Research On Metric Learning Method Based On Manifold Hypothesis

In recent years,within the field of machine learning and different fields,the classification and recognition of image data has become a key concern of the majority of researchers.Traditional algorithms are mostly based on Euclidean space to calculate sample similarity.Although simple and effective,they cannot measure the similarity between sample points more accurately because they do not consider the characteristics of image data such as high dimensionality,sparseness,and manifold.More an d additional analyzers have administrated loads of research work supported the metric learning technique of Riemannian manifold.The manifold hypothesis implies that the discovered knowledge may be a low-dimensional manifold embedded in an exceedingly high-dimensional area.Compared with traditional algorithms,Riemannian Manifold metric learning can make good use of the non-linear structural characteristics of sample data to find a suitable metric for similarity calculation.At the same time,it can direct ly model the manifold of the image set,maintain its internal geometric structure,and extract more complete feature information.In view of the above problems,the main research results of this article are:1.Metric learning method based on Grassmann manifold.First,construct the Grassmann manifold through subspace modeling of the image set,reduce the dimensionality to a more discriminative low-dimensional space using projection mapping,and then transform the element matrix on the original manifold into a symmetric positive semi-definite by establishing a regular term Matrix and define the divergence matrix.In the logarithmic Euclidean space,the objective function is designed to make the distance between the sample points within the class closer,and the distance between the sample points between the classes is more separated,so as to realize the classification and recognition of the image data set.The algorithm was verified on multiple data sets,and good experimental results were obtained.2.A metric learning technique supported multi-manifold fusion.The algorithm uses subspace and covariance to model multi-manifold image sets and uses Riemann metrics to map multiple features to high-dimensional kernel space for fusion,increasing the complementarity of features,and proposes a logdet-based scatter.The objective operates of the metric learning,calculates the Mahalanobis metric matrix,that will increase the sample distance between categories and reduces the gap of sample points among the category at the identical time.This formula has achieved smart experimental results on multi-manifold image information sets.3.Designed and implemented a visualization system for the Riemann metric learning algorithm proposed for text.The system mainly includes four modules: data module,algorithm module,log module,and visualization module.The two algorithms proposed by the text and many classic metric learning algorithms are embedded.It can not only visualize data but also adjust parameters.The effect of numerical display parameters on experimental results.In addition,data sets and algorithms can be added,which has strong scalability.