토러스 공간 상에서의 적합예측 기반 예측 및 클러스터링을 위한 타원형 k-평균 알고리즘과 초모수 선택 전략

학위논문(석사) -- 서울대학교대학원 : 자연과학대학 통계학과, 2022. 8. 정성규.Protein structure data consist of several dihedral angles, lying on a multidimensional torus. Analyzing such data has been and continues to be key in understanding functional properties of proteins. However, most of the existing statistical methods assume that data are on Euclidean spaces, and thus they are improper to deal with angular data. In this paper, we introduce a novel approach specialized to analyzing multivariate angular data, based on elliptical k-means algorithm. Our approach enables the construction of conformal prediction sets and predictive clustering based on mixture model estimates. Moreover, we also introduce a novel hyperparameter selection strategy for predictive clustering, with improved stability and computational efficiency. We demonstrate our achievements with the package ClusTorus, one of our implementations, in clustering protein dihedral angles from two real data sets.단백질 구조 데이터는 다차원 토러스 상의 각도들로 구성되어 있다. 이러한 특성을 가진 데이터에 대한 연구는 단백질의 기능적 특성을 파악하는 데에 중요한 열쇠가 되어왔다. 그러나 대부분의 통계적 방법론들은 유클리드 공간을 가정하기 때문에 다차원 각도 데이터에 부적합하다. 본 논문에서는 타원형 k-평균 알고리즘 을 활용하여 다차원 각도 데이터를 분석하는 법을 소개한다. 특히 본 논문에서는 적합예측집합을 구성하고 혼합 모형 추정을 통한 예측 클러스터링 방법론을 소개 한다. 또한 안정성과 계산 효율성을 확보한 새로운 초모수 선택 전략을 제시한다. 마지막으로, 본 논문의 방법론을 구현한 R 패키지 ClusTorus를 활용하여 실제 데이터셋에 적용한 예시를 소개한다.1 Introduction 1 2 Conformal prediction 5 2.1 Conformal prediction framework 5 2.2 Inductive conformal prediction 6 2.3 Conformity scores from mixtures of multivariate von Mises 7 3 Parameter estimation for multivariate von Mises 12 3.1 Elliptical k-means algorithm 12 3.2 Constraints for mixture models 14 4 Clustering by conformal prediction 15 5 Hyperparameter selection 18 6 Clustering data on T^4 22 7 Summary and discussion 28 참고문헌 29 Abstract 34석

Evaluation of clustering algorithms for gene expression data

BACKGROUND: Cluster analysis is an integral part of high dimensional data analysis. In the context of large scale gene expression data, a filtered set of genes are grouped together according to their expression profiles using one of numerous clustering algorithms that exist in the statistics and machine learning literature. A closely related problem is that of selecting a clustering algorithm that is "optimal" in some sense from a rather impressive list of clustering algorithms that currently exist. RESULTS: In this paper, we propose two validation measures each with two parts: one measuring the statistical consistency (stability) of the clusters produced and the other representing their biological functional congruence. Smaller values of these indices indicate better performance for a clustering algorithm. We illustrate this approach using two case studies with publicly available gene expression data sets: one involving a SAGE data of breast cancer patients and the other involving a time course cDNA microarray data on yeast. Six well known clustering algorithms UPGMA, K-Means, Diana, Fanny, Model-Based and SOM were evaluated. CONCLUSION: No single clustering algorithm may be best suited for clustering genes into functional groups via expression profiles for all data sets. The validation measures introduced in this paper can aid in the selection of an optimal algorithm, for a given data set, from a collection of available clustering algorithms

Fast Recognition of birds in offshore wind farms based on an improved deep learning model

The safety of wind turbines is a prerequisite for the stable operation of offshore wind farms. However, bird damage poses a direct threat to the safe operation of wind turbines and wind turbine blades. In addition, millions of birds are killed by wind turbines every year. In order to protect the ecological environment and maintain the safe operation of offshore wind turbines, and to address the problem of the low detection capability of current target detection algorithms in low-light environments such as at night, this paper proposes a method to improve the network performance by integrating the CBAM attention mechanism and the RetinexNet network into YOLOv5. First, the training set images are fed into the YOLOv5 network with integrated CBAM attention module for training, and the optimal weight model is stored. Then, low-light images are enhanced and denoised using Decom-Net and Enhance-Net, and the accuracy is tested on the optimal weight model. In addition, the k-means++ clustering algorithm is used to optimise the anchor box selection method, which solves the problem of unstable initial centroids and achieves better clustering results. Experimental results show that the accuracy of this model in bird detection tasks can reach 87.40%, an increase of 21.25%. The model can detect birds near wind turbines in real time and shows strong stability in night, rainy and shaky conditions, proving that the model can ensure the safe and stable operation of wind turbines

Clustering Stability: An Overview

A popular method for selecting the number of clusters is based on stability arguments: one chooses the number of clusters such that the corresponding clustering results are "most stable". In recent years, a series of papers has analyzed the behavior of this method from a theoretical point of view. However, the results are very technical and difficult to interpret for non-experts. In this paper we give a high-level overview about the existing literature on clustering stability. In addition to presenting the results in a slightly informal but accessible way, we relate them to each other and discuss their different implications

How Many Topics? Stability Analysis for Topic Models

Topic modeling refers to the task of discovering the underlying thematic structure in a text corpus, where the output is commonly presented as a report of the top terms appearing in each topic. Despite the diversity of topic modeling algorithms that have been proposed, a common challenge in successfully applying these techniques is the selection of an appropriate number of topics for a given corpus. Choosing too few topics will produce results that are overly broad, while choosing too many will result in the "over-clustering" of a corpus into many small, highly-similar topics. In this paper, we propose a term-centric stability analysis strategy to address this issue, the idea being that a model with an appropriate number of topics will be more robust to perturbations in the data. Using a topic modeling approach based on matrix factorization, evaluations performed on a range of corpora show that this strategy can successfully guide the model selection process.Comment: Improve readability of plots. Add minor clarification

Stable Feature Selection for Biomarker Discovery

Feature selection techniques have been used as the workhorse in biomarker discovery applications for a long time. Surprisingly, the stability of feature selection with respect to sampling variations has long been under-considered. It is only until recently that this issue has received more and more attention. In this article, we review existing stable feature selection methods for biomarker discovery using a generic hierarchal framework. We have two objectives: (1) providing an overview on this new yet fast growing topic for a convenient reference; (2) categorizing existing methods under an expandable framework for future research and development

Identifying hidden contexts

In this study we investigate how to identify hidden contexts from the data in classification tasks. Contexts are artifacts in the data, which do not predict the class label directly. For instance, in speech recognition task speakers might have different accents, which do not directly discriminate between the spoken words. Identifying hidden contexts is considered as data preprocessing task, which can help to build more accurate classifiers, tailored for particular contexts and give an insight into the data structure. We present three techniques to identify hidden contexts, which hide class label information from the input data and partition it using clustering techniques. We form a collection of performance measures to ensure that the resulting contexts are valid. We evaluate the performance of the proposed techniques on thirty real datasets. We present a case study illustrating how the identified contexts can be used to build specialized more accurate classifiers