農作物交易價量資料可反映出作物的季節性趨勢，同時亦可作為農業經營者決策的參考。本研究將多種農作物交易價格資料進行群集分析以了解作物彼此在交易價格變動趨勢上之異同。首先將所收集之十五年各類農作物歷史價格進行資料函數化，將原本為離散之價格資訊轉換為平滑之函數型資料。然後並利用函數型主成份分析，找出能夠代表此一農作物的價格曲線以及十五年之價格波動的主要變異以作為群集分析的基礎。其資料分群的目的主要分別以(1)農作物的絕對價格、(2)了解價格波動型態(Pattern)以及(3)了解十五年之價格變異為分群的目的。本研究提出整合函數型主成份分析之階層式分群法，並和以模型為基之分群法(Model-based clustering)進行多重作物分群比較，並且利用誤差平方和(Sum of Square Error, SSE)作為判斷最佳分群數的指標。從實驗結果可發現，本研究所提出的方法能獲得更小的SSE，此也意味著所提出的方法可得到更小的組內變異。此外，本研究亦探討資料分群數(維度)的縮減問題，探討是否能以較少的分群的資料數來獲得類似的分群結果。根據評比指標ARI顯示，使用27週價格資訊，便可解釋農作物的價格分群結果。農作物價格資料的分群結果，在應用面上可提供消費者農作物價格波動資訊，並做出採買選擇；而賣場經營者在銷售策略上，亦可參考過往的價格資料以及作物的分群結果，制定出產品售價的促銷方案以提高利潤。

Understanding crop seasonal effect and price trend is an important decision making for customers, crop farmers, and retailers. This research applied functional data clustering method to analyze crop price trend and variation. 15-year Taiwan agriculture crop price data were collected. The time-series data was first converted to functional data and the smoothing method was applied to obtain the function to represent each price curve. Then, Principal Component Analysis (PCA) was used to investigate the variation among the 15-year data. The hierarchical clustering method integrating PCA was proposed to study (1) absolute price trend, (2) price variation pattern, and (3) variation pattern among 15-year. The clustering result of the proposed method was compared with the model-based clustering method which is also used to cluster crops by their price functional data. The experimental result shows that the proposed clustering method is able to obtain the smaller sum of square error (SSE) which means our method can obtain the more impact clusters. Besides, the dimension-reduction is studied to use the relatively smaller dataset to maintain the same clustering result. The clustering result of agriculture crop price data can be provided to crop customers for enhancing purchasing decision making. The food retailers can also use the clustering result to monitor the price variation and detect the possible abnormal price trend for better operation decision.

Batagelj, V., H.-H. Bock, A. Ferligoj and A. Žiberna (2006). "Data Science and Classification." 209.
Bertka, B. T. (2008). An Introduction to Bezier Curves, B-Splines, and Tensor Product Surfaces with History and Applications.
Coffey, N., A. J. Harrison, O. A. Donoghue and K. Hayes (2011). "Common Functional Principal Components Analysis: A New Approach to Analyzing Human Movement Data." Human Movement Science 30(6): 1144-1166.
Dass, M. and C. Shropshire (2012). "Introducing Functional Data Analysis to Managerial Science." Organizational Research Methods 15(4): 693-721.
De la Cruz-Mesia, R., F. A. Quintana and G. Marshall (2008). "Model-based clustering for longitudinal data." Computational Statistics & Data Analysis 52(3): 1441-1457.
Densing, M. (2012). "Occupation Times of the Ornstein–Uhlenbeck Process: Functional PCA and Evidence From Electricity Prices." Physica A: Statistical Mechanics and its Applications 391(23): 5818-5826.
Escabias, M., A. M. Aguilera and M. J. Valderrama (2005). "Modeling Environmental Data by Functional Principal Component Logistic Regression." Environmetrics 16(1): 95-107.
Ferreira, L. and D. B. Hitchcock (2009). "A Comparison of Hierarchical Methods for Clustering Functional Data."
