Lee, SH, Choi, S · Open Access System for Information Sharing (Pohang University of Science and Technology) · 2016
In this letter, we present a method of two-dimensional canonical correlation analysis (2D-CCA) where we extend the standard CCA in such a way that relations between two different sets of image data are directly sought without reshaping images into,vectors. We stress that 2D-CCA dramatically reduces the computational complexity, compared to the standard CCA. We show the useful behavior of 2D-CCA through numerical examples of correspondence learning between face images in different poses and illumination conditions.
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Caiping Xi, Shuning Zhang, Gang Xiong et al. · Chaos Solitons & Fractals · 2017
Cited by 14
Haixian Wang · IEEE Signal Processing Letters · 2010
Recently, two-dimensional canonical correlation analysis (2DCCA) has been proposed for image analysis. 2DCCA seeks linear correlation based on images directly. It fails to identify nonlinear correlation between two sets of images. In this letter, we present a new manifold learning method called local 2DCCA (L2DCCA) to identify the local correlation. Different from 2DCCA in which images are globally equally treated, L2DCCA weights images differently according to their closeness. That is, the correlation is measured locally, which makes L2DCCA more accurate in finding correlative information. Computationally, L2DCCA is formulated as solving generalized eigenvalue equations tuned by Laplacian matrices. Like 2DCCA, the implementation of L2DCCA is straightforward. Experiments on FERET and UMIST face databases show the effectiveness of the proposed method.
Cited by 28
Xizhan Gao · Code Ocean · 2019
Pattern Recognition; Multi-view learning; Canonical correlation analysis; Two-Directional Two-Dimensional Kernel Canonical Correlation Analysis
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Xizhan Gao, Sijie Niu, Quansen Sun · IEEE Signal Processing Letters · 2019
Two-directional two-dimensional canonical correlation analysis ((2D) <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> CCA) directly seeks linear relationship between different image data sets without reshaping images into vectors. However, it fails in finding the nonlinear correlation. In this letter, a novel method named as two-directional two-dimensional kernel canonical correlation analysis is proposed, which is a nonlinear version of (2D) <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> CCA and is able to find the nonlinear relationship between different image data sets. Experimental results in different expressions, illumination conditions and poses show the effectiveness of the proposed method.
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Wolfgang Alt · Lecture notes in biomathematics · 1990
Cited by 68
M. Herman · OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information) · 2015
Since its introduction by Noda in 1986 two-dimension correlation spectroscopy has been offering polymer scientists an opportunity to look more deeply into collected spectroscopic data. When the spectra are recorded in response to an external perturbation, it is possible to correlate the spectra and expand the information over a separate spectra axis allow for enhancement of spectral resolution, the ability to determine synchronous change, and a unique way to organize observed changes in the spectra into sequential order following a set of three simple rules. By organizing the 2D spectra into synchronous change plots and asynchronous change plots it is possible to correlate change between spectral regions and develop their temporal relationships to one another. With the introduction of moving-window correlation-spectroscopy by Thomas and Richardson in 2000, a method of binning and processing data, it became possible to directly correlate relationships generated in the spectra from the change in the perturbation variable. This method takes advantage of the added resolution of two-dimension spectroscopy and has been applied to study very week transitions found in polymer materials. Appling both of these techniques we are beginning to develop an understanding of how polymers decay under radiolytic aging, to develop a stronger understanding of changes in mechanical properties and the service capabilities of materials.
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M. E. Muratova, Ivan V. Mikheev, Dmitry S. Volkov et al. · Journal of Analytical Chemistry · 2024
The paper proposes an overview of the primary applications of generalized two-dimensional correlation spectroscopy (2D-COS) to analytical chemistry. 2D-COS is a method used to analyze datasets obtained by spectroscopic measurements. This approach is based on the use of 2D correlation maps to detect and analyze correlations between different spectral regions or data from two measurement methods. The objective of employing 2D-COS is to enhance the volume of analytical information by uncovering latent correlations within the data. Analysis of such correlations for series of spectral data, acquired over a range of analyte concentrations, pH values, or component ratios in mixtures, and also under varying temperatures or other external factors, enables investigating and elucidating chemical processes and interactions. This information is not readily attainable directly from the spectra. In comparison to one-dimensional spectra, 2D-COS excels in the significance of analytical information, particularly in the identification of components and the determination of the composition of complex mixtures. 2D-COS can also be used for monitoring changes in a sample over time, which makes it a valuable tool for studying dynamically evolving systems. Overall, 2D-COS is a sufficiently versatile approach that can be employed in conjunction with numerous methods, addressing a wide range of analytical tasks and complex samples, also without sample preparation. The review highlights achievements in the application of 2D-COS by the beginning of September 2023.
Cited by 4
Fatih Dikbaş, Ülker Güner Bacanlı · Teknik Dergi · 2020
The Standardized Precipitation Index (SPI) has been recognized as the standard index that should be used for quantifying and reporting meteorological drought. This study aims to present the application of the two-dimensional correlation method for determining the spatial and temporal variability of drought among the SPI series. Heatmaps were used as a new way of visualizing SPI series which enables visual inspection of dry and wet periods. The developed method was applied on 13 meteorological stations in Central Anatolia. Significant variations in drought behaviour were found in the investigated region even for the stations close to each other.
