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To my knowledge there are no well known classification methods that work directly on dynamically sized input collections. Dimensionality reduction works by reducing high dimensional, but fixed data to lower dimensions, so it really doesn't seem like what you need. One way in which this is handled in machine learning for binary classification (which seems is the problem you're interested in) is by building histograms. For example you can categorize text (of varying length) by building histograms of the words that appear in the text. Several extensions have been presented, histograms of bi-grams, n-grams but they build on the same idea. Another type of idea is structured prediction, a good example of which is when you have a sentence and you need to determine for each word, what part of speech it is, in this type of setup each word has a label, and the interaction between labels is very important. Well understood method for this type of problem are <a href="http://www.cs.cornell.edu/~cnyu/latentssvm/" rel="nofollow">Latent Structural SVM</a>, <a href="http://en.wikipedia.org/wiki/Conditional_random_field" rel="nofollow">CRF</a>, and <a href="http://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&cad=rja&ved=0CDgQFjAA&url=http://books.nips.cc/papers/files/nips16/NIPS2003_AA04.pdf&ei=t9vAUIH2NKm20QGV9YGACw&usg=AFQjCNHzW9Wc68rib1oO9mV71CtHXm7AWg&sig2=nyz53sKhTuQg7n5HFKwtuw" rel="nofollow">Max Margin Markov Network</a>
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