CAJ | 학술논문

局部切空间排列是一种广受关注的流形学习算法，其具备实现简单、全局最优等特点，但其难以有效处理稀疏采样或非均匀分布的高维观测数据。针对这一问题，该文提出一种改进的局部切空间排列算法。首先，提出一种基于L1范数的局部切空间估计方法，由于同时考虑了距离和结构因素，该方法得到的切空间较主成分分析方法更为准确。其次，在坐标排列步骤为了减小排列误差，设计了一种基于流形结构的加权坐标排列方案，并给出了具体的求解方法。基于人造数据和真实数据的实验表明，该算法能够有效地处理稀疏和非均匀分布的流形数据。
국부절공간배렬시일충엄수관주적류형학습산법，기구비실현간단、전국최우등특점，단기난이유효처리희소채양혹비균균분포적고유관측수거。침대저일문제，해문제출일충개진적국부절공간배렬산법。수선，제출일충기우L1범수적국부절공간고계방법，유우동시고필료거리화결구인소，해방법득도적절공간교주성분분석방법경위준학。기차，재좌표배렬보취위료감소배렬오차，설계료일충기우류형결구적가권좌표배렬방안，병급출료구체적구해방법。기우인조수거화진실수거적실험표명，해산법능구유효지처리희소화비균균분포적류형수거。
The Local Tangent Space Alignment (LTSA) is one of the popular manifold learning algorithms since it is straightforward to implementation and global optimal. However, LTSA may fail when high-dimensional observation data are sparse or non-uniformly distributed. To address this issue, a modified LTSA algorithm is presented. At first, a new L1 norm based method is presented to estimate the local tangent space of the data manifold. By considering both distance and structure factors, the proposed method is more accurate than traditional Principal Component Analysis (PCA) method. To reduce the bias of coordinate alignment, a weighted scheme based on manifold structure is then designed, and the detailed solving method is also presented. Experimental results on both synthetic and real datasets demonstrate the effectiveness of the proposed method when dealing with sparse and non-uniformly manifold data.