Bayesian gravitation based classification for hyperspectral images.

Integration of spectral and spatial information is extremely important for the classification of high-resolution hyperspectral images (HSIs). Gravitation describes interaction among celestial bodies which can be applied to measure similarity between data for image classification. However, gravitation is hard to combine with spatial information and rarely been applied in HSI classification. This paper proposes a Bayesian Gravitation based Classification (BGC) to integrate the spectral and spatial information of local neighbors and training samples. In the BGC method, each testing pixel is first assumed as a massive object with unit volume and a particular density, where the density is taken as the data mass in BGC. Specifically, the data mass is formulated as an exponential function of the spectral distribution of its neighbors and the spatial prior distribution of its surrounding training samples based on the Bayesian theorem. Then, a joint data gravitation model is developed as the classification measure, in which the data mass is taken to weigh the contribution of different neighbors in a local region. Four benchmark HSI datasets, i.e. the Indian Pines, Pavia University, Salinas, and Grss_dfc_2014, are tested to verify the BGC method. The experimental results are compared with that of several well-known HSI classification methods, including the support vector machines, sparse representation, and other eight state-of-the-art HSI classification methods. The BGC shows apparent superiority in the classification of high-resolution HSIs and also flexibility for HSIs with limited samples

Hamiltonian Poincar\'e Gauge Theory of Gravitation

We develop a Hamiltonian formalism suitable to be applied to gauge theories in the presence of Gravitation, and to Gravity itself when considered as a gauge theory. It is based on a nonlinear realization of the Poincar\'e group, taken as the local spacetime group of the gravitational gauge theory, with $SO(3)$ as the classification subgroup. The Wigner--like rotation induced by the nonlinear approach singularizes out the role of time and allows to deal with ordinary $SO(3)$ vectors. We apply the general results to the Einstein--Cartan action. We study the constraints and we obtain Einstein's classical equations in the extremely simple form of time evolution equations of the coframe. As a consequence of our approach, we identify the gauge--theoretical origin of the Ashtekar variables.Comment: 38 pages, plainTe

Gravitation Theory Based Model for Multi-Label Classification

The past decade has witnessed the growing popularity in multi-label classification algorithms in the fields like text categorization, music information retrieval, and the classification of videos and medical proteins. In the meantime, the methods based on the principle of universal gravitation have been extensively used in the classification of machine learning owing to simplicity and high performance. In light of the above, this paper proposes a novel multi-label classification algorithm called the interaction and data gravitation-based model for multi-label classification (ITDGM). The algorithm replaces the interaction between two objects with the attraction between two particles. The author carries out a series of experiments on five multi-label datasets. The experimental results show that the ITDGM performs better than some well-known multi-label classification algorithms. The effect of the proposed model is assessed by the example-based F1-Measure and Label-based micro F1-measure

Geometric Classification of Topological Quantum Phases

On the basis of the principle that topological quantum phases arise from the scattering around space-time defects in higher dimensional unification, a geometric model is presented that associates with each quantum phase an element of a transformation group.Comment: 10 pages, Late