在現今智慧型裝置及科技應用普及的世代，大量的數據以既便利又快速的方式被記錄、收集，因此，如何對數據進行處理與分析，並從中得到有價值的訊息，是現今非常受重視的議題。在資料探勘領域，分群分析是一項非常重要的技術，然而針對不同的數據型態應選擇合適的方法著手分析。
本研究針對類別型資料之分群，探討以可能性概念 (possibilistic concept) 結合模糊k-眾數演算法 (Fuzzy k-modes, FKM)，提出一可能性模糊k-眾數演算法(Possibilistic Fuzzy k-modes, PFKM) 以降低資料集中離群值的干擾進而改善分群結果，並進一步應用三種萬用演算法優化分群表現，分別為基因演算法、粒子群演算法和正弦餘弦演算法，進而提出三種分群演算法，分別為基因演算法為基礎之可能性模糊k-眾數演算法 (GA-PFKM)、粒子群演算法為基礎之可能性模糊k-眾數演算法 (PSO-PFKM) 和以正弦餘弦演算法為基礎之可能性模糊k-眾數演算法 (SCA-PFKM)。
本研究之實驗使用八組類別型資料集，分別針對所提出之演算法進行分群分析並使用Sum-of-square-error (SSE) 及準確率兩種評比指標與模糊k-眾數 (FKM)演算法進行比較。根據實驗結果證實，PSO-PFKM與SCA-PFKM兩種演算法在大多數的資料集中能獲得較其他演算法之優異表現。此外，本研究針對Breast cancer資料集的分群結果進一步進行個案研究分析，分析結果顯示，當normal nucleoli、bare nuclei 及clump thickness三種特徵值的類別數值較高，罹患乳癌的風險機率也越高。

Recently, smart devices and technology applications are applied widely in many fields. An enormous amount of information is recorded and collected rapidly. Thus, the process to analyze and obtain valuable information from the data becomes a very crucial issue. Clustering analysis plays an important role to solve the aforementioned issue. However, facing with the different types of data, the appropriate approach should be chosen to handle the data.
This study focuses on categorical data. A possibilistic fuzzy k-modes (PFKM) algorithm is proposed by combining the possibilistic concept with fuzzy k-modes (FKM) algorithm in order to alleviate the effects of outlier points and improve the clustering result. In addition, this study also implements three metaheuristics, namely genetic algorithm (GA), particle swarm optimization (PSO), and sine-cosine algorithm (SCA) in order to enhance the clustering performance. Therefore, three clustering algorithms are proposed in this study, named GA-PFKM, PSO-PFKM, and SCA-PFKM algorithms.
The proposed algorithms are utilized to perform a cluster analysis for eight categorical datasets. The performance of the algorithms is compared with the classical FKM algorithm using two indexes, namely sum-of-squared error (SSE) and accuracy. The experimental results indicate that PSO-PFKM and SCA-PFKM algorithms obtain the better performance for most of the datasets. Furthermore, this study analyzes the clustering result for breast cancer dataset more detailed. The analysis reveals that people with a higher range of normal nucleoli, bare nuclei, and clump thickness have a higher risk of breast cancer.

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