Cited by 3Open access
Nandakishor Desai, Abd‐Krim Seghouane, Marimuthu Palaniswami · Pattern Recognition Letters · 2018
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M. E. Muratova, Ivan V. Mikheev, Dmitry S. Volkov et al. · Журнал аналитической химии · 2024
An overview of the main applications of generalized two-dimensional correlation spectroscopy (2D-COS) in analytical chemistry is presented. 2D-COS is a method used to analyze datasets obtained from spectroscopic measurements. This approach is based on the use of two-dimensional correlation maps to identify and analyze correlations between different regions of the spectrum or data from two measurement methods. The purpose of using 2D-COS is to increase the amount of analytical information by revealing hidden data correlations. Analyzing such correlations for series of spectral data obtained for a certain range of analyte concentrations, pH, or component ratios of a mixture, as well as changes in temperature or other external factors, allows researchers to investigate and identify chemical processes and interactions that cannot be directly obtained from the spectra. Compared to one-dimensional spectra, 2D-COS offers significant analytical information for complex mixtures, particularly in identifying components and determining composition. Additionally, 2D-COS can be used to monitor changes in a sample over time, making it a valuable tool for studying dynamically changing systems. Overall, 2D-COS is a highly versatile approach that can be used in conjunction with a large number of methods for most analytical tasks and complex objects, including those without sample preparation. The review presents advancements in the application of 2D-COS as of early September 2023.
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2004
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Young Mee Jung, Hyeon Suk Shin, Seung Bin Kim et al. · Applied Spectroscopy · 2002
The direct combination of chemometrics and two-dimensional (2D) correlation spectroscopy is considered. The use of a reconstructed data matrix based on the significant scores and loading vectors obtained from the principal component analysis (PCA) of raw spectral data is proposed as a method to improve the data quality for 2D correlation analysis. The synthetic noisy spectra were analyzed to explore the novel possibility of the use of PCA-reconstructed spectra, which are highly noise suppressed. 2D correlation analysis of this reconstructed data matrix, instead of the raw data matrix, can significantly reduce the contribution of the noise component to the resulting 2D correlation spectra.
Cited by 69Open access
박수문 · Open Access System for Information Sharing (Pohang University of Science and Technology) · 2018
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Diana S. Smirnova, Julia A. Kornfield, David J. Lohse · Macromolecules · 2011
Two-dimensional (2D) correlation analysis is applied to synchrotron X-ray scattering data to characterize morphological regimes during nonisothermal crystallization of a model ethylene copolymer (hydrogenated polybutadiene, HPBD). The 2D correlation patterns highlight relationships among multiple characteristics of structure evolution, particularly the extent to which separate features change simultaneously versus sequentially. By visualizing these relationships during cooling, evidence is obtained for two separate physical processes occurring in what is known as “irreversible crystallization” in random ethylene copolymers. Initial growth of primarily lamellae into unconstrained melt (“primary-irreversible crystallization”) is distinguished from subsequent secondary lamellae formation in the constrained, noncrystalline regions between the primary lamellae (“secondary-irreversible crystallization”). At successively lower temperatures (“reversible crystallization”), growth of the crystalline reflections is found to occur simultaneously with the change in shape of the amorphous halo, which is inconsistent with the formation of an additional phase. Rather, the synchronous character supports the view that growth of frustrated crystals distorts the adjacent noncrystalline material. Furthermore, heterocorrelation analysis of small-angle and wide-angle X-ray scattering data from the reversible crystallization regime reveals that the size of new crystals is consistent with fringed-micellar structures (∼9 nm). Thus, 2D correlation analysis provides new insights into morphology development in polymeric systems.
Cited by 23
A. Siegle, Hermann Stoll, P. Castellaz et al. · Applied Surface Science · 1997
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김승빈 · Open Access System for Information Sharing (Pohang University of Science and Technology) · 2018
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김승빈 · Open Access System for Information Sharing (Pohang University of Science and Technology) · 2018
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Thomas G. Mayerhöfer, Marie Richard‐Lacroix, Susanne Pahlow et al. · Applied Spectroscopy · 2022
Based on hybrid 2D correlation analysis, we recently derived and introduced a "smart error sum," a sophisticated loss function that can be used for solving nonlinear inverse problems like the determination of optical constants and oscillator parameters from a series of optical spectra in the infrared spectral region. The advantage of the smart error sum compared to the conventional sum of squared errors lies in its ability to marginalize multiplicative systematic errors such as, for example, reflectance values above unity in transflection spectra. This is enabled by a transformation, which allows fits to not exclusively focus on forcing fit spectra to agree with experimental spectra at every wavenumber point by all means, but also to take correlations such as spectral similarities and their changes with certain perturbations into account. In this work, we extend our approach to accommodate the treatment of individual spectra, instead of only series, based on hybrid two-trace two-dimensional (2T2D) correlation analysis. We evaluate and prove the value of our approach by individually analyzing experimental transflection spectra of polymethyl methacrylate (PMMA) layers on gold substrates. The comparison of the results with those obtained by the original smart error sum based on the whole set of spectra as well as those resulting from conventional fitting of series and individual spectra (using the conventional sum of squared errors) confirms the validity and soundness of the 2T2D smart error sum.
Cited by 9Open access
김승빈 · Open Access System for Information Sharing (Pohang University of Science and Technology) · 2018
Cited by 0