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Found 12 papers, 0 papers with code
Optimal Sparse Linear Encoders and Sparse PCA
Principal components analysis~(PCA) is the optimal linear encoder of data.
Optimal Sparse Linear Auto-Encoders and Sparse PCA
Principal components analysis (PCA) is the optimal linear auto-encoder of data, and it is often used to construct features.
Optimal CUR Matrix Decompositions
The CUR decomposition of an $m \times n$ matrix $A$ finds an $m \times c$ matrix $C$ with a subset of $c < n$ columns of $A,$ together with an $r \times n$ matrix $R$ with a subset of $r < m$ rows of $A,$ as well as a $c \times r$ low-rank matrix $U$ such that the matrix $C U R$ approximates the matrix $A,$ that is, $ || A - CUR ||_F^2 \le (1+\epsilon) || A - A_k||_F^2$, where $||.||_F$ denotes the Frobenius norm and $A_k$ is the best $m \times n$ matrix of rank $k$ constructed via the SVD.
Provable Deterministic Leverage Score Sampling
We explain theoretically a curious empirical phenomenon: "Approximating a matrix by deterministically selecting a subset of its columns with the corresponding largest leverage scores results in a good low-rank matrix surrogate".
Spectral Clustering via the Power Method -- Provably
Spectral clustering is one of the most important algorithms in data mining and machine intelligence; however, its computational complexity limits its application to truly large scale data analysis.
Random Projections for Linear Support Vector Machines
Let X be a data matrix of rank \rho, whose rows represent n points in d-dimensional space.
Near-optimal Coresets For Least-Squares Regression
We study (constrained) least-squares regression as well as multiple response least-squares regression and ask the question of whether a subset of the data, a coreset, suffices to compute a good approximate solution to the regression.
Sparse Features for PCA-Like Linear Regression
Principal Components Analysis~(PCA) is often used as a feature extraction procedure.
Randomized Dimensionality Reduction for k-means Clustering
On the other hand, two provably accurate feature extraction methods for $k$-means clustering are known in the literature; one is based on random projections and the other is based on the singular value decomposition (SVD).
Deterministic Feature Selection for $k$-means Clustering
We study feature selection for $k$-means clustering.
Random Projections for k-means Clustering
This paper discusses the topic of dimensionality reduction for $k$-means clustering.
Unsupervised Feature Selection for the k-means Clustering Problem
We present a novel feature selection algorithm for the $k$-means clustering problem.
