Research On Datasets Application Problem Of Manifold Learning

Manifold learning algorithms as the main nonlinear dimensionality reductionalgorithm have caught the attention of many fields such as math, biology, medical andcomputer science. There have been manifold learning algorithms such as ISOMAP, LLE,LE, MVU, and disconnected manifold learning algorithms such as DC algorithms, butthese algorithms are not applicable for all datasets. We get focused on this topic, and theachievements are introduced in the following.Firstly, a discriminant algorithm of data types of central symmetry manifold isproposed according to the judgement of the central symmetry datasets type. The algorithmconsists of two steps, the first step is to approximate the center of the manifold bycircumcenter and find out the boundary points, the second step is to find out the twoboundary points in the high dimension whose distance are the furthest distance in the lowdimension, then we can judge the datasets that if it’s isometric or not by judge if theshortest way between the two points pass the center point, which is a solution to the“datasets application problem”.Secondly, a compositive disconnected manifold learning algorithm is proposed whichis based on the fact that the decomposition-composition(DC) algorithms in disconnectedmanifold learning algorithms are based on isometric mapping algorithm, which makessome datasets’ inner structure couldn’t be got accurately, so the whole datasets’ innerstructure couldn’t be got accurately. Our algorithm is based on the DC algorithms, andintroduces the LLE, so the basic algorithms become ISOMAP and LLE, and improves theDC algorithms by adjusting its’ steps.Finally, experiments of both algorithms are taken. The experiment of the discriminantalgorithm of data types of central symmetry manifold shows the process of the algorithm,and the result approves the correctness of the algorithm. The experiment of thecompositive disconnected manifold learning algorithm approves the correctness of thealgorithm by comparing with the transition curve algorithm, which shows the advantage ofthe compositive disconnected manifold learning algorithm.