• KSII Transactions on Internet and Information Systems (TIIS)
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• v.16 no.3
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• pp.813-829
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• 2022

In multi-view subspace clustering, how to integrate the complementary information between perspectives to construct a unified representation is a critical problem. In the existing works, the unified representation is usually constructed in the original data space. However, when the data representation in each view is very diverse, the unified representation derived directly in the original data domain may lead to a huge information loss. To address this issue, different to the existing works, inspired by the latest revelation that the data across all perspectives have a very similar or close spectral block structure, we try to construct the unified representation in the spectral embedding domain. In this way, the complementary information across all perspectives can be fused into a unified representation with little information loss, since the spectral block structure from all views shares high consistency. In addition, to capture the global structure of data on each view with high accuracy and robustness both, we propose a novel low-rank approximation via the tight lower bound on the rank function. Finally, experimental results prove that, the proposed method has the effectiveness and robustness at the same time, compared with the state-of-art approaches.

• Journal of the Institute of Electronics and Information Engineers
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• v.52 no.4
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• pp.145-155
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• 2015

Noise reduction has been actively studied in the digital image processing and recently, block-based denoising algorithms are widely used. In particular, a low rank approximation employing WNNM(Weighted Nuclear Norm Minimization) and block-based approaches demonstrated the potential for effective noise reduction. However, the algorithm based on low rank a approximation generates the artifacts in the image restoration step. In this paper, we analyzes the image content using the STFT(Short Time Fourier Transform) and proposes an effective method of minimizing the artifacts generated from the conventional algorithm. To evaluate the performance of the proposed scheme, we use the test images containing a wide range of noise levels and compare the results with the state-of-art algorithms.

• Journal of the Korea Society of Computer and Information
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• v.26 no.7
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• pp.1-7
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• 2021

In this paper, we propose a feature selection technique for multi-label classification. Many existing feature selection techniques have selected features by calculating the relation between features and labels such as a mutual information scale. However, since the mutual information measure requires a joint probability, it is difficult to calculate the joint probability from an actual premise feature set. Therefore, it has the disadvantage that only a few features can be calculated and only local optimization is possible. Away from this regional optimization problem, we propose a feature selection technique that constructs a low-rank space in the entire given feature space and selects features with sparsity. To this end, we designed a regression-based objective function using Nuclear norm, and proposed an algorithm of gradient descent method to solve the optimization problem of this objective function. Based on the results of multi-label classification experiments on four data and three multi-label classification performance, the proposed methodology showed better performance than the existing feature selection technique. In addition, it was showed by experimental results that the performance change is insensitive even to the parameter value change of the proposed objective function.

• East Asian mathematical journal
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• v.25 no.2
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• pp.179-196
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• 2009

Let E be a uniformly convex Banach space and K a nonempty closed convex subset which is also a nonexpansive retract of E. For i = 1, 2, 3, let $T_i:K{\rightarrow}E$ be an asymptotically nonexpansive mappings with sequence ${\{k_n^{(i)}\}\subset[1,{\infty})$ such that $\sum_{n-1}^{\infty}(k_n^{(i)}-1)$ < ${\infty},\;k_{n}^{(i)}{\rightarrow}1$, as $n{\rightarrow}\infty$ and F(T)=$\bigcap_{i=3}^3F(T_i){\neq}{\phi}$ (the set of all common xed points of $T_i$, i = 1, 2, 3). Let {$a_n$},{$b_n$} and {$c_n$} are three real sequences in [0, 1] such that $\in{\leq}\;a_n,\;b_n,\;c_n\;{\leq}\;1-\in$ for $n{\in}N$ and some ${\in}{\geq}0$. Starting with arbitrary $x_1{\in}K$, define sequence {$x_n$} by setting {$$x_{n+1}=P((1-a_n)x_n+a_nT_1(PT_1)^{n-1}y_n)$$ $$y_n=P((1-b_n)x_n+a_nT_2(PT_2)^{n-1}z_n)$$ $$z_n=P((1-c_n)x_n+c_nT_3(PT_3)^{n-1}x_n)$$. Assume that one of the following conditions holds: (1) E satises the Opial property, (2) E has Frechet dierentiable norm, (3) $E^*$ has Kedec -Klee property, where $E^*$ is dual of E. Then sequence {$x_n$} converges weakly to some p${\in}$F(T).