基于随机游走扩散映射的降维算法

传统数据降维算法分为线性或流形学习降维算法,但在实际应用中很难确定需要哪一类算法.设计一种综合的数据降维算法,以保证它的线性降维效果下限为主成分分析方法且在流形学习降维方面能揭示流形的数据结构.通过对高维数据构造马尔可夫转移矩阵,使越相似的节点转移概率越大,从而发现高维数据降维到低维流形的映射关系.实验结果表明,在人造...

DIMENSION REDUCTION ALGORITHM BASED ON RANDOM WALK DIFFUSION MAPPING

Traditional data dimensionality reduction algorithms are divided into linear or manifold learning dimensionality reduction algorithms,but in practical applications,it is difficult to determine which kind of algorithm is needed.A comprehensive data dimensionality reduction algorithm is designed to ensure that the lower limit of its linear dimensionality reduction effect is the principal component analysis(PCA)algorithm,and the data structure of manifold can be revealed in the aspect of manifold learning dimensionality reduction.By constructing Markov transition matrix for high-dimensional data,the more similar nodes have greater transition probability,so as to find the mapping relationship between high-dimensional data dimensionality reduction and low-dimensional manifold.The experimental results show that in the linear dimensionality reduction of artificial data and real data,the dimensionality reduction effect of this algorithm is equivalent to that of PCA algorithm,while the locally linear embedding(LLE)failed.In the manifold learning dimensionality reduction,this algorithm is basically equivalent to that of LLE,but PCA algorithm fails completely.