Classification models with multi-class allowed for each record I am training a multi-class classification model. Each record can belong to one or more classes. (actually can I still call it a classification model? or should it be a topic model or something else?)

The training data looks like this (format_A)

record_id, f_1 , f_2, f_3, ... , f_n, output_A, output_B, output_C
        1,  0.1, 0.2, 0.3, ... , 1.2,        1,        0,        1
        2,  0.3, 1.2, 0.5, ... , 2.1,        1,        0,        0
        3,  0.2, 3.2, 1.3, ... , 0.4,        1,        1,        0
        4,  1.1, 0.1, 0.7, ... , 0.5,        0,        0,        1
        5,  2.1, 0.5, 0.8, ... , 1.9,        0,        1,        1
        6,  0.5, 0.4, 0.2, ... , 0.8,        1,        1,        1
                     :
                     :


Right now, I am using the sklearn logistic regression with multi-class. I preprocess the above training data such that there is only one target per record. For record with more than 1 output, I duplicated the records. That is, the above training data becomes below (format_B):

record_id, f_1 , f_2, f_3, ... , f_n,    target
        1,  0.1, 0.2, 0.3, ... , 1.2,  output_A
        1,  0.1, 0.2, 0.3, ... , 1.2,  output_C
        2,  0.3, 1.2, 0.5, ... , 2.1,  output_A
        3,  0.2, 3.2, 1.3, ... , 0.4,  output_A
        3,  0.2, 3.2, 1.3, ... , 0.4,  output_B
        4,  1.1, 0.1, 0.7, ... , 0.5,  output_C
        5,  2.1, 0.5, 0.8, ... , 1.9,  output_B
        5,  2.1, 0.5, 0.8, ... , 1.9,  output_C
        6,  0.5, 0.4, 0.2, ... , 0.8,  output_A
        6,  0.5, 0.4, 0.2, ... , 0.8,  output_B
        6,  0.5, 0.4, 0.2, ... , 0.8,  output_C
                         :
                         :


I use format_B to train a multi-class logistic regression model. The model then predicts the probability of each category, and I set my own threshold to decide the final outputs.

While I have done the above, I am wondering would it possible to use format_A as the input of sklearn logistic regression with multi-class directly?

Or is there any package/library actually takes format_A as input? Or any other kind of models actually more suitable for this type of problem?

Thank you!
The task is called multilabel modelling. Many libraries in sklearn support this -http://scikit-learn.org/stable/modules/multiclass.html.

These algorithms generally use one vs rest strategy, building separate binary classifiers for each of the label (zero for all others) and assigning all labels which clear a probability threshold.