Let G = （V,E） be a locally finite graph, Ω C V be a finite connected set, A be the graph Laplacian, and suppose that h ： V →R is a function satisfying the coercive condition on Ω, namely there exists some consta...Let G = （V,E） be a locally finite graph, Ω C V be a finite connected set, A be the graph Laplacian, and suppose that h ： V →R is a function satisfying the coercive condition on Ω, namely there exists some constant δ〉 0 such that Ωu（-△＋h）udμ≥δ Ω｜u｜^2dμ, u：VR. By the mountain-pass theorem of Ambrosette-Rabinowitz, we prove that for any p 〉 2, there exists a positive solution to -△μ＋hu=｜u｜^p-2u in Ω. Using the same method, we prove similar results for the p-Laplacian equations. This partly improves recent results of Grigor＇yan-Lin-Yang.展开更多
Due to limitations to extract invariant features for recognition when the aircraft presents various poses and lacks enough samples for training, a novel algorithm called Weighted Marginal Fisher Analysis with Spatiall...Due to limitations to extract invariant features for recognition when the aircraft presents various poses and lacks enough samples for training, a novel algorithm called Weighted Marginal Fisher Analysis with Spatially Smooth （WMFA-SS） for extracting invariant features in aircraft rec- ognition is proposed. According to the Graph Embedding （GE） framework, Heat Kernel function is firstly introduced to characterize the interclass separability when choosing the weights of penalty graph. Furthermore, Laplacian penalty is applied to constraining the coefficients to be spatially smooth in this algorithm. Laplacian penalty is able to incorporate the prior information that neigh- boring pixels are correlated. Besides, using a Laplacian penalty can also avoid the singularity of Laplacian matrix of intrinsic graph. Once compact representations of the images are obtained, it can be considered as invariant features and then be performed in classification to recognize different patterns of aircraft. Real aircraft recognition experiments show the superiority of our proposed WMFA-SS in comparison to other GE algorithms and the current aircraft recognition algorithm; the accuracy rate of our proposed method is 90.00% for dataset BH-AIR1.0 and 99.25% for dataset BH-AIR2.0.展开更多
文摘Let G = （V,E） be a locally finite graph, Ω C V be a finite connected set, A be the graph Laplacian, and suppose that h ： V →R is a function satisfying the coercive condition on Ω, namely there exists some constant δ〉 0 such that Ωu（-△＋h）udμ≥δ Ω｜u｜^2dμ, u：VR. By the mountain-pass theorem of Ambrosette-Rabinowitz, we prove that for any p 〉 2, there exists a positive solution to -△μ＋hu=｜u｜^p-2u in Ω. Using the same method, we prove similar results for the p-Laplacian equations. This partly improves recent results of Grigor＇yan-Lin-Yang.
基金co-supported by the National Key Scientific Instrument and Equipment Development Project (No.2012YQ140032)
文摘Due to limitations to extract invariant features for recognition when the aircraft presents various poses and lacks enough samples for training, a novel algorithm called Weighted Marginal Fisher Analysis with Spatially Smooth （WMFA-SS） for extracting invariant features in aircraft rec- ognition is proposed. According to the Graph Embedding （GE） framework, Heat Kernel function is firstly introduced to characterize the interclass separability when choosing the weights of penalty graph. Furthermore, Laplacian penalty is applied to constraining the coefficients to be spatially smooth in this algorithm. Laplacian penalty is able to incorporate the prior information that neigh- boring pixels are correlated. Besides, using a Laplacian penalty can also avoid the singularity of Laplacian matrix of intrinsic graph. Once compact representations of the images are obtained, it can be considered as invariant features and then be performed in classification to recognize different patterns of aircraft. Real aircraft recognition experiments show the superiority of our proposed WMFA-SS in comparison to other GE algorithms and the current aircraft recognition algorithm; the accuracy rate of our proposed method is 90.00% for dataset BH-AIR1.0 and 99.25% for dataset BH-AIR2.0.
