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Dealing with long sequence labeling

I am dealing with problem in which i have to label the inputs (in a sequence format) to 5 distinct classes. The input would be like:

X = {x_1,_x_2,...,X_500}

and the output should be something like:

Y = {Y_1,Y_2,...,Y_500}

But the problem lies where too many of labels are from first class so a sample output would have many frist class labels and only a few (5 or 6 samples) related to other classes.

The classifier tends to learn to classify everything to first class and yet get higher accuracy which is not correct. What you propose?