Giraldo, R., P. Delicado and J. Mateu (2012). "Hierarchical Clustering of Spatially Correlated Functional Data." Statistica Neerlandica 66(4): 403-421.
Goia, A., C. May and G. Fusai (2010). "Functional Clustering and Linear Regression for Peak Load Forecasting." International Journal of Forecasting 26(4): 700-711.
Hubert, L. and P. Arabie (1985). "Comparing Partitions." Journal of Classification 2(1): 193-218.
Illian, J. B., J. I. Prosser, K. L. Baker and J. I. Rangel-Castro (2009). "Functional Principal Component Data Analysis: A New Method for Analysing Microbial Community Fingerprints." Journal of Microbiological Methods 79(1): 89-95.
Jacques, J. and C. Preda "Model-Based Clustering for Multivariate Functional Data." Computational Statistics & Data Analysis(0).
Jacques, J. and C. Preda (2013). "Funclust: A Curves Clustering Method using Functional Random Variables Density Approximation." Neurocomputing 112(0): 164-171.
Jacques, J. and C. Preda (2013). "Functional Data Clustering: A survey." Advances in Data Analysis and Classification.
Jank, W., G. Shmueli, C. Plaisant and B. Shneiderman (2008). Visualizing Functional Data with an Application to eBay’s Online Auctions. Handbook of Data Visualization, Springer Berlin Heidelberg: 873-898.
Kantanantha, N. (2007). Crop Decision Planning under Yield and Price Uncertainties. Ann Arbor, Georgia Institute of Technology. 3327599: 157.
Kantanantha, N., N. Serban and P. Griffin (2010). "Yield and Price Forecasting for Stochastic Crop Decision Planning." Journal of Agricultural, Biological, and Environmental Statistics 15(3): 362-380.
Kipp, K., S. T. Johnson and M. A. Hoffman (2011). "Functional Principal Component Analysis of H-Reflex Recruitment Curves." Journal of Neuroscience Methods 197(2): 270-273.
Li, X.-B. and V. S. Jacob (2008). "Adaptive Data Reduction for Large-Scale Transaction Data." European Journal of Operational Research 188(3): 910-924.
Lillestol, J. and F. Ollmar (2003). "Functional Data Analysis: Introduction and Applications to Financial Electricity Contracts."
Liu, Y., Z. Li, H. Xiong, X. Gao and J. Wu (2012). "Understanding and Enhancement of Internal Clustering Validation Measures."
Ogden, R. T., C. Miller, K. Takezawa and S. Ninomiya (2002). "Functional Regression in Crop Lodging Assessment with Digital Images." Journal of Agricultural, Biological, and Environmental Statistics 7(3): 389-402.
Ramsay, J. O. and B. W. Silverman (2005). Functional Data Analysis, Springer.
Sakoe, H. and S. Chiba (1978). "Dynamic Programming Algorithm Optimization for Spoken Word Recognition." Acoustics, Speech and Signal Processing, IEEE Transactions on 26(1): 43-49.
Segovia-Gonzalez, M. M., F. M. Guerrero and P. Herranz (2009). "Explaining Functional Principal Component Analysis to Actuarial Science with an Example on Vehicle Insurance." Insurance: Mathematics and Economics 45(2): 278-285.
Tan, P.-N., M. Steinbach and V. Kumar (2005). Introduction to Data Mining.
Ullah, S. and C. F. Finch (2013). "Applications of Functional Data Analysis: A Systematic Review." BMC Medical Research Methodology.
Waring, M. E., C. B. Eaton, T. M. Lasater and K. L. Lapane (2010). "Correlates of Weight Patterns during Middle Age Characterized by Functional Principal Components Analysis." Annals of Epidemiology 20(3): 201-209.
行政院農委會. "農產品交易行情站." from http://amis.afa.gov.tw/.
張育慈 (2006). 試題測驗之函數資料分析. 統計與精算所. 台中市, 逢甲大學. 碩士: 64.
錢佳萱 (2013). 應用於類別屬性資料之基因演算法為基礎之多目標模糊分群法. 工業管理所. 台北市, 臺灣科技大學. 碩士: 69.