• Database Research
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• v.34 no.3
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• pp.159-169
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• 2018

Discretization of continuous variables intended to improve the performance of various algorithms such as data mining by transforming quantitative variables into qualitative variables. If we use appropriate discretization techniques for data, we can expect not only better performance of classification algorithms, but also accurate and concise interpretation of results and speed improvements. Various discretization techniques have been studied up to now, and however there is still demand of research on discretization studies. In this paper, we propose a new discretization technique to set the cut-point using Wasserstein distance with considering the distribution of continuous variable values with classes of data. We show the superiority of the proposed method through the performance comparison between the proposed method and the existing proven methods.

• Journal of the Korean Mathematical Society
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• v.55 no.2
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• pp.447-469
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• 2018

Types (over parameters) in the theory of atomless random variable structures correspond precisely to (conditional) distributions in probability theory. Moreover, the logic (resp. metric) topology on the type space corresponds to the topology of weak (resp. strong) convergence of distributions. In this paper, we study metrics between types. We show that type spaces under $d^{\ast}-metric$ are isometric to Wasserstein spaces. Using optimal transport theory, two formulas for the metrics between types are given. Then, we give a new proof of an integral formula for the Wasserstein distance, and generalize some results in optimal transport theory.

• Korean Journal of Mathematics
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• v.23 no.1
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• pp.1-10
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• 2015

This paper concerns the rate of convergence in the multidimensional normal approximation of functional of Gaussian fields. The aim of the present work is to derive explicit upper bounds of the Kolmogorov distance for the rate of convergence instead of Wasserstein distance studied by Nourdin et al. [Ann. Inst. H. Poincar$\acute{e}$(B) Probab.Statist. 46(1) (2010) 45-98].

• Journal of Korea Multimedia Society
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• v.24 no.1
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• pp.13-20
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• 2021

A Wasserstein GAN(WGAN), optimum in terms of minimizing Wasserstein distance, still suffers from inconsistent convergence or unexpected output due to inherent learning instability. It is widely known some kinds of restriction on the discriminative function should be considered to solve such problems, which implies the importance of Lipschitz continuity. Unfortunately, there are few known methods to satisfactorily maintain the Lipschitz continuity of the discriminative function. In this paper we propose techniques to stably maintain the Lipschitz continuity of the discriminative function by adding effective regularization terms to the objective function, which limit the magnitude of the gradient vectors of the discriminator to one or less. Extensive experiments are conducted to evaluate the performance of the proposed techniques, which shows the single-sided penalty improves convergence compared with the gradient penalty at the early learning process, while the proposed additional penalty increases inception scores by 0.18 after 100,000 number of learning.

• Journal of Internet Computing and Services
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• v.19 no.6
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• pp.91-99
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• 2018

Sketch-based 3D object retrieval is a convenient way to search for various 3D data using human-drawn sketches as query. In this paper, we propose a new method of using Sketch CNN, Wasserstein CNN and Wasserstein center loss for sketch-based 3D object search. Specifically, Wasserstein center loss is a method of learning the center of each object category and reducing the Wasserstein distance between center and features of the same category. To do this, the proposed 3D object retrieval is performed as follows. Firstly, Wasserstein CNN extracts 2D images taken from various directions of 3D object using CNN, and extracts features of 3D data by computing the Wasserstein barycenters of features of each image. Secondly, the features of the sketch are extracted using a separate Sketch CNN. Finally, we learn the features of the extracted 3D object and the features of the sketch using the proposed Wasserstein center loss. In order to demonstrate the superiority of the proposed method, we evaluated two sets of benchmark data sets, SHREC 13 and SHREC 14, and the proposed method shows better performance in all conventional metrics compared to the state of the art methods.

