Efficient calculation by using the **dot product**:
```python
import pandas as pd
df = pd.DataFrame({
'instance': [
'1', '1', '2', '2', '2', '3', '3', '3', '3'
],
'label': [
'A', 'B', 'B', 'C', 'D', 'A', 'C', 'D', 'E'
]
})
binary_df = pd.get_dummies(
df.set_index('instance')['label']
).groupby(level=0).max().astype(int)
co_occurrence_matrix = binary_df.T.dot(binary_df)
```