document: A scalable two-stage approach for a class of dimensionality reduction techniques 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 .
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