Spectral analysis of data

Experimental evidence suggests that spectral techniques are valuable for a wide range of applications. A partial list of such applications include (i) semantic analysis of documents used to cluster documents into areas of interest, (ii) collaborative filtering --- the reconstruction of missing data items, and (iii) determining the relative importance of documents based on citation/link structure. Intuitive arguments can explain some of the phenomena that has been observed but little theoretical study has been done. In this paper we present a model for framing data mining tasks and a unified approach to solving the resulting data mining problems using spectral analysis. These results give strong justification to the use of spectral techniques for latent semantic indexing, collaborative filtering, and web site ranking.