In machine learning and statistics, classification is the a new observation belongs, on the basis of a training set of data problem of identifying to which of a set of categories （sub-populations） containing observa...In machine learning and statistics, classification is the a new observation belongs, on the basis of a training set of data problem of identifying to which of a set of categories （sub-populations） containing observations （or instances） whose category membership is known. SVM （support vector machines） are supervised learning models with associated learning algorithms that analyze data and recognize patterns, used for classification and regression analysis. The basic SVM takes a set of input data and predicts, for each given input, which of two possible classes fon^as the output, making it a non-probabilistic binary linear classifier. In pattern recognition problem, the selection of the features used for characterization an object to be classified is importance. Kernel methods are algorithms that, by replacing the inner product with an appropriate positive definite function, impticitly perform a nonlinear mapping 4~ of the input data in Rainto a high-dimensional feature space H. Cover＇s theorem states that if the transformation is nonlinear and the dimensionality of the feature space is high enough, then the input space may be transformed into a new feature space where the patterns are linearly separable with high probability.展开更多
This paper presents a nonlinear multidimensional scaling model, called kernelized fourth quantifica- tion theory, which is an integration of kernel techniques and the fourth quantification theory. The model can deal w...This paper presents a nonlinear multidimensional scaling model, called kernelized fourth quantifica- tion theory, which is an integration of kernel techniques and the fourth quantification theory. The model can deal with the problem of mineral prediction without defining a training area. In mineral target prediction, the pre-defined statistical cells, such as grid cells, can be implicitly transformed using kernel techniques from input space to a high-dimensional feature space, where the nonlinearly separable clusters in the input space are ex- pected to be linearly separable. Then, the transformed cells in the feature space are mapped by the fourth quan- tifieation theory onto a low-dimensional scaling space, where the sealed cells can be visually clustered according to their spatial locations. At the same time, those cells, which are far away from the cluster center of the majority of the sealed cells, are recognized as anomaly cells. Finally, whether the anomaly cells can serve as mineral potential target cells can be tested by spatially superimposing the known mineral occurrences onto the anomaly ceils. A case study shows that nearly all the known mineral occurrences spatially coincide with the anomaly cells with nearly the smallest scaled coordinates in one-dimensional sealing space. In the case study, the mineral target cells delineated by the new model are similar to those predicted by the well-known WofE model.展开更多
We give a strategy for nonlocal unambiguous discrimination (UD) among N linearly independent nonorthogonal qudit states lying in a higher-dimensional Hilbert space. The procedure we use is a nonlocal positive operator...We give a strategy for nonlocal unambiguous discrimination (UD) among N linearly independent nonorthogonal qudit states lying in a higher-dimensional Hilbert space. The procedure we use is a nonlocal positive operator valued measurement (POVM) in a direct sum space. This scheme is designed for obtaining the conclusive nonlocal measurement results with a finite probability of success. We construct a quantum network for realizing the nonlocal UD with a set of two-level remote rotations, and thus provide a feasible physical means to realize the nonlocal UD.展开更多
文摘In machine learning and statistics, classification is the a new observation belongs, on the basis of a training set of data problem of identifying to which of a set of categories （sub-populations） containing observations （or instances） whose category membership is known. SVM （support vector machines） are supervised learning models with associated learning algorithms that analyze data and recognize patterns, used for classification and regression analysis. The basic SVM takes a set of input data and predicts, for each given input, which of two possible classes fon^as the output, making it a non-probabilistic binary linear classifier. In pattern recognition problem, the selection of the features used for characterization an object to be classified is importance. Kernel methods are algorithms that, by replacing the inner product with an appropriate positive definite function, impticitly perform a nonlinear mapping 4~ of the input data in Rainto a high-dimensional feature space H. Cover＇s theorem states that if the transformation is nonlinear and the dimensionality of the feature space is high enough, then the input space may be transformed into a new feature space where the patterns are linearly separable with high probability.
基金supported by National Natural Science Foundation of China (No.40872193)
文摘This paper presents a nonlinear multidimensional scaling model, called kernelized fourth quantifica- tion theory, which is an integration of kernel techniques and the fourth quantification theory. The model can deal with the problem of mineral prediction without defining a training area. In mineral target prediction, the pre-defined statistical cells, such as grid cells, can be implicitly transformed using kernel techniques from input space to a high-dimensional feature space, where the nonlinearly separable clusters in the input space are ex- pected to be linearly separable. Then, the transformed cells in the feature space are mapped by the fourth quan- tifieation theory onto a low-dimensional scaling space, where the sealed cells can be visually clustered according to their spatial locations. At the same time, those cells, which are far away from the cluster center of the majority of the sealed cells, are recognized as anomaly cells. Finally, whether the anomaly cells can serve as mineral potential target cells can be tested by spatially superimposing the known mineral occurrences onto the anomaly ceils. A case study shows that nearly all the known mineral occurrences spatially coincide with the anomaly cells with nearly the smallest scaled coordinates in one-dimensional sealing space. In the case study, the mineral target cells delineated by the new model are similar to those predicted by the well-known WofE model.
基金supported by the Natural Science Foundation of Guangdong Province, China (Grant No. 06029431)
文摘We give a strategy for nonlocal unambiguous discrimination (UD) among N linearly independent nonorthogonal qudit states lying in a higher-dimensional Hilbert space. The procedure we use is a nonlocal positive operator valued measurement (POVM) in a direct sum space. This scheme is designed for obtaining the conclusive nonlocal measurement results with a finite probability of success. We construct a quantum network for realizing the nonlocal UD with a set of two-level remote rotations, and thus provide a feasible physical means to realize the nonlocal UD.
