5. Experimental results

In this section, we experiment on both synthetic and real-world data sets to evaluate the performance of our method, named FLM. For LEM, LLE, HLLE, LTSA, and our Fusion of local manifolds (FLM) algorithms, we experiment on these data sets to obtain both visualization and quantitative evaluations. We utilize the global smoothness and co-directional consistence (GSCD) criteria [17] to quantitatively compare the embedding qualities of different algorithms: the smaller the value of GSCD, the higher the global smoothness, and the better the codirectional consistence. There are two adjustable parameters in our FLM method, that is, the tuning parameter r and the number of nearest neighbors k. FLM works well when the values of r and k are neither too small nor too large. The reason is that only one local method is chosen when r is too small, while the relative weights of different methods tend to be close to each other when it is too large. As a general recommendation, we suggest to work with r∈½2; 6� and k∈½0:7⌈logðNÞ⌉, 2⌈logðNÞ⌉�.
