Marginal Fisher analysis(MFA)stands out as a prominent dimensionality reduction algorithm,striving to minimize within-class scatter while maximizing the separability between marginal data points.However,MFA and its va...Marginal Fisher analysis(MFA)stands out as a prominent dimensionality reduction algorithm,striving to minimize within-class scatter while maximizing the separability between marginal data points.However,MFA and its variants require substantial computational resources when dealing with large-scale data.To address this,we propose quantum algorithms for MFA(called QMFA).QMFA is composed of two core processes:the first is the efficient construction of the weight matrices for the intrinsic and penalty graphs,and the second is solving the generalized eigenvalue problem(GEP)using the block-encoding technique.Compared to classical MFA,the proposed QMFA achieves a polynomial acceleration in the number of samples and exponential acceleration in the dimensionality.Additionally,we investigate quantum algorithms for different variants of MFA.Specifically,for enhanced MFA and multiple MFA,we address the construction of the related weight matrix,which differs from that in standard MFA.For kernel MFA,we solve the GEP associated with the corresponding kernel matrix.The proposed quantum algorithms achieve a speedup equivalent to that of QMFA.展开更多
Marginal Fisher analysis （MFA） not only aims to maintain the original relations of neighboring data points of the same class but also wants to keep away neighboring data points of the different classes.MFA can effec...Marginal Fisher analysis （MFA） not only aims to maintain the original relations of neighboring data points of the same class but also wants to keep away neighboring data points of the different classes.MFA can effectively overcome the limitation of linear discriminant analysis （LDA） due to data distribution assumption and available projection directions.However,MFA confronts the undersampled problems.Generalized marginal Fisher analysis （GMFA） based on a new optimization criterion is presented,which is applicable to the undersampled problems.The solutions to the proposed criterion for GMFA are derived,which can be characterized in a closed form.Among the solutions,two specific algorithms,namely,normal MFA （NMFA） and orthogonal MFA （OMFA）,are studied,and the methods to implement NMFA and OMFA are proposed.A comparative study on the undersampled problem of face recognition is conducted to evaluate NMFA and OMFA in terms of classification accuracy,which demonstrates the effectiveness of the proposed algorithms.展开更多
Effective and robust recognition and tracking of objects are the key problems in visual surveillance systems. Most existing object recognition methods were designed with particular objects in mind. This study presents...Effective and robust recognition and tracking of objects are the key problems in visual surveillance systems. Most existing object recognition methods were designed with particular objects in mind. This study presents a general moving objects recognition method using global features of targets. Targets are extracted with an adaptive Gaussian mixture model and their silhouette images are captured and unified. A new objects silhouette database is built to provide abundant samples to train the subspace feature. This database is more convincing than the previous ones. A more effective dimension reduction method based on graph embedding is used to obtain the projection eigenvector. In our experiments, we show the effective performance of our method in addressing the moving objects recognition problem and its superiority compared with the previous methods.展开更多
Marginal Fisher analysis （MFA） is a repre- sentative margin-based learning algorithm for face recognition. A major problem in MFA is how to select appropriate parameters, k1 and k2, to construct the respective intri...Marginal Fisher analysis （MFA） is a repre- sentative margin-based learning algorithm for face recognition. A major problem in MFA is how to select appropriate parameters, k1 and k2, to construct the respective intrinsic and penalty graphs. In this paper, we propose a novel method called nearest-neighbor （NN） classifier motivated marginal discriminant projections （NN-MDP）. Motivated by the NN classifier, NN-MDP seeks a few projection vectors to prevent data samples from being wrongly categorized. Like MFA, NN-MDP can characterize the compactness and separability of samples simultaneously. Moreover, in contrast to MFA, NN-MDP can actively construct the intrinsic graph and penalty graph without unknown parameters. Experimental results on the 0RL, Yale, and FERET face databases show that NN-MDP not only avoids the intractability, and high expense of neighborhood parameter selection, but is also more applicable to face recognition with NN classifier than other methods.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.62372048,62371069,62272056,and U25B2014)。
文摘Marginal Fisher analysis(MFA)stands out as a prominent dimensionality reduction algorithm,striving to minimize within-class scatter while maximizing the separability between marginal data points.However,MFA and its variants require substantial computational resources when dealing with large-scale data.To address this,we propose quantum algorithms for MFA(called QMFA).QMFA is composed of two core processes:the first is the efficient construction of the weight matrices for the intrinsic and penalty graphs,and the second is solving the generalized eigenvalue problem(GEP)using the block-encoding technique.Compared to classical MFA,the proposed QMFA achieves a polynomial acceleration in the number of samples and exponential acceleration in the dimensionality.Additionally,we investigate quantum algorithms for different variants of MFA.Specifically,for enhanced MFA and multiple MFA,we address the construction of the related weight matrix,which differs from that in standard MFA.For kernel MFA,we solve the GEP associated with the corresponding kernel matrix.The proposed quantum algorithms achieve a speedup equivalent to that of QMFA.
基金supported by Science Foundation of the Fujian Province of China (No. 2010J05099)
文摘Marginal Fisher analysis （MFA） not only aims to maintain the original relations of neighboring data points of the same class but also wants to keep away neighboring data points of the different classes.MFA can effectively overcome the limitation of linear discriminant analysis （LDA） due to data distribution assumption and available projection directions.However,MFA confronts the undersampled problems.Generalized marginal Fisher analysis （GMFA） based on a new optimization criterion is presented,which is applicable to the undersampled problems.The solutions to the proposed criterion for GMFA are derived,which can be characterized in a closed form.Among the solutions,two specific algorithms,namely,normal MFA （NMFA） and orthogonal MFA （OMFA）,are studied,and the methods to implement NMFA and OMFA are proposed.A comparative study on the undersampled problem of face recognition is conducted to evaluate NMFA and OMFA in terms of classification accuracy,which demonstrates the effectiveness of the proposed algorithms.
基金Project (No. 60805001) partially supported by the National NaturalScience Foundation of China
文摘Effective and robust recognition and tracking of objects are the key problems in visual surveillance systems. Most existing object recognition methods were designed with particular objects in mind. This study presents a general moving objects recognition method using global features of targets. Targets are extracted with an adaptive Gaussian mixture model and their silhouette images are captured and unified. A new objects silhouette database is built to provide abundant samples to train the subspace feature. This database is more convincing than the previous ones. A more effective dimension reduction method based on graph embedding is used to obtain the projection eigenvector. In our experiments, we show the effective performance of our method in addressing the moving objects recognition problem and its superiority compared with the previous methods.
文摘Marginal Fisher analysis （MFA） is a repre- sentative margin-based learning algorithm for face recognition. A major problem in MFA is how to select appropriate parameters, k1 and k2, to construct the respective intrinsic and penalty graphs. In this paper, we propose a novel method called nearest-neighbor （NN） classifier motivated marginal discriminant projections （NN-MDP）. Motivated by the NN classifier, NN-MDP seeks a few projection vectors to prevent data samples from being wrongly categorized. Like MFA, NN-MDP can characterize the compactness and separability of samples simultaneously. Moreover, in contrast to MFA, NN-MDP can actively construct the intrinsic graph and penalty graph without unknown parameters. Experimental results on the 0RL, Yale, and FERET face databases show that NN-MDP not only avoids the intractability, and high expense of neighborhood parameter selection, but is also more applicable to face recognition with NN classifier than other methods.
