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I have data in following form:

a: 1,2,3,2,3
a: 2,4,5,6,7,8,0,9,7,6,5,6,2
a: 7,8,9,3,4
b: 4,5,3,5,6,3,5,1,2
b: 1,6,3,2,4,5
b: 2,4,5,6,7,8,0,9,7,6,5,6,2
c: 7,8,9,3,4
c: 4,5,3,5,6,3,5,1,2
...

(in reality, each case has about 100-200 numbers, though the length is variable)

Here, a, b and c are groups (their number is fixed - taken as 3 here) and the numbers indicate a vector associated with each case. How can I apply supervised machine learning with such a data so that if I get a new series of numbers, e.g. following:

3,2,3,4,1,5,6

I should be able to determine which group (a, b or c) does this case belongs to.

Following features of each list of numbers may be important:

length of series
mean value of series
variance of series
maximum of series
minimum of series
type of distribution of series (normal or non-normal)

How can I apply machine learning methods to such data. Thanks for your insight.

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This is a typical scenario in language processing, e.g. if you want to read a product review representing each word with a number and output a 1-5 star rating.

You can use a recurrent many-to-one RNN/GRU/LSTM network: After feeding each word it generates a feature vector which can be fed into a classifier. https://en.wikipedia.org/wiki/Recurrent_neural_network

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