Similar to other algorithm, K-mean clustering has many weaknesses:
1 When the numbers of data are not so many, initial grouping will determine the cluster significantly. 當數據數量不是足夠大時，初始化分組很大程度上決定了聚類，影響聚類結果。
2 The number of cluster, K, must be determined before hand. 要事先指定K的值。
3 We never know the real cluster, using the same data, if it is inputted in a different order may produce different cluster if the number of data is a few. 數據數量不多時，輸入的數據的順序不同會導致結果不同。
4 Sensitive to initial condition. Different initial condition may produce different result of cluster. The algorithm may be trapped in the local optimum. 對初始化條件敏感。
5 We never know which attribute contributes more to the grouping process since we assume that each attribute has the same weight. 無法確定哪個屬性對聚類的貢獻更大。
6 weakness of arithmetic mean is not robust to outliers. Very far data from the centroid may pull the centroid away from the real one. 使用算術平均值對outlier不魯棒。
7 The result is circular cluster shape because based on distance. 因為基於距離，故結果是圓形的聚類形狀。
One way to overcome those weaknesses is to use K-mean clustering only if there are available many data. To overcome outliers problem, we can use median instead of mean. 克服缺點的方法： 使用盡量多的數據；使用中位數代替均值來克服outlier的問題。
Some people pointed out that K means clustering cannot be used for other type of data rather than quantitative data. This is not true! See how you can use multivariate data up to n dimensions (even mixed data type) here. The key to use other type of dissimilarity is in the distance matrix.
http://people.revoledu.com/kardi/tutorial/kMean/Weakness.htm