• Journal of Internet Computing and Services
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• v.21 no.1
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• pp.33-43
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• 2020

Retrieving a 3D model from a 3D database and augmenting the retrieved model in the Augmented Reality system simultaneously became an issue in developing the plausible AR environments in a convenient fashion. It is considered that the sketch-based 3D object retrieval is an intuitive way for searching 3D objects based on human-drawn sketches as query. In this paper, we propose a novel deep learning based approach of retrieving a sketch-based 3D object as for an Augmented Reality Model. For this work, we introduce a new method which uses Sketch CNN, Wasserstein CNN and Wasserstein center loss for retrieving a sketch-based 3D object. Especially, Wasserstein center loss is used for learning the center of each object category and reducing the Wasserstein distance between center and features of the same category. The proposed 3D object retrieval and augmentation consist of three major steps as follows. Firstly, Wasserstein CNN extracts 2D images taken from various directions of 3D object using CNN, and extracts features of 3D data by computing the Wasserstein barycenters of features of each image. Secondly, the features of the sketch are extracted using a separate Sketch CNN. Finally, we adopt sketch-based object matching method to localize the natural marker of the images to register a 3D virtual object in AR system. Using the detected marker, the retrieved 3D virtual object is augmented in AR system automatically. By the experiments, we prove that the proposed method is efficiency for retrieving and augmenting objects.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.20 no.1
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• pp.239-246
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• 2020

The recently proposed Wasserstein generative adversarial network (WGAN) has improved some of the tricky and unstable training processes that are chronic problems of the generative adversarial network(GAN), but there are still cases where it generates poor samples or fails to converge. In order to solve the problems, this paper proposes algorithms to improve the sampling process so that the discriminator can more accurately estimate the data probability distribution to be modeled and to stably maintain the discriminator should be Lipschitz continuous. Through various experiments, we analyze the characteristics of the proposed techniques and verify their performances.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.37 no.5
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• pp.323-330
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• 2019

Radiometric normalization with multi-temporal satellite images is essential for time series analysis and change detection. Generally, relative radiometric normalization, which is an image-based method, is performed, and histogram matching is a representative method for normalizing the non-linear properties. However, since it utilizes global statistical information only, local information is not considered at all. Thus, this paper proposes a histogram matching method considering local information. The proposed method divides histograms based on density, mean, and standard deviation of image intensities, and performs histogram matching locally on the sub-histogram. The matched histogram is then further partitioned and this process is performed again, iteratively, controlled with the wasserstein distance. Finally, the proposed method is compared to global histogram matching. The experimental results show that the proposed method is visually and quantitatively superior to the conventional method, which indicates the applicability of the proposed method to the radiometric normalization of multi-temporal images with non-linear properties.

• Proceedings of the Korea Information Processing Society Conference
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• 2022.11a
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• pp.628-629
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• 2022

딥러닝의 높은 예측 정확도를 위해서는 많은 양의 학습 데이터가 필요하다. 그러나 실세계에서 많은 양의 레이블이 붙은 데이터를 구하는 것은 어렵고 많은 비용이 든다. 때문에 레이블이 없이도 양질의 표현 학습이 가능한 자기지도학습이 각광을 받고 있다. 와서스타인 거리는 생성모델에도 쓰이지만 의사 레이블 (pseudo label) 을 만들어 레이블이 없는 데이터들을 분류 하는데도 좋은 성능을 보이고 있다. 따라서. 본 연구는 와서스타인 거리를 자기지도학습에 접목시키는 방법을 제안한다. 실험을 통해 연구의 가능성을 보인다.

• Journal of Broadcast Engineering
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• v.23 no.5
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• pp.614-621
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• 2018

This paper proposes a method of restoring corrupted depth image captured by depth camera through unsupervised learning using generative adversarial network (GAN). The proposed method generates restored face depth images using 3D morphable model convolutional neural network (3DMM CNN) with large-scale CelebFaces Attribute (CelebA) and FaceWarehouse dataset for training deep convolutional generative adversarial network (DCGAN). The generator and discriminator equip with Wasserstein distance for loss function by utilizing minimax game. Then the DCGAN restore the loss of captured facial depth images by performing another learning procedure using trained generator and new loss function.