arXiv subjects

Jisu Kim

Publications and source records attributed to Jisu Kim.

At least 55 records · Page 3Linked to original sources

arXiv2021

Generalized Penalty for Circular Coordinate Representation

Topological Data Analysis (TDA) provides novel approaches that allow us to analyze the geometrical shapes and topological structures of a dataset. As one important application, TDA can be used for data visualization and dimension reduction. We follow the framework of circular coordinate representation, which allows us to perform dimension reduction and visualization for high-dimensional datasets on a torus using persistent cohomology. In this paper, we propose a method to adapt the circular coordinate framework to take into account the roughness of circular coordinates in change-point and high-dimensional applications. We use a generalized penalty function instead of an $L_{2}$ penalty in the traditional circular coordinate algorithm. We provide simulation experiments and real data analysis to support our claim that circular coordinates with generalized penalty will detect the change in high-dimensional datasets under different sampling schemes while preserving the topological structures.

stat.ML↗

arXiv2021

Restore from Restored: Single-image Inpainting

Recent image inpainting methods have shown promising results due to the power of deep learning, which can explore external information available from the large training dataset. However, many state-of-the-art inpainting networks are still limited in exploiting internal information available in the given input image at test time. To mitigate this problem, we present a novel and efficient self-supervised fine-tuning algorithm that can adapt the parameters of fully pre-trained inpainting networks without using ground-truth target images. We update the parameters of the pre-trained state-of-the-art inpainting networks by utilizing existing self-similar patches (i.e., self-exemplars) within the given input image without changing the network architecture and improve the inpainting quality by a large margin. Qualitative and quantitative experimental results demonstrate the superiority of the proposed algorithm, and we achieve state-of-the-art inpainting results on publicly available benchmark datasets.

cs.CV↗

arXiv2021

The masses of hadrons in the chiral symmetry restored vacuum

We calculate the masses of the vector and axial-vector mesons as well as the nucleon and the delta resonance in the chiral symmetry restored vacuum. This is accomplished by separating the quark operators appearing in the QCD sum rules for these hadrons into the chiral symmetric and symmetry breaking parts depending on the contributions of the fermion zero modes. We then extract the vacuum expectation values of all the separated parts of the quark operators using the QCD sum rule relations for these hadrons with their vacuum masses and widths. By taking the chiral symmetry breaking parts to be zero while keeping the symmetric operators to their vacuum values, we obtain the chiral symmetric part of the hadron masses. We find that the masses of chiral partners, such as the $(ρ,a_1)$ and $(K^*,K_1)$, become degenerate to values between 500 and 600 MeV in the chiral symmetry restored vacuum, while parity partners $(ω,f_1)$ that are chiral partners only in the limit where the disconnected diagrams are neglected remain non-degenerate with masses $(655,1060)$ MeV, respectively. The masses of the nucleon and the Delta are also found to reduce to about 500 and 600 MeV, respectively, in the chiral symmetric vacuum. This shows that while chiral symmetry breaking is responsible for the mass difference between chiral partner, both the meson and baryon retain non-trivial fraction of their masses in the chiral symmetry restored vacuum.

hep-ph↗

arXiv2021

Restore from Restored: Single-image Inpainting

Recent image inpainting methods show promising results due to the power of deep learning, which can explore external information available from a large training dataset. However, many state-of-the-art inpainting networks are still limited in exploiting internal information available in the given input image at test time. To mitigate this problem, we present a novel and efficient self-supervised fine-tuning algorithm that can adapt the parameters of fully pre-trained inpainting networks without using ground-truth target images. We update the parameters of the pre-trained state-of-the-art inpainting networks by utilizing existing self-similar patches within the given input image without changing network architecture and improve the inpainting quality by a large margin. Qualitative and quantitative experimental results demonstrate the superiority of the proposed algorithm, and we achieve state-of-the-art inpainting results on publicly available numerous benchmark datasets.

cs.CV↗

arXiv2021

Characterising different communities of Twitter users: Migrants and natives

Today, many users are actively using Twitter to express their opinions and to share information. Thanks to the availability of the data, researchers have studied behaviours and social networks of these users. International migration studies have also benefited from this social media platform to improve migration statistics. Although diverse types of social networks have been studied so far on Twitter, social networks of migrants and natives have not been studied before. This paper aims to fill this gap by studying characteristics and behaviours of migrants and natives on Twitter. To do so, we perform a general assessment of features including profiles and tweets, and an extensive network analysis on the network. We find that migrants have more followers than friends. They have also tweeted more despite that both of the groups have similar account ages. More interestingly, the assortativity scores showed that users tend to connect based on nationality more than country of residence, and this is more the case for migrants than natives. Furthermore, both natives and migrants tend to connect mostly with natives.

