在大數據分析中填補缺失數據是一個重要且具有挑戰性的問題。在本文中，我們提出了一種新的有效的基於維度和灰色理論關聯性的模糊 (DGC-fuzzy) c-means 方法來估算不完整數據。對於每個數據集，所提出的DGC-fuzzy c-means方法首先建立一個維度優先的陣列，用於保存要補值維度的優先順序。接下來，第一優先度的不完整維度通過在相同維度 中的均值來補值。然後，僅考慮完整維度和以補完值的維度，應用模糊 c-means 將數據集劃分為c個群，並且在每個群中，第二優先維度中的每個缺失值都由同一群中前一半高度相關的值的平均值來補值。重複上述分群和補值過程，直到插補所有不完整的維度。實驗結果表明，與最先進的 方法相比，所提出的用於估算不完整數據的DGC-fuzzy c-means 方法具有更好的準確性和分群優勢。

Imputing missing data in big data analysis is an important and challenging problem. In this thesis, a new and effective dimension- and grey theory correlation-based fuzzy (DGC-fuzzy) c-means method had been proposed for imputing incomplete data. For each dataset, the proposed DGC-fuzzy c-means method first builds up a dimension-priority array for saving the order of every dimension to be imputed. Next, the first-priority incomplete dimension is imputed by mean-filling in the same dimension. Then, by only considering the complete and imputed dimensions, the fuzzy c-means method is applied to partition the dataset into c clusters, and in each cluster, every missing attribute in the second-priority dimension is imputed by the mean value of the half higher correlated available attributes in the same dimension. The above clustering and imputation processes are repeated until all incomplete dimensions are imputed. Experimental results demonstrate that the proposed DGC-fuzzy c-means method for imputing incomplete data achieves better accuracy and clustering benefits when compared with the state-of-the-art methods.

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