# missing value patterns

I am doing some data preparation with Python using Pandas and I am working with a dataset that has about 80 variables with missing values and I want to capture any patterns of missingness to cut down on the amount of missing value indicators I have but I am having trouble finding any good strategies for doing this. here is an example of what I am getting at:

MISS_1 MISS_2 MISS_3 MISS_4 MVP1 MVP2 MVP3 MISS_STR
0      0      1      0    0    0    1     0010
1      0      1      0    1    0    0     1010
1      1      1      1    0    1    0     1111
1      1      1      1    0    1    0     1110
1      0      1      0    1    0    0     1010
0      0      1      0    0    0    1     0010
0      0      1      0    0    0    1     0010
0      0      1      0    0    0    1     0010
1      0      1      0    1    0    0     1010


One thing I tried was to create a string variable that concatenated all the missing value indicator variables like the 'MISS_STR', unfortunately the number of unique values in this variable was around 2000. Also, I know I am missing patterns that may be useful because if a pattern exists between Variable_1 and Variable_2 and Variable_3 and Variable_4 are missing completely at random, then concatenating them as strings will not capture the pattern between Variable_1 and Variable_2. Is there a better way of doing this? A good clustering algorithm perhaps? Whatever I do, I need to be able to do the same thing to my scoring data.