cs.SI↗

arXiv2021

Home and destination attachment: study of cultural integration on Twitter

The cultural integration of immigrants conditions their overall socio-economic integration as well as natives' attitudes towards globalisation in general and immigration in particular. At the same time, excessive integration -- or acculturation -- can be detrimental in that it implies forfeiting one's ties to the home country and eventually translates into a loss of diversity (from the viewpoint of host countries) and of global connections (from the viewpoint of both host and home countries). Cultural integration can be described using two dimensions: the preservation of links to the home country and culture, which we call home attachment, and the creation of new links together with the adoption of cultural traits from the new residence country, which we call destination attachment. In this paper we introduce a means to quantify these two aspects based on Twitter data. We build home and destination attachment indexes and analyse their possible determinants (e.g., language proximity, distance between countries), also in relation to Hofstede's cultural dimension scores. The results stress the importance of host language proficiency to explain destination attachment, but also the link between language and home attachment. In particular, the common language between home and destination countries corresponds to increased home attachment, as does low proficiency in the host language. Common geographical borders also seem to increase both home and destination attachment. Regarding cultural dimensions, larger differences among home and destination country in terms of Individualism, Masculinity and Uncertainty appear to correspond to larger destination attachment and lower home attachment.

cs.LG↗

arXiv2021

PLLay: Efficient Topological Layer based on Persistence Landscapes

We propose PLLay, a novel topological layer for general deep learning models based on persistence landscapes, in which we can efficiently exploit the underlying topological features of the input data structure. In this work, we show differentiability with respect to layer inputs, for a general persistent homology with arbitrary filtration. Thus, our proposed layer can be placed anywhere in the network and feed critical information on the topological features of input data into subsequent layers to improve the learnability of the networks toward a given task. A task-optimal structure of PLLay is learned during training via backpropagation, without requiring any input featurization or data preprocessing. We provide a novel adaptation for the DTM function-based filtration, and show that the proposed layer is robust against noise and outliers through a stability analysis. We demonstrate the effectiveness of our approach by classification experiments on various datasets.

cs.LG↗

arXiv2020

Detecting Group Anomalies in Tera-Scale Multi-Aspect Data via Dense-Subtensor Mining

How can we detect fraudulent lockstep behavior in large-scale multi-aspect data (i.e., tensors)? Can we detect it when data are too large to fit in memory or even on a disk? Past studies have shown that dense subtensors in real-world tensors (e.g., social media, Wikipedia, TCP dumps, etc.) signal anomalous or fraudulent behavior such as retweet boosting, bot activities, and network attacks. Thus, various approaches, including tensor decomposition and search, have been proposed for detecting dense subtensors rapidly and accurately. However, existing methods have low accuracy, or they assume that tensors are small enough to fit in main memory, which is unrealistic in many real-world applications such as social media and web. To overcome these limitations, we propose D-CUBE, a disk-based dense-subtensor detection method, which also can run in a distributed manner across multiple machines. Compared to state-of-the-art methods, D-CUBE is (1) Memory Efficient: requires up to 1,561X less memory and handles 1,000X larger data (2.6TB), (2) Fast: up to 7X faster due to its near-linear scalability, (3) Provably Accurate: gives a guarantee on the densities of the detected subtensors, and (4) Effective: spotted network attacks from TCP dumps and synchronized behavior in rating data most accurately.

cs.DB↗

arXiv2020

Vector meson mass in the chiral symmetry restored vacuum

We calculate the mass of the vector meson in the chiral symmetry restored vacuum. This is accomplished by separating the four quark operators appearing in the vector and axial vector meson sum rules into chiral symmetric and symmetry breaking parts depending on the contribution of the fermion zero modes. We then identify each part from the fit to the vector and axial vector meson masses. By taking the chiral symmetry breaking part to be zero while keeping the symmetric operator to the vacuum value, we find that the chiral symmetric part of the vector and axial vector meson mass to be between 550 and 600 MeV. This demonstrates that chiral symmetry breaking, while responsible for the mass difference between chiral partner, accounts only for a small fraction of the symmetric part of the mass.

