Research On High-dimensional Multi-manifold Classification Algorithms

As an important data processing method in machine learning,classification is widely used in various fields such as medical diagnosis,image processing,text analysis,etc.With the evolvement of information technology,most of the data is extremely complex high-dimensional data,and it is difficult for traditional classification methods to handle this kind of data.In order to deal with this problem,many well-known dimensionality reduction algorithms have been proposed by experts and scholars.Among them,manifold learning algorithms have attracted much attention in recent years.As a non-linear dimensionality reduction algorithm,the main idea of manifold learning is to obtain the low-dimensional representation of high-dimensional data,and to discover the underlying laws and structural characteristics of things.However,the traditional manifold learning algorithm has the following disadvantages when dealing with classification problems.First,manifold learning algorithms are unsupervised.They cannot use category information to increase the discriminativeness,so that it may not improve the classification performance of the algorithm.Second,traditional manifold learning algorithms suppose the data is located on a single manifold structure,but high-dimensional data is extremely complex.They often span multiple manifold structures.If we simply use the single manifold learning algorithm,the essential characteristics of the data cannot be extracted effectively.Third,traditional manifold learning algorithms do not consider the noisy data in the real world very well,so they are susceptible to interference of noise data when extracting the intrinsic features of the data.Finally,traditional manifold learning algorithms generally treat all data features equally without the prior information,and cannot adaptively learn the importance of different features from the data.To handle the above problems,our paper will focus on the manifold learning algorithm of multi-manifold structure,improve the noise immunity of the algorithm through low-rank representation,and adaptively learn the importance of different features through adaptive composition methods.The main research contents are as follows:(1)A multi-manifold classification algorithm based on local spline embedding is proposed.It maps the data of different labels to different sub-manifolds,and retains the local manifold structure of similar data through local spline embedding algorithm.At the same time,in order to distinguish heterogeneous data,the selection of heterogeneous neighbor points is used to construct regularization terms between classes so that the heterogeneous data in the low-dimensional space are farther apart.Experiments on numerous image data sets prove the effectiveness of our algorithm.(2)A multi-manifold classification algorithm based on low rank representation is proposed.For the problem that the real-world data contains a lot of invalid noise,we introduce low-rank representation learning into related manifold learning algorithms and improve the robustness of the algorithm.First.we construct a robust linear low-dimensional subspace for the training data,and then retain the manifold structure and discriminative information of the data through the multi-manifold local spline embedding algorithm.A multi-manifold classification algorithm based on low rank representation cannot only ensure that the local manifold structure does not change,but also enhance its discrimination ability.The most important thing is that it has excellent processing ability for noisy data.Many experiments have proved the effectiveness of our algorithm.(3)A multi-manifold classification algorithm based on adaptive composition is proposed.The traditional manifold learning algorithm treats all features equally.We introduce the idea of adaptive composition into the manifold learning algorithm.In fact,there are many noise samples in the real data set.Our algorithm adaptively assigns weights to these noise samples,thereby minimizing the negative impact of experimental results.Similarly,our algorithm will adaptively assign weights to different features of the data,effectively improving the robustness of the model.We prove the effectiveness of our algorithm through noise dataset and real-world dataset.