Pandas DataFrame: How to convert numeric columns into pairwise categorical data?

Question

Given a pandas dataFrame, how does one convert several numeric columns (where x≠1 denotes the value exists, x=0 denotes it doesn't) into pairwise categorical dataframe? I know it is similar to one-hot decoding but the columns are not exactly one hot.

An example:

 df
id A  B  C  D
0  3  0  0  1
1  4  1  0  0
2  1  7  20 0
3  0  0  0  4
4  0  0  0  0
5  0  1  0  0

The result would be: df id match

 result 
0  A
0  D 
1  A
1  B
2  A
2  B
2  C
3  D
5  B

Answer 1

Use DataFrame.stack with filtering and Index.to_frame:

s = df.stack()

df = s[s!=0].index.to_frame(index=False).rename(columns={1:'result'})
print (df)
   id result
0   0      A
1   0      D
2   1      A
3   1      B
4   2      A
5   2      B
6   2      C
7   3      D
8   5      B

Or if performance is important use numpy.where for indices by matched values with DataFrame constructor:

i, c = np.where(df != 0)

df = pd.DataFrame({'id':df.index.values[i],
                   'result':df.columns.values[c]})
print (df)
   id result
0   0      A
1   0      D
2   1      A
3   1      B
4   2      A
5   2      B
6   2      C
7   3      D
8   5      B

EDIT:

For first:

s = df.stack()

df = s[s!=0].reset_index()
df.columns= ['id','result','vals']
print (df)
   id result  vals
0   0      A     3
1   0      D     1
2   1      A     4
3   1      B     1
4   2      A     1
5   2      B     7
6   2      C    20
7   3      D     4
8   5      B     1

For second:

df = pd.DataFrame({'id':df.index.values[i],
                   'result':df.columns.values[c],
                   'vals':df.values[i,c]})