nucl-th↗

arXiv2020

Homotopy Reconstruction via the Cech Complex and the Vietoris-Rips Complex

We derive conditions under which the reconstruction of a target space is topologically correct via the Čech complex or the Vietoris-Rips complex obtained from possibly noisy point cloud data. We provide two novel theoretical results. First, we describe sufficient conditions under which any non-empty intersection of finitely many Euclidean balls intersected with a positive reach set is contractible, so that the Nerve theorem applies for the restricted Čech complex. Second, we demonstrate the homotopy equivalence of a positive $μ$-reach set and its offsets. Applying these results to the restricted Čech complex and using the interleaving relations with the Čech complex (or the Vietoris-Rips complex), we formulate conditions guaranteeing that the target space is homotopy equivalent to the Čech complex (or the Vietoris-Rips complex), in terms of the $μ$-reach. Our results sharpen existing results.

math.AT↗

arXiv2020

NTIRE 2020 Challenge on Image Demoireing: Methods and Results

This paper reviews the Challenge on Image Demoireing that was part of the New Trends in Image Restoration and Enhancement (NTIRE) workshop, held in conjunction with CVPR 2020. Demoireing is a difficult task of removing moire patterns from an image to reveal an underlying clean image. The challenge was divided into two tracks. Track 1 targeted the single image demoireing problem, which seeks to remove moire patterns from a single image. Track 2 focused on the burst demoireing problem, where a set of degraded moire images of the same scene were provided as input, with the goal of producing a single demoired image as output. The methods were ranked in terms of their fidelity, measured using the peak signal-to-noise ratio (PSNR) between the ground truth clean images and the restored images produced by the participants' methods. The tracks had 142 and 99 registered participants, respectively, with a total of 14 and 6 submissions in the final testing stage. The entries span the current state-of-the-art in image and burst image demoireing problems.

cs.CV↗

arXiv2019

Uniform Convergence Rate of the Kernel Density Estimator Adaptive to Intrinsic Volume Dimension

We derive concentration inequalities for the supremum norm of the difference between a kernel density estimator (KDE) and its point-wise expectation that hold uniformly over the selection of the bandwidth and under weaker conditions on the kernel and the data generating distribution than previously used in the literature. We first propose a novel concept, called the volume dimension, to measure the intrinsic dimension of the support of a probability distribution based on the rates of decay of the probability of vanishing Euclidean balls. Our bounds depend on the volume dimension and generalize the existing bounds derived in the literature. In particular, when the data-generating distribution has a bounded Lebesgue density or is supported on a sufficiently well-behaved lower-dimensional manifold, our bound recovers the same convergence rate depending on the intrinsic dimension of the support as ones known in the literature. At the same time, our results apply to more general cases, such as the ones of distribution with unbounded densities or supported on a mixture of manifolds with different dimensions. Analogous bounds are derived for the derivative of the KDE, of any order. Our results are generally applicable but are especially useful for problems in geometric inference and topological data analysis, including level set estimation, density-based clustering, modal clustering and mode hunting, ridge estimation and persistent homology.

math.ST↗

arXiv2019

Minimax Rates for Estimating the Dimension of a Manifold

Many algorithms in machine learning and computational geometry require, as input, the intrinsic dimension of the manifold that supports the probability distribution of the data. This parameter is rarely known and therefore has to be estimated. We characterize the statistical difficulty of this problem by deriving upper and lower bounds on the minimax rate for estimating the dimension. First, we consider the problem of testing the hypothesis that the support of the data-generating probability distribution is a well-behaved manifold of intrinsic dimension $d_1$ versus the alternative that it is of dimension $d_2$, with $d_{1}<d_{2}$. With an i.i.d. sample of size $n$, we provide an upper bound on the probability of choosing the wrong dimension of $O\left( n^{-\left(d_{2}/d_{1}-1-ε\right)n} \right)$, where $ε$ is an arbitrarily small positive number. The proof is based on bounding the length of the traveling salesman path through the data points. We also demonstrate a lower bound of $Ω\left( n^{-(2d_{2}-2d_{1}+ε)n} \right)$, by applying Le Cam's lemma with a specific set of $d_{1}$-dimensional probability distributions. We then extend these results to get minimax rates for estimating the dimension of well-behaved manifolds. We obtain an upper bound of order $O \left( n^{-(\frac{1}{m-1}-ε)n} \right)$ and a lower bound of order $Ω\left( n^{-(2+ε)n} \right)$, where $m$ is the embedding dimension.

