A Scalable Two-Stage Approach for a Class of Dimensionality Reduction Techniques
published: Oct. 1, 2010, recorded: July 2010, views: 3625
Report a problem or upload filesIf you have found a problem with this lecture or would like to send us extra material, articles, exercises, etc., please use our ticket system to describe your request and upload the data.
Enter your e-mail into the 'Cc' field, and we will keep you updated with your request's status.
Dimensionality reduction plays an important role in many data mining applications involving high-dimensional data. Many existing dimensionality reduction techniques can be formulated as a generalized eigenvalue problem, which does not scale to large-size problems. Prior work transforms the generalized eigenvalue problem into an equivalent least squares formulation, which can then be solved efficiently. However, the equivalence relationship only holds under certain assumptions without regularization, which severely limits their applicability in practice. In this paper, an efficient two-stage approach is proposed to solve a class of dimensionality reduction techniques, including Canonical Correlation Analysis, Orthonormal Partial Least Squares, linear Discriminant Analysis, and Hypergraph Spectral Learning. The proposed two-stage approach scales linearly in terms of both the sample size and data dimensionality. The main contributions of this paper include (1) we rigorously establish the equivalence relationship between the proposed two-stage approach and the original formulation without any assumption; and (2) we show that the equivalence relationship still holds in the regularization setting. We have conducted extensive experiments using both synthetic and real-world data sets. Our experimental results confirm the equivalence relationship established in this paper. Results also demonstrate the scalability of the proposed two-stage approach.
Download slides: kdd2010_sun_stsa_01.pdf (840.3 KB)
Download slides: kdd2010_sun_stsa_01.ppt (1.9 MB)
Link this pageWould you like to put a link to this lecture on your homepage?
Go ahead! Copy the HTML snippet !