局部线性嵌入算法中参数的选取

Determining Parameter for Locally Linear Embedding Algorithm

局部线性嵌入(LLE)算法是有效的非线性降维方法,时间复杂度低并具有强的流形表达能力。与其他降维方法相比,局部线性嵌入算法的优势在于只定义唯一的参数,即邻域数。因此算法的性能主要依靠此邻域参数的选取,这就产生问题:怎样选取邻域参数的最佳值。通过对两种自动选取最佳参数值的方法,即简单方法和分层方法进行试验比较与分析,归纳出在实践中确定邻域参数的启发式策略。

The Locaally Linear Embedding（LLE） algorithm is an effective technique for nonlinear dimensionality reduction of high-dimensional data. It has low time-complexity and strong ability to express manifold. Compared with other dimensionality reduction algorithms, the advantage of the locally linear embedding algorithm is only defining unique parameter： number of nearest neighbors. Performance of algorithm mainly depends on selection of parameter of neighbors. Then one question which is how to select an optimal parameter value of neighbors emerges. After comparing and analysing two methods for automatic selection of an optimal parameter value, which are a straightforward method and a hierarchical method, heuristic strategy for determining parameter of neighbors in practice has been concluded.