Local linear transformation embedding
Local linear transformation embedding
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DOI：
10.1016/j.neucom.2008.12.002
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发表时间：
2009-06
期刊：
影响因子：
6
通讯作者：
Chenping Hou;J. Wang;Yi Wu;Dong-yun Yi
中科院分区：
文献类型：
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作者：
Chenping Hou;J. Wang;Yi Wu;Dong-yun Yi
降维在许多领域都是至关重要的，局部线性嵌入(LLE)是其中最重要的方法之一。然而，当数据样本密度较低或采样不均匀时，LLE不可避免地会产生不均匀的包络和折叠。当数据受到哪怕是很小的噪声污染时，LLE也会失败。分析了LLE的性能，指出了LLE失败的原因。提出了一种改进的局部线性变换嵌入算法(LLTE)。对邻近的点进行局部线性变换。当数据有异常值时，也提供了‘三阶段LLTE’。与LLE和局部切线空间对齐(LTSA)算法相比，LLTE算法具有更好的嵌入效果，具有更广阔的应用前景。同时，它利用了LLE/LLTE和LTSA之间的紧密关系。几个实验和数值结果证明了该算法的潜力。
Dimensionality reduction is vital in many fields and locally linear embedding (LLE) is one of the most important approaches. However, LLE is unavoidable to derive the nonuniform wraps and folds when the data are of low sample density or unevenly sampled. LLE would also fail when the data are contaminated by even small noises. We have analyzed the performance of LLE and pointed out the reason why LLE fails. An improved algorithm, local linear transformation embedding (LLTE), is then proposed. Local linear transformation is performed on nearby points. The ‘Three-stage LLTE’ is also provided when the data has outliers. Comparing with LLE and Local tangent space alignment (LTSA), LLTE could derive more practical embedding than LLE and has wider application prospect than LTSA. Meanwhile, it exploits the tight relations between LLE/LLTE and LTSA. Several experiments and numerical results demonstrate the potential of our algorithm.