Supported by the National Natural Science Foundation of China under Grant No.60175023(国家自然科学基金);the NationalGrand Fundamental Research 973 Program of China under Grant No.2004CB318103(国家重点基础研究发展规划(973))
局部切空间排列算法(local tangent space alignment,简称LTSA)是一种新的流形学习算法,能有效地学习出高维采样数据的低维嵌入坐标,但也存在一些不足,如不能处理样本数较大的样本集和新来的样本点.针对这些缺点,提出了一种基于划分的局部切空间排列算法(partitional local tangent space alignment,简称PLTSA).它建立在VQPCA(vector quantization principal component analysis)算法和LTSA
Recently, a new manifold learning algorithm, LTSA (local tangent space alignment), has been proposed. It is efficient for many nonlinear dimension reduction problems but unfit for large data sets and newcome data. In this paper, an improved algorithm called partitional local tangent space alignment (PLTSA) is presented, which is based on VQPCA (vector quantization principal component analysis) and LTSA. In the algorithm, the sample space is first divided into overlapping blocks using the X-Means algorithm. Then each block is projected to its local tangent space to get local low-dimensional coordinates of the points in it. At last, the global low-dimensional embedded manifold is obtained by local affine transformations. PLTSA is better than VQPCA in that it gives the global coordinates of the data. It works on a much smaller optimization matrix than that of LTSA and leads to a better-scaled algorithm. The algorithm also provides a set of transformations that allow to calculate the global embedded coordinates of the newcome data. Experiments illustrate the validity of this algorithm.