Loading...
|
Please use this identifier to cite or link to this item:
https://nccur.lib.nccu.edu.tw/handle/140.119/152774
|
| Title: | 以基於熵值模擬之演算法探討類別資料中的複雜關聯
Investigating the Complex Associations in Categorical Data through an Entropy-Based Simulation Algorithm |
| Authors: | 高宏維
Kao, Hong-Wei |
| Contributors: | 周珮婷
謝復興
高宏維
Kao, Hong-Wei |
| Keywords: | Behavioral Risk Factor Surveillance System (BRFSS)
條件熵
熵
統計模擬
探索性資料分析
類別資料分析
熱度圖
Behavioral Risk Factor Surveillance System (BRFSS)
Conditional Entropy
Entropy
Statistical Simulation
Exploratory Data Analysis
Categorical Data Analysis
Heatmap |
| Date: | 2024 |
| Issue Date: | 2024-08-05 13:59:05 (UTC+8) |
| Abstract: | 本研究設計了一套基於熵值模擬的探索性類別資料分析方法，用於了解BRFSS 資料中，心臟病、中風(兩者共同組成反應變數)與風險因子之間存在的複雜關聯，並對其作易於解讀的視覺化呈現。該資料經過整理後，所有的變數皆為類別型態，並且具有資料不平衡以及異質性的特色，而本研究會針對整體健康度最差的樣本，探討以年齡組別分成的四組子樣本各自的風險特徵，藉以對其疾病機制做詳盡的了解。在提出的分析方法中會根據反應變數和風險因子的列聯表來獲取重要的資訊，透過虛無假設及對立假設下的兩種多項分配來生成資料與計算熵值，配合去關聯化的運作和可靠性檢查來決定各階層的主風險類別，並會以直方圖作關聯方向與交互作用之呈現。而透過階層分群的熱度圖可以觀察反應變數與主風險類別的關聯模式，主風險類別越高階的熱度圖，越能展示不同年齡組別的子樣本間，不同的疾病機制，且能從熱度圖中找到非典型的個體，其存在可用以說明機器學習模型在分類上錯誤的原因之一，此外熱度圖中的資料經過簡單的處理後，能夠為個體患病的可能性作具體的評估。
This study proposes an exploratory categorical data analysis method based on entropy simulation to understand the complex relationships among heart disease, stroke (both forming the composite response variable), and risk factors in BRFSS data, and to visually present them for easy interpretation. After data preprocessing, all variables are categorical and exhibit characteristics of data imbalance and heterogeneity. This study focuses on the sample with the poorest general health and investigates the risk characteristics of four sub-samples divided by age groups to gain a comprehensive understanding of their disease mechanisms. The proposed analysis method extracts important information from contingency tables of the response variable and risk factors, generates data and calculates entropy through two types of multinomial distributions under null and alternative hypotheses. This process, combined with de-association and reliability checks, determines the major-risk-categories of varying orders. The directional associations and interactions between risk factors are presented through histograms. Through hierarchical clustering heatmaps, the association patterns between the response variable and major-risk-categories can be observed. Heatmaps of higher-order major-risk-categories better demonstrate the different disease mechanisms among sub-samples of different age groups. Atypical subjects, which can explain one of the reasons for classification errors in machine learning models, can be identified from the heatmaps. Furthermore, after simple processing, the data in the heatmaps can provide a specific assessment of the likelihood of individual illness. |
| Reference: | Benzécri, J. P., & Bellier, L. (1973). L'analyse des données: Benzécri, J.-P. et al. L'analyse des correspondances. Dunod. https://books.google.fr/books?id=sDTwAAAAMAAJ
Centers for Disease Control and Prevention. (2014). About BRFSS. Centers for Disease Control and Prevention. Retrieved April 29 from https://www.cdc.gov/brfss/about/index.htm
Cramer, H. (1946). Mathematical methods of statistics, Princeton, 1946. Math Rev (Math‐SciNet) MR16588 Zentralblatt MATH, 63, 300.
Fushing, H., Chou, E. P., & Chen, T.-L. (2023). Multiscale major factor selections for complex system data with structural dependency and heterogeneity. Physica A: Statistical Mechanics and its Applications, 630, 129227.
Fushing, H., Kao, H.-W., & Chou, E. P. (2024). Topological Risk-Landscape in Metric-Free Categorical Database. IEEE Access.
Hirschfeld, H. O. (1935). A connection between correlation and contingency. Mathematical Proceedings of the Cambridge Philosophical Society,
Lucas-Kao. (2024). Histograms-of-simulation. Github. Retrieved April 29 from https://github.com/Lucas-Kao/Histograms-of-simulation
Metropolis, N., & Ulam, S. (1949). The monte carlo method. Journal of the American statistical association, 44(247), 335-341.
Pearson, K. (1900). X. On the criterion that a given system of deviations from the probable in the case of a correlated system of variables is such that it can be reasonably supposed to have arisen from random sampling. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 50(302), 157-175.
Pearson, K. (1904). On the theory of contingency and its relation to association and normal correlation. Drapers’ Co. Memoirs.
Press, W. H. (2007). Numerical recipes 3rd edition: The art of scientific computing. Cambridge university press.
Shannon, C. E. (1948). A mathematical theory of communication. The Bell system technical journal, 27(3), 379-423.
Teboul, A. (2022). Heart Disease Health Indicators Dataset. Kaggle. Retrieved October 2 from https://www.kaggle.com/datasets/alexteboul/heart-disease-health-indicators-dataset/data
Theil, H. (1972). Statistical decomposition analysis: With applications in the social and administrative sciences. North-Holland Pub. Co.
Wilkinson, L., & Friendly, M. (2009). The history of the cluster heat map. The American Statistician, 63(2), 179-184. |
| Description: | 碩士
國立政治大學
統計學系
111354002 |
| Source URI: | http://thesis.lib.nccu.edu.tw/record/#G0111354002 |
| Data Type: | thesis |
| Appears in Collections: | [統計學系] 學位論文
|
Files in This Item:
| File |
Description |
Size | Format | |
|---|
| 400201.pdf | | 7671Kb | Adobe PDF | 0 | View/Open |
|
All items in 政大典藏 are protected by copyright, with all rights reserved.
|
