Multiclass Classification
If the intent is to make the model perform the following multiclass classification task, where the output is only one integer corresponding to one class, and all possible classes are mutually exclusive (thus output can only be one class at a time)
Schematic
input -> model -> output
------------------------
audio -> model -> most likely emotion class of 6
Then you can simply take that data table, and calculate the argmax of values across the 6 emotion columns
import numpy as np
# Making example data
dat = np.random.rand(4,6)
ex = np.vstack([dat, np.zeros(6)])
# Find all rows with the same values in each column (e.g. all zeros, no argmax)
idx_of_all_same = (ex == ex[:, 0:1]).all(1).reshape(-1,1)
# Argmax across all emotion columns to find most likely emotion
label_encs = ex.argmax(1).reshape(-1,1)
# Assign a unique value for when emotions all the same value (no argmax, defaults to zero)
label_encs[idx_of_all_same] = 7
# Append the label_encs as a new column to the original data
new_ex = np.hstack([ex, label_encs])
# If pandas dataframe
# df['Emotion Index'] = label_encs
These integers can now serve as the class label that your classifier will predict.
Multi-label Classification
Multilabel classification is different from multiclass classification in that it has multiple outputs, each as their own (potentially multiclass) classification output. In your case, the most outputs you'd have would be 6, one for each emotion, and the output labels would either be continuous for regression, to specify the strength of the emotion, or would be logistic regression for binary classification: 0 for none of that emotion and 1 for the presence of that emotion.
If subsets of emotions were mutually exclusive, then you'd have less than 6 outputs, and the outputs that correspond to those that are mutually exclusive would be multiclass classification outputs.
This would probably be trained as a multi-task problem, and typically is more nuanced to code up correctly, and to get it to train well.