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Dimension Reduction
, 2007
"... When data objects that are the subject of analysis using machine learning techniques are described by a large number of features (i.e. the data is high dimension) it is often beneficial to reduce the dimension of the data. Dimension reduction can be beneficial not only for reasons of computational e ..."
Abstract
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Cited by 10 (0 self)
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When data objects that are the subject of analysis using machine learning techniques are described by a large number of features (i.e. the data is high dimension) it is often beneficial to reduce the dimension of the data. Dimension reduction can be beneficial not only for reasons of computational
On directional regression for dimension reduction
- J. Amer. Statist. Ass
, 2007
"... By slicing the region of the response (Li, 1991, SIR) and applying local ker-nel regression (Xia et al., 2002, MAVE) to each slice, a new dimension reduction method is proposed. Compared with the traditional inverse regression methods, e.g. sliced inverse regression (Li, 1991), the new method is fre ..."
Abstract
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Cited by 40 (3 self)
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By slicing the region of the response (Li, 1991, SIR) and applying local ker-nel regression (Xia et al., 2002, MAVE) to each slice, a new dimension reduction method is proposed. Compared with the traditional inverse regression methods, e.g. sliced inverse regression (Li, 1991), the new method
Dimension Reduction of Image Manifolds
"... Dimension reduction of datasets is very useful in different application including classification, compression, feature extraction etc.; Linear methods such as principal Component Analysis, have been used for a long time and ..."
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Dimension reduction of datasets is very useful in different application including classification, compression, feature extraction etc.; Linear methods such as principal Component Analysis, have been used for a long time and
Classes of Dimension Reduction Methods
, 2000
"... Dimension reduction in regression analysis reduces the dimension of the predictor vector x without specifying a parametric model and without loss of information about the distribution of y given x. We study three existing methods, SIR (Li, 1991), SAVE (Cook and Weisberg, 1991) and pHd (Li, 1992) in ..."
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Dimension reduction in regression analysis reduces the dimension of the predictor vector x without specifying a parametric model and without loss of information about the distribution of y given x. We study three existing methods, SIR (Li, 1991), SAVE (Cook and Weisberg, 1991) and pHd (Li, 1992
Supervised dimension reduction mappings
"... Abstract. We propose a general principle to extend dimension reduction tools to explicit dimension reduction mappings and we show that this can serve as an interface to incorporate prior knowledge in the form of class labels. We explicitly demonstrate this technique by combining locally linear mappi ..."
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Abstract. We propose a general principle to extend dimension reduction tools to explicit dimension reduction mappings and we show that this can serve as an interface to incorporate prior knowledge in the form of class labels. We explicitly demonstrate this technique by combining locally linear
A Review on Dimension Reduction
- INTERNATIONAL STATISTICAL REVIEW (2013), 81, 1, 134–150
, 2013
"... Summarizing the effect of many covariates through a few linear combinations is an effective way of reducing covariate dimension and is the backbone of (sufficient) dimension reduction. Because the replacement of high-dimensional covariates by low-dimensional linear combinations is performed with a m ..."
Abstract
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Cited by 3 (0 self)
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Summarizing the effect of many covariates through a few linear combinations is an effective way of reducing covariate dimension and is the backbone of (sufficient) dimension reduction. Because the replacement of high-dimensional covariates by low-dimensional linear combinations is performed with a
Dimension reduction regression in R
- Journal of Statistical Software. 7. Available
, 2002
"... Regression is the study of the dependence of a response variable on a collection predictors collected in. In dimension reduction regression, we seek to find a few linear combinations, such that all the information about the regression is contained in these linear combinations. If is very small, perh ..."
Abstract
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Cited by 12 (1 self)
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Regression is the study of the dependence of a response variable on a collection predictors collected in. In dimension reduction regression, we seek to find a few linear combinations, such that all the information about the regression is contained in these linear combinations. If is very small
Dimension-Reduction and Discrimination
"... The cover illustrates the two-class problem in two dimensions and the functioning of the dimension reduction approach based on radial basis functions (RBF). Randomly selected measurements (centres) serve as construction aids for a non-linear contour map. In a classification task, unlabeled measureme ..."
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The cover illustrates the two-class problem in two dimensions and the functioning of the dimension reduction approach based on radial basis functions (RBF). Randomly selected measurements (centres) serve as construction aids for a non-linear contour map. In a classification task, unlabeled
Transformed sufficient dimension reduction
"... A novel general framework is proposed in this paper for dimension reduction in regression to fill the gap between linear and fully nonlinear dimension reduction. The main idea is to transform first each of the raw predictors monotonically, and then search for a low-dimensional projection in the spac ..."
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A novel general framework is proposed in this paper for dimension reduction in regression to fill the gap between linear and fully nonlinear dimension reduction. The main idea is to transform first each of the raw predictors monotonically, and then search for a low-dimensional projection
Results 1 - 10
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