Best Way to tackle to time series classification problem?
Since I don't see the data and I cannot fully understand the data format, I am just giving some general advice. But first, I should mention that it doesn't make sense to consider each output (each 20-element array) as timeseries sequence unless there is a priority among them (by priority, I mean if you know a particular lab value is obtained before others)
So, if you have 20-element array of binary numbers as output, you might find out there is no two ouput exactly the same or there might be only a few observations with exactly similar output (because you can have $2^{20}$ combinations!). So, let's say if you have N observations, and you may see N distinct output array as well. Therefore, you may first cluster the labels into k groups and assign new labels to each group (the label of group i-th is i). Then, find the closest distance between your query and each group, so you can then find the appropriate class. Then, you can predict the ouput in array format (e.g. let's say you realize your query belongs to a group of 20 members). So, you can say, the output is expected value of output arrays in element-wise manner. So, e.g. your first element of 20-element output array might be 0.9. Or, you can be more precise and after finding the appropriate group, define a weight based on the distance between your query and members and find the weighted average of output arrays of that group!