混和型資料之距離矩陣計算

Calculation of Dissimilarity Matrix for Mixed-type Data

姜順貿(Jiang Shun-Mao)

指導教授 ： 周珮婷

國立政治大學/商學院/統計學系/碩士(2018年)

https://doi.org/10.6814/THE.NCCU.STAT.002.2018.B03

摘要

資料分群是資料探勘常見的一種方式，而分群需使用資料間距離的資訊，如何定義資料間距離成為一大挑戰。在資料收集越來越便利的情況下，資料通常為混和型資料，這會產生兩類型的問題，分別為類別距離的計算與結合連續與類別變數的方式。本篇方法透過區分其它相關變數的能力來定義類別距離，如未有相關變數則只考慮變數自己本身。另一方面，連續變數經過離散化計算對應權重後，再對原始連續變數做正規化轉換，以歐式距離的計算方式乘上權重，最後與類別距離做結合得到最終總距離。
為驗證本篇方法的合理性，使用階層式分群，透過一些真實的資料與過去文獻的方法做比較，結果顯示提出的方法具有可比性(comparable)，且整體平均表現最佳，可應用在各種類型資料上。此外對本篇方法求得的距離矩陣，做熱圖視覺化可以發現在大部份資料上，仍保有原始類別數等特質或從資料變數上，找到另一種相近的詮釋。

關鍵字

混和型資料 ； 分群 ； 距離矩陣 ； 距離學習

並列摘要

Clustering is a common method for data mining. It requires the information about the distance between observations. The way to define the distance becomes a big challenge due to the convenience of data collection. Datasets are in more complex structures, such as mixed-type. Two types of problems have arisen: how to measure the distances between categorical variables and how to measure the distances for mixed variables. The current study proposed an algorithm to define the distance of categorical variables by the ability of distinguishing other related variables. On the other hand, for continuous variables, first, variables were normalized and weighted Euclidean distances were calculated. Then, two distances we calculated above were combined to find a final distance.
Hierarchical clustering was used to verify the performance of proposed method, through some real-world data compared with the methods of the previous paper. The experiments results showed that the proposed method was comparable with other methods. The overall average performance was the best. The technique can be applied to all types of the data. In addition, by visualizing the proposed distance matrix from the heat maps, we found that the number of cluster patterns were the same as the level of class in the majority of our examples.

並列關鍵字

Mixed-type data ； Clustering ； Distance matrix ； Distance learning

參考文獻

1.A. Ahmad, L. Dey, “A k-mean clustering algorithm for mixed numeric and categorical data” , Data & Knowledge Engineering vol. 63, November 2007, pp.503-527.

2.C. Stanfill, D. Waltz, “Toward memory-based reasoning” , Commun. ACM 29(12), 1986, pp. 1213-1228.

3.D.R. Wilson, T.R. Martinez, “Improved heterogeneous distance functions” , J. Artif. Intell. Res. 6, 1997, pp. 1-34.

4.D. Ienco, R. G. Pensa, and R. Meo, “From context to distance: Learning dissimilarity for categorical data clustering” , ACM Transactions on Knowledge Discovery from Data (TKDD), vol. 6, no. 1, March 2012.

5.J. C. Gower and P. Legendre, “Metric and Euclidean properties of dissimilarity coefficients” , J. Classification, vol. 3, no. 1, 1986, pp. 5–48.