# Multiclass classification in a balanced dataset with one high-priority label

I have a balanced dataset for a multiclass classification problem with one high-priority label (this ought to be classified properly at all costs). How do I go about creating a workflow for this problem? What specific feature engineering/selection methods and classifiers should I be considering for this problem?

To be more specific, the data I'm dealing with (including labels) is completely anonymized, so I don't have a clue as to what it actually stands for.

Some approaches I am considering -

1. Creating synthetic data points for the priority label through oversampling.
2. Creating a highly non-linear model for prediction as accuracy is very important.

Any help is much appreciated!

1. Data: as you mentioned, this is done by artificially increasing the number of samples from critical class $$cc$$. This produces the same effect as data-sets that are naturally imbalanced,
2. Model: this is generally done by over-penalizing the miss-classification of $$cc$$ compared to other classes. One place for this modification is the loss function. A frequently used loss function in classification is cross entropy. It can be modified for this purpose as follows. Let $$y_{ik} = 1$$ if $$k$$ is the true class of data point $$i$$, otherwise $$y_{ik} = 0$$, and $$y'_{ik} \in (0, 1]$$ be the corresponding model estimation. The original cross-entropy can be written as: $$H_y(y')=-\sum_{i}\sum_{k=1}^{K}y_{ik}log(y'_{ik})$$
which can be changed to $$H_y(y')=-\sum_{i}\sum_{k=1}^{K}\color{blue}{w_{k}}y_{ik}log(y'_{ik})$$ For example, by setting $$w_{cc} = 10$$ and $$w_{k \neq cc}=1$$, you are essentially telling the model that miss-classifying $$1$$ member from $$cc$$ is as punishable as miss-classifying $$10$$ members from other classes. This is roughly equivalent to increasing the ratio of class $$cc$$ $$10$$ times in the training set using method (1).