[2023 Spring Semester]
지정 날짜 금요일 12:00
운영위원 : 권혜민 ( khmin1121@ajou.ac.kr, 팔달관 622호 )
감독위원 : 표성인( luinn27@ajou.ac.kr, 팔달관 435호 )
Title : Brooks-type theorems for relaxations of square coloring
Abstract : The following relaxation of a proper coloring of the square of a graph was recently introduced: for a positive integer $h$, the proper $h$-conflict-free $k$-coloring of a graph $G$ is a proper $k$-coloring of $G$ such that for every vertex $v$ has $\min\{\deg_G(v),h\}$ colors uniquely appearing on its neighborhood. The proper $h$-conflict-free chromatic number of a graph $G$, denoted $\chi_{pcf}^{h}(G)$, is the minimum $k$ such that $G$ has a proper $h$-conflict-free $k$-coloring. A Brooks-type conjecture was proposed by Caro, Petru\v sevski, and \v Skrekovski, and its content is as follows: if $G$ is a graph with $\Delta(G)\ge 3$, then $\chi_{pcf}^{1}(G)\le \Delta(G)+1$. Regarding the conjecture, Pach and Tardos proved $\chi_{pcf}^{1}\le 2\Delta(G)+1$. We improve the result for all $h$: if $G$ is a graph with $\Delta(G)\ge h+2$, then $\chi_{pcf}^{h}(G)\le (h+1)\Delta(G)-1$. Also, we show that the conjecture is true for chordal graphs, and obtain partial results for quasi-line graphs and claw-free graphs. This talk is based on joint work with Eun-Kyung Cho, Ilkyoo Choi, and Boram Park.
Title : DTW based t-SNE for trajectory data
Abstract : t-Distributed Stochastic Neighbor Embedding (t-SNE) specializes in dimension reduction for visualization. In t-SNE, similarity between data points is calculated as Euclidean distance. Euclidean distance is the best for determining the similarity between two data points. However, it may not be appropriate for calculating a similarity between more complex forms of data, such as trajectory. A data we’re interested in is multi-dimensional trajectory, which is a type of time series consisting of multiple variables and objects. Therefore, we suggest a method of using Dynamic Time Warping (DTW) instead of Euclidean to determine the similarity of trajectories. Also, to compare the similarity of multivariate trajectory, we suggest t-SNE algorithm using DTW_I and DTW_D, an extended version of DTW, considering the correlation between variables. Finally, our simulation work will present a performance improvement of t-SNE visualization through distance method selection with Gait data, a multi-dimensional trajectory.
Title : The Betti numbers of real toric varieties associated to Weyl chambers of E7 and E8
Abstract : We compute the rational Betti numbers of the real toric varieties associated to Weyl chambers of types E7 and E8, completing the computations for all types of root systems.
Title : Visualization algorithm based on FDR control testing for dimension reduction of textual data
Abstract : Textual data differs in the analysis method depending on its domain or various characteristics. Korean Text Data Analysis Algorithms were presented to provide a pipeline for statistical analysis of Korean text for the above reasons. However, in the process of dimension reduction and correlation cutting, a cutoff setting with insufficient statistical inference was accompanied. The dense visualization result also weaken the interpretabiltiy of the plot. To improve the algorithm, this study presented statistical inference for dimension reduction for sparse matrix and word-to-word relationships using FDR(False Discovery Rate) control and improved visualization by applying LDA(Latent Dirichlet Allocation) topic modeling. New algorithm is expected to improve the reliability and interpretation of the results of analysis.
Title : Machine learning and its applications of object detection
Abstract : In this talk, two machine learning applications are introduced. First, the results for anomaly detection using YOLOv3 in the oral care application are presented. The oral care application shows the result of oral health via machine learning algorithms when users upload the picture. Since this application does not classify the input images, it provides results even if it is not a picture of someone's mouth. This degrades the user's reliability. To address this issue, existing object detection algorithms are employed to classify normal and outlier images by detecting teeth and lips in the images. The second topic focuses on the development of a sequence-based accident detection model. YOLOv7 was used for object detection on a frame-by-frame basis. Based on the results of object detection for each image, the algorithm determines whether the video sequence contains an accident or not. This decision is made using metrics related to the sequence.