QAP方法原理·基本步骤steps：一第一步，计算已知两个矩阵之间的相关系数。·把每个矩阵中的所有取值看成是一个长向量，每个向量包含n(n-1)个数字（对角线数字忽略不计）；然后像比较任何两个变量之间的相关性那样计算这两个向量之间的相关系数- The first step is to calculate the correlation coefficientbetweenknowntwomatricesThink of all the values in each matrix as a long vector, eachcontaining n (n-1) digits (diagonal digits are neglected); thencalculate the correlation between the two vectors as ifcomparing the correlation between any two variables6
6 QAP方法原理 • 基本步骤steps ： – 第一步，计算已知两个矩阵之间的相关系数。 • 把每个矩阵中的所有取值看成是一个长向量，每个向量包含 n(n-1)个数字（对角线数字忽略不计）；然后像比较任何两个 变量之间的相关性那样计算这两个向量之间的相关系数 – The first step is to calculate the correlation coefficient between known two matrices. Think of all the values in each matrix as a long vector, each containing n (n-1) digits (diagonal digits are neglected); then calculate the correlation between the two vectors as if comparing the correlation between any two variables
第二步，对其中一个矩阵的行和相应的列同时进行随机置换，然后计算置换后的矩阵与另一个矩阵之间的相关系数。·重复这种计算过程几千次，将得到一个相关系数的分布，从中可以看到这种随机置换后计算出来的几千个相关系数大于或等于在第一步中计算出来的观察到的相关系数的比例 In the second step, the rows and corresponding columnsof one matrix are randomly permuted at the same time,and then the correlation coefficient between the permutedmatrix and the other matrix is calculated.- Repeat this process thousands of times and you get a distributionof correlation coefficients, from which you can see that thethousands of correlation coefficients calculated by this randomsubstitution are greater than or equal to theratio of the observedcorrelation coefficients calculated in the first step
第二步，对其中一个矩阵的行和相应的列同时进行随机置 换，然后计算置换后的矩阵与另一个矩阵之间的相关系数。 • 重复这种计算过程几千次，将得到一个相关系数的分布，从中可 以看到这种随机置换后计算出来的几千个相关系数大于或等于在 第一步中计算出来的观察到的相关系数的比例 • In the second step, the rows and corresponding columns of one matrix are randomly permuted at the same time, and then the correlation coefficient between the permuted matrix and the other matrix is calculated. – Repeat this process thousands of times and you get a distribution of correlation coefficients, from which you can see that the thousands of correlation coefficients calculated by this random substitution are greater than or equal to the ratio of the observed correlation coefficients calculated in the first step
QAP方法原理·基本步骤：一最后一步，比较在第一步中计算出来的观察到的相关系数与根据随机重排计算出来的相关系数的分布，看观察到的相关系数是落入拒绝域还是接受域，进而做出判断。也就说，如果上述比例低于0.05（假设研究者确定的显著性水平为0.05），就在统计意义上表明所研究的两个矩阵之间存在相关关系。 Inthelast step,the observed correlation coefficientcalculated inthefirst step is compared with the distribution of the correlationcoefficient calculated according to the random rearrangement, andthe observed correlation coefficient falls into the rejection domain ortheacceptancedomain,soastomakea judgment.Inotherwords,ifthe above ratiois less than0.05 (assuming that the significancelevel determined by the researcher is 0.05),there is a statisticalcorrelationbetweenthetwomatrices studied.8
8 QAP方法原理 • 基本步骤： – 最后一步，比较在第一步中计算出来的观察到的相关系数 与根据随机重排计算出来的相关系数的分布，看观察到的 相关系数是落入拒绝域还是接受域，进而做出判断。也就 说，如果上述比例低于0.05（假设研究者确定的显著性水 平为0.05），就在统计意义上表明所研究的两个矩阵之间 存在相关关系。 – In the last step, the observed correlation coefficient calculated in the first step is compared with the distribution of the correlation coefficient calculated according to the random rearrangement, and the observed correlation coefficient falls into the rejection domain or the acceptance domain, so as to make a judgment. In other words, if the above ratio is less than 0.05 (assuming that the significance level determined by the researcher is 0.05), there is a statistical correlation between the two matrices studied
QAP方法原理001110000111100001011000011110001111100000111000011110000101100001111000001110009
QAP方法原理 9 1000 0 0 1 1 0 1000 1 1 1 0 1 1000 0 1 1 1 0 1000 1 1 1 1 1 1000 1000 0 0 1 1 0 1000 1 1 1 0 1 1000 1 0 1 1 1 1000 0 1 1 0 0 1000
QAP方法原理000011011101101110110010011100010111100000011100010111100011111100010100011000101111000100110001101111100000110100011110.356348322549899110
QAP方法原理 10 1000 0 0 1 1 0 1000 1 1 1 0 1 1000 0 1 1 1 0 1000 1 1 1 1 1 1000 1000 0 0 1 1 0 1000 1 1 1 0 1 1000 1 0 1 1 1 1000 0 1 1 0 0 1000 00110111010111011111 00110111011011101100 0.356348322549899