document: IDR\/QR : an incremental dimension reduction algorithm via QR decomposition Dimension reduction is critical for many database and data mining applications , such as efficient storage and retrieval of high-dimensional data . In the literature , a well-known dimension reduction scheme is Linear Discriminant Analysis ( LDA ) . The common aspect of previously proposed LDA based algorithms is the use of Singular Value Decomposition ( SVD ) . Due to the difficulty of designing an incremental solution for the eigenvalue problem on the product of scatter matrices in LDA , there is little work on designing incremental LDA algorithms . In this paper , we propose an LDA based incremental dimension reduction algorithm , called IDR\/QR , which applies QR Decomposition rather than SVD . Unlike other LDA based algorithms , this algorithm does not require the whole data matrix in main memory . This is desirable for large data sets . More importantly , with the insertion of new data items , the IDR\/QR algorithm can constrain the computational cost by applying efficient QR-updating techniques . Finally , we evaluate the effectiveness of the IDR\/QR algorithm in terms of classification accuracy on the reduced dimensional space . Our experiments on several real-world data sets reveal that the accuracy achieved by the IDR\/QR algorithm is very close to the best possible accuracy achieved by other LDA based algorithms . However , the IDR\/QR algorithm has much less computational cost , especially when new data items are dynamically inserted .
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