Binary classification with time-series features
I would plot the measurements time $t$ and the corresponding measurement 5 to 10 samples for each category. Try to detect some patterns. Possible patterns are the trend (Is the cure growing? Is it linearly? Exponentially?), frequencies of oscillations (Does one category have oscillations with higher magnitude or frequencies? You can use Fast Fourier Transform for this) self similarity of signal (autocorrelation) Then look at means, median, standard deviation, skewness and kurtosis of your signals. 

After having extracted all these features I would try to calculate the correlations of your features with the target variable. Then you can eliminate variables that are not very highly correlated with your target variable. In the next step, I would look at the correlations between your features and eliminate the variables that are highly correlated by eliminating the one variable which less correlated with the target variable. Then I would use some classical binary classifiers like discriminant analysis or logistic regression. 

If you see that this method will not lead to sufficient results then you should try more sophisticated methods like neural networks/decision trees for the features that you extracted.