Abstract
In many emerging real-life problems, the number of dimensions in the data sets can be from thousands to millions. The large number of features poses great challenge to existing high-dimensional data analysis methods. One particular issue is that the latent patterns may only exist in subspaces of the full-dimensional space. In this chapter, we discuss the problem of finding correlations hidden in feature subspaces. Both linear and nonlinear cases will be discussed. We present efficient algorithms for finding such correlated feature subsets.
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Notes
- 1.
CARE stands for finding loCAl lineaR corrElations.
- 2.
REDUS stands for REDUcible Subspaces.
- 3.
In this chapter, we assume that the eigenvalues are always arranged in increasing order. Their corresponding eigenvectors are \(\{\mathbf{v}_1, \mathbf{v}_2, \ldots, \mathbf{v}_n\}\).
- 4.
This theorem also applies to Hermitian matrix [35]. Here we focus on the covariance matrix, which is semi-positive definite and symmetric.
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Zhang, X., Pan, F., Wang, W. (2010). Finding High-Order Correlations in High-Dimensional Biological Data. In: Yu, P., Han, J., Faloutsos, C. (eds) Link Mining: Models, Algorithms, and Applications. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-6515-8_19
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