• The Pure and Applied Mathematics
• /
• v.16 no.1
• /
• pp.121-131
• /
• 2009

In this paper we examine the relation among law-invariant coherent risk measures with the Fatou property, distortion risk measures and spectral risk measures, and give a new proof of the relation among them. It is also shown that the spectral risk measure satisfies the monotonicity with respect to stochastic dominance and the comonotonic additivity.

• ETRI Journal
• /
• v.38 no.3
• /
• pp.540-550
• /
• 2016

Spectral clustering is a powerful tool for exploratory data analysis. Many existing spectral clustering algorithms typically measure the similarity by using a Gaussian kernel function or an undirected k-nearest neighbor (kNN) graph, which cannot reveal the real clusters when the data are not well separated. In this paper, to improve the spectral clustering, we consider a robust similarity measure based on the shared nearest neighbors in a directed kNN graph. We propose two novel algorithms for spectral clustering: one based on the number of shared nearest neighbors, and one based on their closeness. The proposed algorithms are able to explore the underlying similarity relationships between data points, and are robust to datasets that are not well separated. Moreover, the proposed algorithms have only one parameter, k. We evaluated the proposed algorithms using synthetic and real-world datasets. The experimental results demonstrate that the proposed algorithms not only achieve a good level of performance, they also outperform the traditional spectral clustering algorithms.

• ETRI Journal
• /
• v.35 no.2
• /
• pp.311-320
• /
• 2013

In most spectral clustering approaches, the Gaussian kernel-based similarity measure is used to construct the affinity matrix. However, such a similarity measure does not work well on a dataset with a nonlinear and elongated structure. In this paper, we present a new similarity measure to deal with the nonlinearity issue. The maximum flow between data points is computed as the new similarity, which can satisfy the requirement for similarity in the clustering method. Additionally, the new similarity carries the global and local relations between data. We apply it to spectral clustering and compare the proposed similarity measure with other state-of-the-art methods on both synthetic and real-world data. The experiment results show the superiority of the new similarity: 1) The max-flow-based similarity measure can significantly improve the performance of spectral clustering; 2) It is robust and not sensitive to the parameters.

• ETRI Journal
• /
• v.44 no.5
• /
• pp.769-779
• /
• 2022

Spectral clustering has become a typical and efficient clustering method used in a variety of applications. The critical step of spectral clustering is the similarity measurement, which largely determines the performance of the spectral clustering method. In this paper, we propose a novel spectral clustering algorithm based on the local similarity measure of shared neighbors. This similarity measurement exploits the local density information between data points based on the weight of the shared neighbors in a directed k-nearest neighbor graph with only one parameter k, that is, the number of nearest neighbors. Numerical experiments on synthetic and real-world datasets demonstrate that our proposed algorithm outperforms other existing spectral clustering algorithms in terms of the clustering performance measured via the normalized mutual information, clustering accuracy, and F-measure. As an example, the proposed method can provide an improvement of 15.82% in the clustering performance for the Soybean dataset.

• Mass Spectrometry Letters
• /
• v.9 no.3
• /
• pp.73-76
• /
• 2018

The number of matched peaks (NMP) is estimated as the spectral similarity measure in tandem mass spectral library searches of small molecules. In the high resolution mode, NMP provides the same reliable identification as in the case of a common dot-product function. Corresponding true positive rates are ($94{\pm}3$) % and ($96{\pm}3$) %, respectively.

• Journal of applied mathematics & informatics
• /
• v.22 no.1_2
• /
• pp.209-222
• /
• 2006

Estimation of the spectral measure, covariance and spectral density functions of a strictly stationary r-vector valued time series is considered, under the assumption that some of the observations are missed. The modified periodograms are calculated using data window. The asymptotic normality is studied.

• Earthquakes and Structures
• /
• v.21 no.5
• /
• pp.551-562
• /
• 2021

In this study, the generalized intensity measure (IM) named I_Npg is analyzed. The recently proposed proxy of the spectral shape named N_pg is the base of this intensity measure, which is similar to the traditional N_p based on the spectral shape in terms of pseudo-acceleration; however, in this case the new generalized intensity measure can be defined through other types of spectral shapes such as those obtained with velocity, displacement, input energy, inelastic parameters and so on. It is shown that this IM is able to increase the efficiency in the prediction of nonlinear behavior of structures subjected to earthquake ground motions. For this work, the efficiency of two particular cases (based on acceleration and velocity) of the generalized I_Npg to predict the peak floor acceleration demands on steel frames under 30 earthquake ground motions with respect to the traditional spectral acceleration at first mode of vibration Sa(T₁) is compared. Additionally, a 3D reinforced concrete building and an irregular steel frame is used as a basis for comparison. It is concluded that the use of velocity and acceleration spectral shape increase the efficiency to predict peak floor accelerations in comparison with the traditional and most used around the world spectral acceleration at first mode of vibration.

• Journal of the Ergonomics Society of Korea
• /
• v.29 no.5
• /
• pp.741-750
• /
• 2010

The objective of this paper is to study if the EEG spectral relative power would be a reasonable measure of expertise level. EEG electrodes were placed on the locations of Fp1, Fp2, F3, F4, T3, T4, O1, O2 while 5 subjects were playing 4 kinds of game on PC. EEG spectral relative power was significantly related with expertise level on the locations of Fp1, T3, T4, O1, O2. And the results showed that the $\theta$ and $\alpha$ activities were decreased, while $\beta$ and $\gamma$ activities were increased. The results indicated that the EEG spectral relative power would be applicable as a quantitative measure of expertise level.

• Journal of the Korean Mathematical Society
• /
• v.57 no.4
• /
• pp.935-955
• /
• 2020

In this paper we present a measurable version of the Smale's spectral decomposition theorem for homeomorphisms on compact metric spaces. More precisely, we prove that if a homeomorphism f on a compact metric space X is invariantly measure expanding on its chain recurrent set CR(f) and has the eventually shadowing property on CR(f), then f has the spectral decomposition. Moreover we show that f is invariantly measure expanding on X if and only if its restriction on CR(f) is invariantly measure expanding. Using this, we characterize the measure expanding diffeomorphisms on compact smooth manifolds via the notion of Ω-stability.

• Korean Journal of Remote Sensing
• /
• v.25 no.3
• /
• pp.263-270
• /
• 2009

Noise band removal is a crucial step before spectral matching since the noise bands can distort the typical shape of spectral reflectance, leading to degradation on the matching results. This paper proposes a statistical noise band removal method for hyperspectral data using the correlation coefficient between two bands. The correlation coefficient measures the strength and direction of a linear relationship between two random variables. Considering each band of the hyperspectral data as a random variable, the correlation between two signal bands is high; existence of a noisy band will produce a low correlation due to ill-correlativeness and undirected ness. The unsupervised k-nearest neighbor clustering method is implemented in accordance with three well-accepted spectral matching measures, namely ED, SAM and SID in order to evaluate the validation of the proposed method. This paper also proposes a hierarchical scheme of combining those measures. Finally, a separability assessment based on the between-class and the within-class scatter matrices is followed to evaluate the applicability of the proposed noise band removal method. Also, the paper brings out a comparison for spectral matching measures. The experimental results conducted on a 228-band hyperspectral data show that while the SAM measure is rather resistant, the performance of SID measure is more sensitive to noise.