Research Of Manifold Classification Algorithm Based On Local Spline Embedding And Its Applications

With the applying of data mining in various industries,as a kind of important technique,classification is paid more attention than before.However,the difficulty of classification increases very quickly with the sharp increasing of the quantity and complexity of the data.Therefore,the traditional classification algorithms cannot appropriately handle the data with high dimensionality.For this reason,researchers tried to simplify the original data by employing dimension reduction techniques before classification.Manifold Learning is an effective way to work out the curse of dimensionality by reducing the dimension to simplify the complex data.It aims at recovering the low-dimensional structure from the high-dimensional sample data.That is to obtain the corresponding mappings to reducing the dimension.But the results of manifold learning may not suitable for classification because manifold learning is only designed to reduce dimension instead of classification.Local Spline Embedding algorithm is an outstanding manifold learning algorithm which acquires global coordinates in low-dimensional space by embedding the spline into local coordinates in local tangent space.It goes through two mappings in total to finish the dimension reduction.In the processes of two mappings,it tries to decrease the mapping error so that it can preserve the local structure features as much as possible.Whereas,it's also trapped in the drawbacks of manifold learning which is not fit for classification.It cannot make use of the label information to enhance the discrimination of the results after reducing dimension.Hence,it's necessary to improve the Local Spline Embedding algorithm to make it beneficial to classification of the high-dimensional data.In this paper,we mainly research the classification of manifold learning as well as two classification algorithms which are based on local spline embedding algorithms.And we apply them to the practical applications.Specific research work and achievements are as follows:(1)In this paper,we proposed an improved supervised local spline embedding for classification.By incorporating the merit of linear discriminant analysis,we make use of label information what we have got to maximize the scatter of between-class and minimize the scatter of within-class simultaneously.And regard the variant of objective function of local spline embedding as regularization item to preserve the local structure information of data because of the merit of local spline embedding which can preserve the local structure information.And we also use the obtained optimal mapping to expand the out-of-sample data.(2)In this paper,we proposed a linear classification algorithm based on local spline embedding.It exploits the supervised information of training data to construct the inter-class graph and intra-class graph respectively.According to the selected neighborhoods,we construct the intra-class tangent space and inter-class tangent space.Then,it maps the local coordinates to global coordinate systems to obtain the global low-dimensional coordinates and we can get the optimal linear mapping.At last,by means of the optimal linear mapping we can accomplish the extending of out-of sample data.(3)In this paper,we proposed a nonlinear classification algorithm based on local spline embedding.By improving the linear classification algorithm proposed before,apply the kernel function to linear algorithm to acquire the nonlinear embedding of sample data.In this way,we can get better classification results and it comes to be more suitable to the classification of real-world data.(4)In this paper,we design a system of classifying the medical data and apply the proposed algorithms to deal with the medical data.This system mainly consists of three groups:disposing of medical data,display of classifying results,and management of medical data.