Research And Application Of Spectral Clustering Algorithm

Graph theory is used as a natural data model in many data mining applications,because the point structure in the graph theory is consistent with the entity-relation structure of the data.Spectral clustering is an unsupervised algorithm based on graph theory,which has many applications in clustering,image segmentation and other fields.Spectral clustering algorithm is often time consuming and laborious because of its high dimension,complexity and redundancy.As the deep learning has also been concerned widely in recent years,it has the advantage of extracting the deep-seated features of data so can be combined with the spectral clustering.Spectral clustering algorithm first needs to establish a similarity matrix according to the relationship between the data sets.The establishment of the matrix has a great influence on the clustering effect.So how to effectively use the data set to build a similarity matrix,and its application to the image segmentation is the main problem discussed in this paper.In view of the above problems,the specific work of this paper is as follows:(1)The spectral clustering generally constructs a similarity matrix directly under the point-to-point relationship of the original data,but the original data is often complex and redundant.The sparse auto-encoder model in the deep learning can extract the high-level structure of the data set,and it can reflect the most essential features of the original data.Therefore,data can be preprocessed and then clustered.However,in the establishment of similarity matrix,the traditional spectral clustering does not consider the data of the manifold neighborhood,but only a single cluster.The algorithm proposed in this paper is based on the linear reconstruction of data point,using the reconstruction weight instead of the Gaussian kernel function to construct the similarity matrix,and the data is mapped to the clustering index to coordinate the clustering index,and obtain a more accurate clustering result.(2)The clustering algorithm clustering is largely dependent on the construction of similar matrices.Most traditional spectral clustering algorithms use Gaussian kernel functions,but they are sensitive to scale parameters.Based on the problem of sensitivity to scale parameters,a new adaptive spectral clustering algorithm based on weighted density is proposed.The algorithm uses the weighted K nearest neighbor distance of the data points as the scale parameter,the reciprocal of the scale parameter as the density of the data points,and introduces the new density difference to adjust the similarity matrix,and satisfies the principle that the same manifold or similar data density is close.The new algorithm is no longer sensitive,but also a certain degree of robust to noise.(3)When spectral clustering is applied to the image segmentation,the similarity matrix is based on the pixel,and the data volume is too large,so the image can be preprocessed.The secondary watershed can be used to ensure that the original image is not destroyed while getting less pixels of the over-segmented image,which can be used for subsequent spectral clustering work.Finally,the over-segmented image obtained in this paper is used as image input.The adaptive spectral clustering algorithm based on weighted density is applied to image segmentation.The algorithm is evaluated by qualitative and quantitative criteria.