On selecting a maximum volume sub-matrix of a matrix and related problems

By A. Çivril, Malik Magdon-Ismail. 2009

251 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Computational Mechanics, Computational Theory and Mathematics

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Citations in the corpus

Determinantal Point Processes for Machine Learning (2012, methodology): “Here, we adapt the argument of C ¸ ivril and Magdon-Ismail [2009], who studied the problem of finding maximum-volume submatrices.”
A Signal Processing Perspective on Hyperspectral Unmixing: Insights from Remote Sensing (2014, background): “In successive volume maximization (SVMAX) [20] (also [37]), the principle is to exploit the successive structure of (22) to recursively generate an approximate solution to (21).”
Efficient Volume Sampling for Row/Column Subset Selection (2010, methodology): “A recent article by Mahoney and Drineas [18] highlights the limitations of PCA and gives experimental data on practical applications of low-rank approximation based on row/column-subset selection.”
Fast Greedy MAP Inference for Determinantal Point Process to Improve Recommendation Diversity (2017, background): “Despite its relatively weak theoretical guarantees [13], it is widely used due to its promising empirical performance [29, 19, 49].”
Weakly Admissible Meshes and Discrete Extremal Sets (2010, background): “…to be NP-hard, so heuristic or stochastic algorithms are mandatory; cf. [10] for the notion of volume generated by a set of vectors (which generalizes the geometric concept related to parallelograms and parallelepipeds), and an analysis of the problem from a computational complexity point of view.”
Optimal approximation for submodular and supermodular optimization with bounded curvature (2013, background): “Even for the case of a cardinality constraint k, it is impossible to approximate the maximum subdeterminant to factor better than c for some constant c > 1 [7, 39].”
Individualness and Determinantal Point Processes for Pedestrian Detection (2016, background): “Generally, the problem is NP-hard because all possible subsets have to be examined [17].”