IDR/QR: An incremental dimension reduction algorithm via QR decomposition

Jieping Ye, Qi Li, Hui Xiong, Haesun Park, Ravi Janardan, Vipin Kumar

Research output: Contribution to journalArticle

79 Scopus citations

Abstract

Dimension reduction is a critical data preprocessing step 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 algorithm 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 has been little work on designing incremental LDA algorithms that can efficiently incorporate new data items as they become available. 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 error rate on the reduced dimensional space. Our experiments on several real-world data sets reveal that the classification error rate achieved by the IDR/QR algorithm is very close to the best possible one achieved by other LDA-based algorithms. However, the IDR/QR algorithm has much less computational cost, especially when new data items are inserted dynamically.

Original languageEnglish (US)
Pages (from-to)1208-1221
Number of pages14
JournalIEEE Transactions on Knowledge and Data Engineering
Volume17
Issue number9
DOIs
StatePublished - Sep 1 2005

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Keywords

  • Dimension reduction
  • Incremental learning
  • Linear discriminant analysis
  • QR decomposition
  • Singular value decomposition (SVD)

ASJC Scopus subject areas

  • Information Systems
  • Computer Science Applications
  • Computational Theory and Mathematics

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