to make complexity sublinearly increased with the number of topics. It fits for a large collection with many topics. Besides, RLD (Riemannian Langevin dynamics) [35] algorithm was proposed by [PERSON]. It is a kind of Langevin dynamics algorithm based on Riemannian manifold of MH correction. [PERSON] proposed SGLD (stochastic gradient Langevin dynamics) [36] algorithm, which reserved stochastic gradient optimization algorithm, and can sample from the posterior distribution. [PERSON] proposed SGRLD (stochastic gradient Riemannian Langevin dynamics) [37] by combining RLD and SGLD algorithm. In addition, [PERSON] et al. [38] proposed new learning algorithms for activity analysis in video, which are based on the expectation maximization approach and variational Bayes inference.