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The existence of various natural objects such as grass, trees, and rivers along with artificial manmade features such as buildings and roads, make it difficult to classify ground objects. Consequently...
Many tasks (e.g., clustering) in machine learning only require the distances instead of the original data. For dimension reductions in the norm (0 < α ≤ 2), the method of stable random projectio...
For1 dimension reduction in the l1 norm, the method of Cauchy random projections multiplies the original data matrix A ∈ Rn×D with a random matrix R RD×k (k  D) whose entries are i.i.d. samples of ...
Over the past thirty years, the hyperspectral remote sensing technology is attracted more and more attentions by the researchers. The dimension reduction technology for hyperspectral remote sensing im...
Limitations and deficiencies of different remote sensing sensors in extraction of different objects caused fusion of data from different sensors to become more widespread for improving classificatio...
Most business processes are, by nature, multivariate and autocorrelated. Highdimensionality is rooted in processes where more than one variable is considered simultaneously to provide a more comprehen...
Successful modeling and/or design of engineering systems often requires one to address the impact of multiple design variables on the prescribed outcome. There are often multiple, competing objectiv...
In this paper, we consider regression models with a Hilbert-space-valued predictor and a scalar response, where the response depends on the predictor only through a finite number of projections. The ...
Deformation-based nonlinear dimension reduction: applications to nuclear morphometry.
We consider a $l_1$-penalization procedure in the non-parametric Gaussian regression model. In many concrete examples, the dimension $d$ of the input variable $X$ is very large (sometimes depending on...
We analyse the properties of the Principal Fitted Components (PFC) algorithm proposed by Cook. We derive theoretical properties of the resulting estimators, including sufficient conditions under which...
Recently, feature-based solid modeling systems have been widely used in product design. However, for engineering analysis of a product model, an abstracted CAD model composed of mid-surfaces is desira...
Based on the fundamental thermodynamic principle the relationships of the residual properties, the property changes of mixing and the excess properties between the hypothetical solution of unreacted i...
Dimension Reduction Method in Thermodynamics of Multireaction Systems (I) Mole Numbers, Thermodynamic Properties and Partial Molar Properties Relations.
Suppose the data consist of a set S of points xj , 1 ≤ j ≤ J, distributed in a bounded domain D RN, where N is a large number. An algorithm is given for finding the sets Lk of dimension k N, k = 1, ...

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