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Suppose that we use very similar methods(suppose now there are two such similar methods) to process upon each sample of a dataset. For each sample of the dataset with one of the two methods, we obtain a set of observations. Every observation has the same dimension and the same range(e.g. 0.0~1.0) for every data point, even between the two methods, they are the same. From now on, we say these two methods are method 1 and method 2. For method 1, there are observations, M1_O_1, M1_O_2, ...... , M1_O_n; for method2, there are observations, M2_O_1, M2_O_2, ...... , M2_O_n. Say M1_O_i and M2_O_i are the two obsevations taken on the same sample of the considered dataset. For observation M1_O_i, there are p data points, d_1_M1_O_i, d_2_M1_O_i, ...... , d_p_M1_O_i, although their dimension and range are the same, their order is important, we cannot, for example, mix d_p_M1_O_4 with d_p_M1_O_5. The same for method2, so there are observations, M2_O_1, M2_O_2, ...... , M2_O_n, and for observation M2_O_i, there are d_1_M2_O_i, d_2_M2_O_i, ...... , d_p_M2_O_i. We want to measure the distance between d_j_M1_O_i and d_k_M2_O_i for each j and k by iterating over i. The final distance designated by each j and k is irrelevant with i, but we have to iterate over i to get it. We want to measuring them to have an insight of these two methods(The methods are given and cannot be changed). Besides average Euclidean distance, what other measuring method can we taken? Or if there is any other distance measuring method even neural network ones can be adopted?

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