Discussions, Limitations and Recommendations

In this chapter, we presented the efficiency of our proposed approach for decomposing the tensor and learning the factors, predicting future events and mainly detecting abnormal events in real-time. We demonstrated these applications based on the performance of a 3D tensor modeling the environment based on contexts of person/taxi, hour of the day and time.

However, a key limitation of the proposed method is the definition of contextual dimensions. Because the tensor’s dimensions need to be clearly defined, incorporating additional dimen- sions for analyzing events, can be difficult. The environment must thus, be well understood to realize the contexts defining an event.

Another limitation arises with adaptation to changing environments over time. The proposed approach models the event observations by learning a batch of observations. Once the factors have learned the empirical joint probability of the observed events, they are used as is to pre- dict future events and detect abnormal behavior. However, in real-life scenario, the behaviors change and hence, we need a model that adapts to that changing behavior. For this purpose, our model needs to be extended in order to have the latent factor values updated corresponding

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to the changing environment. The model in its current batch-learning state, will need to retrain based on all observed events even if the training data contains only one new observations. This approach of having the latent factors learn again from new random initialization is inefficient for long-term application viewpoint. We need to have the latent factors merelyupdate upon observing a new normal event and notre-learneverything from scratch.

This is where our model’s extensibility can be useful. An online version for training the model is presented in Appendix I. Based on this online version, the applications of the proposed approach may be extended to change detection and concept drift.

CONCLUSION

We presented a new approach, based on LLTF method, for the detection of contextual anoma- lies. Through this approach, we can perform abnormal behavior detection forreal-time contex- tual anomaly detection in a large, open environment.

Real Time Location Systems need to surveil a very large open environment busy with activities. Any of these activities could be malicious and preemptive measures to avoid any undesirable circumstances require almost immediate detection of anything out of the ordinary. The data collected from the environment is also a challenge to organize for analysis. Therefore, we need to analyze the context of these activities/events to make an informed decision corresponding to thenormalityof the event.

From the literature, we realized that probabilistic approaches have proven to be quite popular based on their success for detection of abnormal activities. But their applications have been limited to a closed static environment where it is easy to build a behavioral template of the contextual entities. Trajectory based approaches have also been successful but require repeat- able patterns. Due to the application in an open environment, information at a higher-level of complexity, needs to be analyzed. Therefore, we used LSA based tensor factorization models. The data representation in the form of a higher-order model called tensor allows us to incor- porate any number of contextual dimensions considered necessary to analyze the behavior in a given environment. Unlike existing tensor factorization approaches, through our LLTF factor- ization method, we learn the true probability of events. The log-linear formulation implicitly eliminates need for added complexities corresponding to constraint-integration, such as non- negativity, in the model. Moreover, as demonstrated through the experiments, the model also captures the complex inter-dimensional relations better.

For a faster convergence we show how replacing ordinary gradient descent with Nesterov’s accelerated gradient method leads us from a linear to quadratic rate for convergence. We outperformed other methods applied, in terms of training speed. For testing in a real-time environment, LLTF is the fastest in comparison too. For estimating the probability of incoming events and predicting anomalies, LLTF outperformed other methods. It also demonstrated its robustness to the type of anomaly by requiring minimum tuning of parameters, in comparison. We tested LLTF’s application over three problems: the low-rank approximation of synthetic tensors, the prediction of future of events in real-life data and the detection of events represent- ing abnormal behaviors. In all these problems, LLTF has proved to surpass the performance of state of the art methods and showed efficiency over synthetic as well as real-life datasets. Through our discussions, we have realized certain limitations of the proposed LLTF based approach. One such limitation is of the inconvenience of training the latent factors in batch. To overcome this limitation, we have proposed an online extension of LLTF formulation, which will allow us to update the latent factors as new normal events are observed in the environment. The integration of this extension in the existing approach will extend the application of the proposed method to concept drift and change detection thus, maximizing the productivity as an abnormal behavior detection method.