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| Title: | 多項分配之分類方法比較與實證研究
An empirical study of classification on multinomial data |
| Authors: | 高靖翔
Kao, Ching Hsiang |
| Contributors: | 余清祥
Yue, Jack C.
高靖翔
Kao, Ching Hsiang |
| Keywords: | 多項分配
熵
相似指標
電腦模擬
支持向量機
冪次定理
Multinomial distribution
Entropy
Similarity index
Computer simulation
Support vector machine
Power Law
Zipf`s Law |
| Date: | 2008 |
| Issue Date: | 2009-09-18 20:10:38 (UTC+8) |
| Abstract: | 由於電腦科技的快速發展，網際網路(World Wide Web；簡稱WWW)使得資料共享及搜尋更為便利，其中的網路搜尋引擎(Search Engine)更是尋找資料的利器，最知名的「Google」公司就是藉由搜尋引擎而發跡。網頁搜尋多半依賴各網頁的特徵，像是熵(Entropy)即是最為常用的特徵指標，藉由使用者選取「關鍵字詞」，找出與使用者最相似的網頁，換言之，找出相似指標函數最高的網頁。藉由相似指標函數分類也常見於生物學及生態學，但多半會計算兩個社群間的相似性，再判定兩個社群是否相似，與搜尋引擎只計算單一社群的想法不同。
本文的目標在於研究若資料服從多項分配，特別是似幾何分配的多項分配（許多生態社群都滿足這個假設），單一社群的指標、兩個社群間的相似指標，何者會有較佳的分類正確性。本文考慮的指標包括單一社群的熵及Simpson指標、兩社群間的熵及相似指標(Yue and Clayton, 2005)、支持向量機(Support Vector Machine)、邏輯斯迴歸等方法，透過電腦模擬及交叉驗證(cross-validation)比較方法的優劣。本文發現單一社群熵指標之表現，在本文的模擬研究有不錯的分類結果，甚至普遍優於支持向量機，但單一社群熵指標分類法的結果並不穩定，為該分類方法之主要缺點。
Since computer science had changed rapidly, the worldwide web made it much easier to share and receive the information. Search engines would be the ones to help us find the target information conveniently. The famous Google was also founded by the search engine. The searching process is always depends on the characteristics of the web pages, for example, entropy is one of the characteristics index. The target web pages could be found by combining the index with the keywords information given by user. Or in other words, it is to find out the web pages which are the most similar to the user’s demands. In biology and ecology, similarity index function is commonly used for classification problems. But in practice, the pairwise instead of single similarity would be obtained to check if two communities are similar or not. It is dislike the thinking of search engines.
This research is to find out which has better classification result between single index and pairwise index for the data which is multinomial distributed, especially distributed like a geometry distribution. This data assumption is often satisfied in ecology area. The following classification methods would be considered into this research: single index including entropy and Simpson index, pairwise index including pairwise entropy and similarity index (Yue and Clayton, 2005), and also support vector machine and logistic regression. Computer simulations and cross validations would also be considered here. In this research, it is found that the single index, entropy, has good classification result than imagine. Sometime using entropy to classify would even better than using support vector machine with raw data. But using entropy to classify is not very robust, it is the one needed to be improved in future. |
| Reference: | 中文部分
1. 余清祥 (1998), “統計在紅樓夢的應用”, 政大學報, 76, 303-327.
英文部分
1. Agresti, A. (2007), An Introduction to Categorical Data Analysis, 2nd ed., John Wiley & Sons, Inc.
2. Boser, B. E., Guyon, I.M., Vapnik, V. N. (1992), “A training algorithm for optimal margin classifiers”, Proceedings of the fifth annual workshop on Computational learning theory, 144-152.
3. Cortes, C. & Vapnik, V. (1995), “Support-vector network”, Machine Learning, 20, 1-25.
4. Drucker, P. F. (1999), “Beyond the information revolution”, The Atlantic Monthly, 284, 47-59
5. Meyer, D. (2009), “Support Vector Machines: The Interface to libsvm in package e1071”, Technische Universität Wien, Austria.
6. Page, L., Brin, S., Motwani, R. and Winograd, T. (1998), “The PageRank citation ranking: Bringing order to the Web”, Standford Digital Library Technologies Project.
7. Reed, W. J. (2001), “The Pareto, Zipf and other power laws”, Economics Letters 74 (1), 15–19.
8. Shannon, C. E. (1948), “A mathematical theory of communication”, Bell System Technical Journal, 27, 379-423, 623-656.
9. Sharma, S (1996), Applied Multivariate Techniques, John Wiley & Sons, Inc.
10. Simpson, E. H. (1949), “Measurement of diversity”, Nature, 163, 688.
11. Yue, C. J. and Clayton, M. K. (2005), “A Similarity Measures based on Species Proportions”, Communications in Statistics: Theory and Methods, 34, 2123-2131.
12. Wikipedia, Web search engine, http://en.wikipedia.org/wiki/Web_search_engine (as of June 15, 2009).
13. Zipf, G. K. (1935), The Psychobiology of Language: An Introduction to Dynamic Phinology, Houghton-Mifflin.
14. Zipf, G. K. (1949), Human behavior and the principle of least effort: An introduction to human ecology, Addison-Wesley, Cambridge, MA. |
| Description: | 碩士
國立政治大學
統計研究所
96354005
97 |
| Source URI: | http://thesis.lib.nccu.edu.tw/record/#G0096354005 |
| Data Type: | thesis |
| Appears in Collections: | [統計學系] 學位論文
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