The Neighborhood Preserving Embedding(NPE) algorithm is recently proposed as a new dimensionality reduction method.However, it is confined to linear transforms in the data space.For this, based on the NPE algorithm, a...The Neighborhood Preserving Embedding(NPE) algorithm is recently proposed as a new dimensionality reduction method.However, it is confined to linear transforms in the data space.For this, based on the NPE algorithm, a new nonlinear dimensionality reduction method is proposed, which can preserve the local structures of the data in the feature space.First, combined with the Mercer kernel, the solution to the weight matrix in the feature space is gotten and then the corresponding eigenvalue problem of the Kernel NPE(KNPE) method is deduced.Finally, the KNPE algorithm is resolved through a transformed optimization problem and QR decomposition.The experimental results on three real-world data sets show that the new method is better than NPE, Kernel PCA(KPCA) and Kernel LDA(KLDA) in performance.展开更多
In [J. Algeb. Combin. 19(2004), 123-141], Du et al. classified the orientable regular embeddings of connected simple graphs of order pq for any two primes p and q. In this paper, we shall classify the nonorientable re...In [J. Algeb. Combin. 19(2004), 123-141], Du et al. classified the orientable regular embeddings of connected simple graphs of order pq for any two primes p and q. In this paper, we shall classify the nonorientable regular embeddings of these graphs, where p ≠ q. Our classification depends on the classification of primitive permutation groups of degree p and degree pq but is independent of the classification of the arc-transitive graphs of order pq.展开更多
文摘The Neighborhood Preserving Embedding(NPE) algorithm is recently proposed as a new dimensionality reduction method.However, it is confined to linear transforms in the data space.For this, based on the NPE algorithm, a new nonlinear dimensionality reduction method is proposed, which can preserve the local structures of the data in the feature space.First, combined with the Mercer kernel, the solution to the weight matrix in the feature space is gotten and then the corresponding eigenvalue problem of the Kernel NPE(KNPE) method is deduced.Finally, the KNPE algorithm is resolved through a transformed optimization problem and QR decomposition.The experimental results on three real-world data sets show that the new method is better than NPE, Kernel PCA(KPCA) and Kernel LDA(KLDA) in performance.
基金support of National Natural Science Foun- dation of China (Grant No. 10971144)Natural Science Foundation of Beijing (Grant No. 1092010)
文摘In [J. Algeb. Combin. 19(2004), 123-141], Du et al. classified the orientable regular embeddings of connected simple graphs of order pq for any two primes p and q. In this paper, we shall classify the nonorientable regular embeddings of these graphs, where p ≠ q. Our classification depends on the classification of primitive permutation groups of degree p and degree pq but is independent of the classification of the arc-transitive graphs of order pq.
