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Satellite Imaging and Sensing
Published in John G. Webster, Halit Eren, Measurement, Instrumentation, and Sensors Handbook, 2017
The first step in analyzing multichannel data is to reduce the dimension of the data space. It is particularly important when the analysis method requires a training step, for example, supervised classification (see next section). The main issue in this case has often been referred as “the Curse of Dimensionality” [51]. If the original data have a large number of bands (e.g., for hyperspectral data), theoretical studies have shown that a very large training set should be utilized; but using a large training set deteriorates the estimation of the kernel density. To solve this problem, various dimension reduction schemes enable to perform classification in a smaller-dimensional subspace. Since the information contained in multiple channels is often redundant, it is possible to decorrelate spectrally the channels and reduce the number of channels to be analyzed without losing any information. Principal Component Analysis (PCA) and Projection Pursuit are the most common techniques for dimensionality reduction. For more information on these methods, refer to Refs. [39–42].
Data Tours
Published in Wendy L. Martinez, Angel R. Martinez, Jeffrey L. Solka, Exploratory Data Analysis with MATLAB®, 2017
Wendy L. Martinez, Angel R. Martinez, Jeffrey L. Solka
Friedman and Tukey (1974) describe projection pursuit as a way of searching for and exploring nonlinear structure in multi-dimensional data by examining many 2-D projections. The idea is that 2-D orthogonal projections of the data should reveal structure in the original data. The projection pursuit technique can also be used to obtain 1-D projections, but we look only at the 2-D case. Extensions to this method are also described in the literature by Friedman (1987), Posse (1995a, 1995b), Huber (1985), and Jones and Sibson (1987). In our presentation of projection pursuit exploratory data analysis, we follow the method of Posse (1995a, 1995b).
Projection pursuit Gaussian process regression
Published in IISE Transactions, 2023
Understanding this difference between the linear and nonlinear models helps build a better projection pursuit regression model. Traditionally, the projection pursuit method is usually regarded as a dimension reduction approach (Ferraty et al., 2013; Gilboa et al., 2013), and greedy algorithms are usually applied to identify wi’s (James and Silverman, 2005; Muller and Yao, 2008; Gilboa et al., 2013). These strategies have the following deficiencies: (i) it is often hard to accurately approximate the underlying functions through dimension reduction (). For example, the function cannot be recovered through a one-dimensional factor. (ii) Greedy algorithms, which proceed by picking the current “most significant” direction in each step, cannot perform well when there is no order of importance in the directions, as in the example shown in Figure 3. In this work, we propose a method, which conducts a dimension expansion () to improve the approximation power substantially.
Research on optimal decision-making of cloud manufacturing service provider based on grey correlation analysis and TOPSIS
Published in International Journal of Production Research, 2020
Yanjuan Hu, Lizhe Wu, Chao Shi, Yilin Wang, Feifan Zhu
In multi-attribute decision-making (Tian et al. 2018), it is very important to determine the weight of the evaluation index of the cloud manufacturing service provider accurately and effectively. Projection Pursuit (PP) (Manchuk, Barnett, and Deutsch 2017) is an exploratory and effective data analysis method for processing and analysing high dimensional data. Each evaluation index of scheme is projected linearly, and the optimal projection direction vector is found according to certain rules. The optimal projection direction vectors reflect the importance of each evaluation index, that is, the objective weight. In this paper, the improved PSO algorithm is used to optimise the projection pursuit model, and the objective weights are combined with the subjective weights calculated by AHP, then the comprehensive weights are obtained, which make the evaluation indexes more realistic. This research provides a new research idea for multi-objective and multi-factor decision-making of cloud manufacturing service provider.
Defect localisation and quantitative identification in multi-layer conductive structures based on projection pursuit algorithm
Published in Nondestructive Testing and Evaluation, 2019
Pingjie Huang, Tianyu Ding, Qing Luo, Dibo Hou, Jie Yu, Guangxin Zhang
Studies have shown that the complex electromagnetic relationship in PEC testing makes it highly nonlinear [20] and non-normally distribution [16] between the high-dimensional response signals and the features of defects. Projection pursuit (PP) algorithm [21] is an emerging statistical method for analysing and processing high-dimensional data, especially for non-linear and non-normal problems. Compared to PCA, it has a smaller amount of information loss. The feature extracted by the PP method can estimate two parameters simultaneously and reflect the inherent laws of the data, which is more physically meaningful. This method has been successfully applied in many fields such as image processing [22,23], which seeks to find a set of projections for image compression, segmentation, or enhancement in visual analysis. The basic principle of this method is to project high-dimensional data into low dimensions (1~3). The projection index is maximised or minimised to find a projection direction that can reflect the high-dimensional data’s structure. Considering the high dimensionality of PEC signals and the non-linearity, non-normality between signals and defect features, this paper introduces the PP method into PEC signal processing, which tries to analyse the structure information and change pattern in the PEC data with minimal information loss. This method is used to overcome the interferences of lift-off jitter, inner air gap and environmental noises to enhance inspection capabilities.