Research On Dimensionality Reduction Technique And Its Application Based On Manifold Learning

With the quick advancement and extensive application of information technology, wewill come into contact with extremely complex mass of information, which not only have ahigh dimension but also unstructured. In addition, these complex data in high-dimension arenot only difficult to be intuitively understood by people, but also have brought new challengesto the current machine learning and date mining algorithms, so that they cannot be effectivelydealt with, and seriously affects the efficiency of the algorithm and accuracy. Dimensionalityreduction methods have become a powerful tool and means of dealing with these data whichhave high dimension and complex structure, and play a vital role in the field of patternrecognition and many other fields. As everyone knows, after decades of development, datareduction techniques have now made considerable progress and encouraging results. But thereare still some worthy of issues for research workers to continue to study and explore, such assome worthy of further study and challenging problems in linear and nonlinear dimensionalityreduction field. In 2000, three articles published on Science magazine as the starting point,which made the manifold learning algorithms become a research hotspot.Papers from the two categories, namely, linear manifold and nonlinear dimensionalityreduction algorithm of the generalized learning algorithm starting, introduced the typical ofsome commonly used manifold learning algorithm in these two categories, and gives themtheir own ideas and algorithms specific implementation steps, and the advantages and thedisadvantages of the algorithm itself. All of the above explore the ideas and provide atheoretical basis for the specific studies and improvements of algorithms.The emphasis of this paper is as follows: Firstly, we studied a Riemannian manifoldbased on the geodesic distance approach dimension reduction algorithm (TRIMAP),andelaborated on improved TRIMAP, and gave a new definition of distance on the map. This newidea takes into account the size of different class and density of their impact on distancecalculations. Then, this paper gives a detailed implementation step of the algorithm, andmakes a large number of experiments in the ORL face data set with the improved algorithm.After comparing the experiment shows that the improvement is reasonable and effective.Secondly, on the basis of the TRIMAP algorithm which described above, we conductedin-depth consideration and research of the error function. TRIMAP uses the Error and as areference standard between the original distance and projection distance of neighboring points,but this error function doesn't take into account the relation of the map distance and theprojection distance, that is, what the percentage of the two distances can we find the bestprojection. In order to fully reflect the relationship between them and find the best projectionconvenience, this paper has presented an innovation point which is to add a contrast parameter to solve the problem. In this paper, we using MATLAB language design related procedure andin the standard image database for verification. A large number of experimental results showthat the proposed method is effective and feasible.