CAJ | 학술논문

神经网络在线提取子分量并不成功。基于 Oja-Brockett-Xu 并行神经网络拓扑结构，通过紧致 Stiefel 流形上加权 Rayleigh 商目标函数的优化框架，提出一个通过改变搜索方向并行提取主分量和子分量的自适应对偶学习算法。在正交矩阵群上采用基于右平移不变的 Killing 度量，通过在单位元处基于指数映射的测地线搜索，得到Stiefel 流形上主（子）分量分析的对偶学习算法，提出的算法通过简单的变换步长参数符号，从主分量分析切换至子分量分析，权值矩阵在任意迭代时刻保持正交归一性。数值仿真验证了该算法的有效性。
신경망락재선제취자분량병불성공。기우 Oja-Brockett-Xu 병행신경망락탁복결구，통과긴치 Stiefel 류형상가권 Rayleigh 상목표함수적우화광가，제출일개통과개변수색방향병행제취주분량화자분량적자괄응대우학습산법。재정교구진군상채용기우우평이불변적 Killing 도량，통과재단위원처기우지수영사적측지선수색，득도Stiefel 류형상주（자）분량분석적대우학습산법，제출적산법통과간단적변환보장삼수부호，종주분량분석절환지자분량분석，권치구진재임의질대시각보지정교귀일성。수치방진험증료해산법적유효성。
Using the same topology as that of Oja-Brockett-Xu parallel neural network,a novel dual purpose adaptive algorithm for principal and minor component extraction was proposed by the optimization framework of a weighted Ray-leigh quotient on the compact Stiefel manifold. By taking the right translation invariant Killing metric on orthogonal ma-trix group and search along the geodesic emanating from identity by means of exponential map,a novel dual learning al-gorithm for principal and minor component analysis was proposed. The proposed algorithm could switch from PCA (Principal Component Analysis)to MCA(Minor Component Analysis)with a simple sign change of its stepsize pa-rameter. Moreover,orthonormality of the weight matrix was guaranteed at any iteration step. The effectiveness of the proposed algorithm was further verified in the section of numerical simulation.