Distance Dimension Reduction on QR Factorization for Efficient Clustering Semantic XML Document Using the QR Fuzzy C-Mean (QR-FCM)

The rapid growth of XML adoption has urged for the need of a proper representation for semi-structured documents, where the document semantic structural information has to be taken into account so as to support more precise document analysis. In order to analyze the information represented in XML documents efficiently, researches on XML document clustering are actively in progress. The key issue is how to devise the similarity measure between XML documents to be used for clustering. Since XML documents have hierarchical structure, it is not appropriate to cluster them by using a general document similarity measure. Dimension reduction plays an important role in handling the massive quantity of high dimensional data such as mass semantic structural documents. In this paper, we introduce distance dimension reduction (DDR) based on the QR factorization (DDR/QR) or the Cholesky factorization (DDR/C). DDR generates lower dimensional representations of the high-dimensional XML document, which can exactly preserve Euclidean distances and cosine similarities between any pair of XML documents in the original dimensional space. After projecting XML documents to the lower dimensional space obtained from DDR, our proposed method QR fuzzy c-mean to execute the document-analysis clustering algorithms (we called the QR-FCM). DDR can substantially reduce the computing time and/or memory requirement of a given document-analysis clustering algorithm, especially when we need to run the document analysis algorithm many times for estimating parameters or searching for a better solution.