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Irrelevant Features and the Subset Selection Problem
 MACHINE LEARNING: PROCEEDINGS OF THE ELEVENTH INTERNATIONAL
, 1994
"... We address the problem of finding a subset of features that allows a supervised induction algorithm to induce small highaccuracy concepts. We examine notions of relevance and irrelevance, and show that the definitions used in the machine learning literature do not adequately partition the features ..."
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Cited by 741 (26 self)
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We address the problem of finding a subset of features that allows a supervised induction algorithm to induce small highaccuracy concepts. We examine notions of relevance and irrelevance, and show that the definitions used in the machine learning literature do not adequately partition the features
On Lagrangian relaxation and subset selection problems
 In Proc. 6th Workshop on Approximation and Online Algorithms
, 2009
"... We prove a general result demonstrating the power of Lagrangian relaxation in solving constrained maximization problems with arbitrary objective functions. This yields a unified approach for solving a wide class of subset selection problems with linear constraints. Given a problem in this class and ..."
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Cited by 2 (1 self)
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We prove a general result demonstrating the power of Lagrangian relaxation in solving constrained maximization problems with arbitrary objective functions. This yields a unified approach for solving a wide class of subset selection problems with linear constraints. Given a problem in this class
An Algebraic Approach to the Subset Selection Problem
"... The need for decomposing a signal into its optimal representation arises in many applications. In such applications, one can usually represent the signal as a combination of an overcomplete dictionary elements. The nonuniqueness of signal representation, in such dictionaries, provides us with the o ..."
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The need for decomposing a signal into its optimal representation arises in many applications. In such applications, one can usually represent the signal as a combination of an overcomplete dictionary elements. The nonuniqueness of signal representation, in such dictionaries, provides us with the opportunity to adapt the signal representation to the signal. The adaptation is based on sparsity, resolution and stability of the signal representation. In this paper, we propose an algebraic approach for identifying the sparsest representation of a given signal in terms of a given overcomplete dictionary. Unlike other current techniques, our approach is guaranteed to find the solution, given that certain conditions apply. We explain these conditions. 1 Introduction In many applications one needs to identify the sparsest representation of the given signal in terms of the elements of an overcomplete set of vectors or signals. Such applications include signal coding for compression, chemica...
ON THE GENERAL POSITION SUBSET SELECTION PROBLEM
, 2013
"... Let f(n, ) be the maximum integer such that every set of n points in the plane with at most collinear contains a subset of f(n, ) points with no three collinear. First we prove that if O(√n), then f(n, ) Ω(√n / ln ). Second we prove that if O(n(1−)/2), then f(n, ) Ω( n log n), which impl ..."
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Cited by 2 (1 self)
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implies all previously known lower bounds on f(n, ) and improves them when is not fixed. A more general problem is to consider subsets with at most k collinear points in a point set with at most collinear. We also prove analogous results in this setting.
Solving Feature Subset Selection Problem by a Hybrid
"... The aim of this paper is to develop a hybrid metaheuristic based on Variable neighborhood Search and Tabu Search for solving the Feature Subset Selection Problem in classification. Given a set of instances characterized by several features, the classification problem consists of assigning a class t ..."
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The aim of this paper is to develop a hybrid metaheuristic based on Variable neighborhood Search and Tabu Search for solving the Feature Subset Selection Problem in classification. Given a set of instances characterized by several features, the classification problem consists of assigning a class
Solving Feature Subset Selection Problem by a Hybrid
, 2005
"... The aim of this paper is to develop a hybrid metaheuristic based on Variable Neighbourhood Search and Tabu Search for solving the Feature Subset Selection Problem in classification. Given a set of instances characterized by several features, the classification problem consists of assigning a class t ..."
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The aim of this paper is to develop a hybrid metaheuristic based on Variable Neighbourhood Search and Tabu Search for solving the Feature Subset Selection Problem in classification. Given a set of instances characterized by several features, the classification problem consists of assigning a class
An Improved Approximation Algorithm for the Column Subset Selection Problem
"... We consider the problem of selecting the “best ” subset of exactly k columns from an m × n matrix A. In particular, we present and analyze a novel twostage algorithm that runs in O(min{mn 2, m 2 n}) time and returns as output an m × k matrix C consisting of exactly k columns of A. In the first stag ..."
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Cited by 71 (13 self)
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We consider the problem of selecting the “best ” subset of exactly k columns from an m × n matrix A. In particular, we present and analyze a novel twostage algorithm that runs in O(min{mn 2, m 2 n}) time and returns as output an m × k matrix C consisting of exactly k columns of A. In the first
On The Optimallity Of The Backward Greedy Algorithm For The Subset Selection Problem
, 1998
"... The following linear inverse problem is considered: given a full column rank m \Theta n data matrix A and a length m observation vector b, find the best least squares solution to Ax = b with at most r ! n nonzero components. The backward greedy algorithm computes a sparse solution to Ax = b by remo ..."
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Cited by 42 (2 self)
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by removing greedily columns from A until r columns are left. A simple implementation based on a QR downdating scheme by Givens rotations is described. The backward greedy algorithm is shown to be optimal for this problem in the sense that it selects the "correct" subset of columns from A
REVERSE ENGINEERING AS A SUBSET SELECTION PROBLEM
"... Problem motivation DNA microarrays are an increasingly important technology. Studies of coexpression of genes are a common way to infer function. However, to take into account combined effects of multiple genes, some kind of network is needed. Here we explore a linear, deterministic model of a netw ..."
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Problem motivation DNA microarrays are an increasingly important technology. Studies of coexpression of genes are a common way to infer function. However, to take into account combined effects of multiple genes, some kind of network is needed. Here we explore a linear, deterministic model of a
Solving Feature Subset Selection Problem by a Parallel Scatter Search
 European Journal of Operational Research
"... The aim of this paper is to develop a parallel Scatter Search metaheuristic for solving the Feature Subset Selection Problem in classification. Given a set of instances characterized by several features, the classification problem consists of assigning a class to each instance. Feature Subset Select ..."
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Cited by 10 (1 self)
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The aim of this paper is to develop a parallel Scatter Search metaheuristic for solving the Feature Subset Selection Problem in classification. Given a set of instances characterized by several features, the classification problem consists of assigning a class to each instance. Feature Subset
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