KL Divergence-Based Fuzzy Cluster Ensemble for Image Segmentation

Attention to the Variation of Probabilistic Events: Information Processing with Message Importance Measure

Different probabilities of events attract different attention in many scenarios such as anomaly detection and security systems. To characterize the events’ importance from a probabilistic perspective, the message importance measure (MIM) is proposed as a kind of semantics analysis tool. Similar to Shannon entropy, the MIM has its special function in information representation, in which the parameter of MIM plays a vital role. Actually, the parameter dominates the properties of MIM, based on which the MIM has three work regions where this measure can be used flexibly for different goals. When the parameter is positive but not large enough, the MIM not only provides a new viewpoint for information processing but also has some similarities with Shannon entropy in the information compression and transmission. In this regard, this paper first constructs a system model with message importance measure and proposes the message importance loss to enrich the information processing strategies. Moreover, the message importance loss capacity is proposed to measure the information importance harvest in a transmission. Furthermore, the message importance distortion function is discussed to give an upper bound of information compression based on the MIM. Additionally, the bitrate transmission constrained by the message importance loss is investigated to broaden the scope for Shannon information theory.

A Nonparametric Model for Multi-Manifold Clustering with Mixture of Gaussians and Graph Consistency

Multi-manifold clustering is among the most fundamental tasks in signal processing and machine learning. Although the existing multi-manifold clustering methods are quite powerful, learning the cluster number automatically from data is still a challenge. In this paper, a novel unsupervised generative clustering approach within the Bayesian nonparametric framework has been proposed. Specifically, our manifold method automatically selects the cluster number with a Dirichlet Process (DP) prior. Then, a DP-based mixture model with constrained Mixture of Gaussians (MoG) is constructed to handle the manifold data. Finally, we integrate our model with the k-nearest neighbor graph to capture the manifold geometric information. An efficient optimization algorithm has also been derived to do the model inference and optimization. Experimental results on synthetic datasets and real-world benchmark datasets exhibit the effectiveness of this new DP-based manifold method.

Recognizing Information Feature Variation: Message Importance Transfer Measure and Its Applications in Big Data

Information transfer that characterizes the information feature variation can have a crucial impact on big data analytics and processing. Actually, the measure for information transfer can reflect the system change from the statistics by using the variable distributions, similar to Kullback-Leibler (KL) divergence and Renyi divergence. Furthermore, to some degree, small probability events may carry the most important part of the total message in an information transfer of big data. Therefore, it is significant to propose an information transfer measure with respect to the message importance from the viewpoint of small probability events. In this paper, we present the message importance transfer measure (MITM) and analyze its performance and applications in three aspects. First, we discuss the robustness of MITM by using it to measuring information distance. Then, we present a message importance transfer capacity by resorting to the MITM and give an upper bound for the information transfer process with disturbance. Finally, we apply the MITM to discuss the queue length selection, which is the fundamental problem of caching operation on mobile edge computing.