In this paper, we investigate the factor properties and gap sequence of the Tri- bonacci sequence, the fixed point of the substitution σ（a, b, c） = （ab, ac, a）. Let Wp be the p-th occurrence of w and Gp（ω） be ...In this paper, we investigate the factor properties and gap sequence of the Tri- bonacci sequence, the fixed point of the substitution σ（a, b, c） = （ab, ac, a）. Let Wp be the p-th occurrence of w and Gp（ω） be the gap between Wp and Wp＋l. We introduce a notion of kernel for each factor w, and then give the decomposition of the factor w with respect to its kernel. Using the kernel and the decomposition, we prove the main result of this paper： for each factor w, the gap sequence {Gp（ω）}p≥1 is the Tribonacci sequence over the alphabet {G1 （ω）, G2（ω）, G4（ω）}, and the expressions of gaps are determined completely. As an application, for each factor w and p C ∈N, we determine the position of Wp. Finally we introduce a notion of spectrum for studying some typical combinatorial properties, such as power, overlap and separate of factors.展开更多
Histogram Intersection Kernel Support Vector Machines (SVM) was used for the image classification problem. Specifically, each image was split into blocks, and each block was represented by the Scale Invariant Feature ...Histogram Intersection Kernel Support Vector Machines (SVM) was used for the image classification problem. Specifically, each image was split into blocks, and each block was represented by the Scale Invariant Feature Transform (SIFT) descriptors;secondly, k-means cluster method was applied to separate the SIFT descriptors into groups, each group represented a visual keywords;thirdly, count the number of the SIFT descriptors in each image, and histogram of each image should be constructed;finally, Histogram Intersection Kernel should be built based on these histograms. In our experimental study, we use Corel-low images to test our method. Compared with typical RBF kernel SVM, the Histogram Intersection kernel SVM performs better than RBF kernel SVM.展开更多
基金supported by grants from the National Science Foundation of China(114310071127122311371210)
文摘In this paper, we investigate the factor properties and gap sequence of the Tri- bonacci sequence, the fixed point of the substitution σ（a, b, c） = （ab, ac, a）. Let Wp be the p-th occurrence of w and Gp（ω） be the gap between Wp and Wp＋l. We introduce a notion of kernel for each factor w, and then give the decomposition of the factor w with respect to its kernel. Using the kernel and the decomposition, we prove the main result of this paper： for each factor w, the gap sequence {Gp（ω）}p≥1 is the Tribonacci sequence over the alphabet {G1 （ω）, G2（ω）, G4（ω）}, and the expressions of gaps are determined completely. As an application, for each factor w and p C ∈N, we determine the position of Wp. Finally we introduce a notion of spectrum for studying some typical combinatorial properties, such as power, overlap and separate of factors.
文摘Histogram Intersection Kernel Support Vector Machines (SVM) was used for the image classification problem. Specifically, each image was split into blocks, and each block was represented by the Scale Invariant Feature Transform (SIFT) descriptors;secondly, k-means cluster method was applied to separate the SIFT descriptors into groups, each group represented a visual keywords;thirdly, count the number of the SIFT descriptors in each image, and histogram of each image should be constructed;finally, Histogram Intersection Kernel should be built based on these histograms. In our experimental study, we use Corel-low images to test our method. Compared with typical RBF kernel SVM, the Histogram Intersection kernel SVM performs better than RBF kernel SVM.