math.ST↗

arXiv2019

A Penetration Metric for Deforming Tetrahedra using Object Norm

In this paper, we propose a novel penetration metric, called deformable penetration depth PDd, to define a measure of inter-penetration between two linearly deforming tetrahedra using the object norm. First of all, we show that a distance metric for a tetrahedron deforming between two configurations can be found in closed form based on object norm. Then, we show that the PDd between an intersecting pair of static and deforming tetrahedra can be found by solving a quadratic programming (QP) problem in terms of the distance metric with non-penetration constraints. We also show that the PDd between two, intersected, deforming tetrahedra can be found by solving a similar QP problem under some assumption on penetrating directions, and it can be also accelerated by an order of magnitude using pre-calculated penetration direction. We have implemented our algorithm on a standard PC platform using an off-the-shelf QP optimizer, and experimentally show that both the static/deformable and deformable/deformable tetrahedra cases can be solvable in from a few to tens of milliseconds. Finally, we demonstrate that our penetration metric is three-times smaller (or tighter) than the classical, rigid penetration depth metric in our experiments.

cs.CG↗

arXiv2019

Diagnosis of Pediatric Obstructive Sleep Apnea via Face Classification with Persistent Homology and Convolutional Neural Networks

Obstructive sleep apnea is a serious condition causing a litany of health problems especially in the pediatric population. However, this chronic condition can be treated if diagnosis is possible. The gold standard for diagnosis is an overnight sleep study, which is often unobtainable by many potentially suffering from this condition. Hence, we attempt to develop a fast non-invasive diagnostic tool by training a classifier on 2D and 3D facial images of a patient to recognize facial features associated with obstructive sleep apnea. In this comparative study, we consider both persistent homology and geometric shape analysis from the field of computational topology as well as convolutional neural networks, a powerful method from deep learning whose success in image and specifically facial recognition has already been demonstrated by computer scientists.

cs.CV↗

arXiv2019

Time Series Featurization via Topological Data Analysis

We develop a novel algorithm for feature extraction in time series data by leveraging tools from topological data analysis. Our algorithm provides a simple, efficient way to successfully harness topological features of the attractor of the underlying dynamical system for an observed time series. The proposed methodology relies on the persistent landscapes and silhouette of the Rips complex obtained after a de-noising step based on principal components applied to a time-delayed embedding of a noisy, discrete time series sample. We analyze the stability properties of the proposed approach and show that the resulting TDA-based features are robust to sampling noise. Experiments on synthetic and real-world data demonstrate the effectiveness of our approach. We expect our method to provide new insights on feature extraction from granular, noisy time series data.

cs.CG↗

arXiv2019

Estimating the Reach of a Manifold

Various problems in manifold estimation make use of a quantity called the reach, denoted by $τ\_M$, which is a measure of the regularity of the manifold. This paper is the first investigation into the problem of how to estimate the reach. First, we study the geometry of the reach through an approximation perspective. We derive new geometric results on the reach for submanifolds without boundary. An estimator $\hatτ$ of $τ\_{M}$ is proposed in a framework where tangent spaces are known, and bounds assessing its efficiency are derived. In the case of i.i.d. random point cloud $\mathbb{X}\_{n}$, $\hatτ(\mathbb{X}\_{n})$ is showed to achieve uniform expected loss bounds over a $\mathcal{C}^3$-like model. Finally, we obtain upper and lower bounds on the minimax rate for estimating the reach.

math.ST↗

arXiv2019

Intensive Monitoring Survey of Nearby Galaxies (IMSNG)

Intensive Monitoring Survey of Nearby Galaxies (IMSNG) is a high cadence observation program monitoring nearby galaxies with high probabilities of hosting supernovae (SNe). IMSNG aims to constrain the SN explosion mechanism by inferring sizes of SN progenitor systems through the detection of the shock-heated emission that lasts less than a few days after the SN explosion. To catch the signal, IMSNG utilizes a network of 0.5-m to 1-m class telescopes around the world and monitors the images of 60 nearby galaxies at distances D < 50 Mpc to a cadence as short as a few hours. The target galaxies are bright in near-ultraviolet (NUV) with M_NUV < -18.4 AB mag and have high probabilities of hosting SNe (0.06 SN/yr per galaxy). With this strategy, we expect to detect the early light curves of 3.4 SNe per year to a depth of R ~ 19.5 mag, enabling us to detect the shock-heated emission from a progenitor star with a radius as small as 0.1 R_sun. The accumulated data will be also useful for studying faint features around the target galaxies and other science projects. So far, 18 SNe have occurred in our target fields (16 in IMSNG galaxies) over 5 years, confirming our SN rate estimate of 0.06 SN/yr per galaxy.

astro-ph.GA↗