EM-LDA model of user behavior detection for energy efficiency

In energy efficient analysis, user behavior detection related to the dynamic demands of energy is a critical aspect to support the intelligent control schema of Building Management System. In this paper, anomalous occupancy of user behavior tends to be figured out from multiple time-series of occupancy record. The problems in this issue include the time-stamp detection and time-span identification of anomaly events. Most inference model based on Markov Chain can illustrate the time-stamp detection problem reasonably, but the time-span identification problem is just vaguely explained. Therefore, a Latent Dirichlet Allocation (LDA) model is declared to figure out those two problems efficiently. First, the discrete data of occupancy are expressed as mixture model of Poisson distribution, and are transformed to a dataset with several semantic concepts via Expectation-Maximization Algorithm. Then, the denotation of LDA components (including the words, the topic, the document, and the relevant parameters and hyper-parameters) are illustrated, according to the semantic dataset. Finally, particle filter algorithm is leveraged to sample latent variable of topic, according to the conditional posterior probability of word for specific topic. After iterations, the probability of samples is closely approximated the true marginal distribution of words with specific topic. Through the relation matrix of words and topic, the most possible topic can be explained for the specific document. If a document's topic is different with other document's topic, this document can be identified as a bias of point anomaly (noting generally the amount of topics setup to two). Due to a word can involve several time-stamps of the time-series in a time, other contextual anomalies nearby the point anomaly can be marked, and they are the notation of time-spans for anomalous events. With a step by step along the time-series, all time-stamps can be ergodic as the documents, then all the contextual anomalies can be explained as following the happening of point anomalous event.