1D Embedding Multi-category Classification Methods

As one of the basic problems in machine learning,classification is widely used in finan-cial sector,internet industry,equipment manufacturing and pharmaceutical industries.Consequently,many classification algorithms have emerged and are widely used in vi-rous fields.Nevertheless,these algorithms have some limitations that many algorithms can not achieve the satisfactory effect when processing the high-dimensional data,es-pecially in small-sample learning which the number of labeled samples is small.One-dimensional embedding algorithm embeds high-dimensional data into one-dimensional manifold by smooth ordering method and one-one mapping,therefore,the complex high dimensional learning problem is changed into a simple one-dimensional interpo-lation problem.On this basis,this paper proposes a semi-supervised multi-category classification algorithm based on one-dimensional multi-embedding.In this paper,the proposed algorithm uses one-versus-rest and one-versus-one methods to decompose the problem into many binary classification problems.Accord-ing to the results of the binary classification,the classification results are obtained.Firstly,a smoothing ordering algorithm is used to reorder the high-dimensional data to a ordering result and a one-one mapping is used to embed the ordering result to one-dimensional manifold according to the distance relationship of the data.As a result,we get a one-dimensional embedding result of the high-dimensional data.Then,using the interpolation algorithm to get a decision function of binary classification based on the one-dimensional embedding result of the high-dimensional data.Finally,on the basic of the decision function of binary classification,using one-versus-rest and one-versus-one to construct the multi-category classifier,respectively.A weight strategy is employed in our algorithm for improving the classification performance.The proposed method shows promising results in the classification of handwritten digits and face data sets.It obviously that the multi-category classification method based on one-dimensional multi-embedding has a better effect than other methods for handwritten digits recognition and face recognition,especially when the number of labeled samples is small.