Constrained affinity matrix for spectral clustering: A basic semi-supervised extension

Spectral clustering has represented a good alternative in digital signal processing and pattern recognition; however a decision concerning the affinity functions among data is still an issue. In this work it is presented an extended version of a traditional multiclass spectral clustering method which employs prior information about the classified data into the affinity matrixes aiming to maintain the background relation that might be lost in the traditional manner, that is using a scaled exponential affinity matrix constrained by weighting the data according to some prior knowledge and via k-way normalized cuts clustering, results in a semi-supervised methodology of traditional spectral clustering. Test was performed over toy data classification and image segmentation and evaluated with and unsupervised performance measures (group coherence, fisher criteria and silhouette).