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According to the basic principles and methods of information theory, the operation way of neural coding is studied and analyzed by using the minimum mutual information and the maximum entropy principle. This paper describes how the principles of minimum mutual information and maximum entropy are used to evaluate the amount of information in neural responses. Its main contribution is as follows: (1) that the expression of neural information is closely related to the utilization of neural energy, and it is found that the highly evolved nervous system strictly follows the two basic principles of economy and efficiency in energy consumption and utilization; (2) In order to verify the relationship between neural information processing and energy utilization, this paper uses the concept of energy-efficiency ratio to measure the economy and high efficiency of the nervous system in term of energy utilization by using the maximum entropy principle; (3) The numerical results show that the energy consumed by the nervous system reflects not only the internal law of neural information conduction and processing, but also the self-organization structure of neural information coding. The results suggest that energy neural coding, a novel neural information processing method, can be used to understand how brain activity works. Such a coding pattern can not only be extended to research the large-scale neuroscience field, but also unify brain models at all levels by use of the energy theory. This will provide a scientific theoretical basis for the exploration of how the brain works and the computational principles of brain-like artificial intelligence. [ABSTRACT FROM AUTHOR]

Spectral clustering is a group of graph-based clustering methods in which the columns of the scaled cluster indicator matrix can be obtained by stacking the eigenvectors of the Laplacian matrix corresponding to the top c smallest eigenvalues (c is the number of clusters). This leads to the possible existence of negative values in the scaled indicator matrix and therefore a post-processing step such as K means clustering or spectral rotation is necessary to get the discrete cluster assignments. Moreover, such obtained results lack of the interpretability for data points in the boundary area of multiple clusters. To simultaneously address both limitations, we propose a two-stage clustering model, termed FGC (fuzzy graph clustering) in this paper. In FGC, we first construct a doubly stochastic graph affinity matrix which is then approximated by the scaled product of the fuzzy cluster indicator matrices. The newly designed fuzzy cluster indicator matrix has two desirable properties of non-negativity and row normalization, which can bring us two benefits. On one hand, we can directly get the cluster assignment of a certain data point by checking the largest value in the corresponding row of the fuzzy cluster indicator matrix; and on the other hand, we can obtain the membership of each data point to different clusters. An iterative method under the alternative optimization framework is proposed to solve the objective function of FGC. We conduct data clustering experiments on both synthetic and benchmark data sets and the results demonstrate the effectiveness of our proposed FGC model. [ABSTRACT FROM AUTHOR]