Ordinal classification packages and algorithms

Question

I'm attempting to make a classifier that chooses a rating (1-5) for a item i. For each item i, I have a vector x containing about 40 different quantities pertaining to i. I also have a gold standard rating for each item. Based on some function of x, I want to train a classifier to give me a rating 1-5 that closely matches the gold standard.

Most of the information I've seen on classifiers deal with just binary decisions, while I have a rating decision. Are there common techniques or code libraries out there to deal with this sort of problem?

Answer 1

I agree with you that ML problems in which the response variable is on an ordinal scale require special handling--'machine-mode' (i.e., returning a class label) seems insufficient because the class labels ignore the relationship among the labels ("1st, 2nd, 3rd"); likewise, 'regression-mode' (i.e., treating the ordinal labels as floats, {1, 2, 3}) because it ignores the metric distance between the response variables (e.g., 3 - 2 != 1).

R has (at least) several packages directed to ordinal regression. One of these is actually called Ordinal, but i haven't used it. I have used the Design Package in R for ordinal regression and i can certainly recommend it. Design contains a complete set of functions for solution, diagnostics, testing, and results presentation of ordinal regression problems via the Ordinal Logistic Model. Both Packages are available from CRAN) A step-by-step solution of an ordinal regression problem using the Design Package is presented on the UCLA Stats Site.

Also, i recently looked at a paper by a group at Yahoo working on ordinal classification using Support Vector Machines. I have not attempted to apply their technique.

Answer 2

Have you tried using Weka? It supports binary, numerical, and nominal attributes out of the box, the latter two of which might work well enough for your purposes.

Furthermore, it looks like one of the classifiers that's available is a meta-classifier called OrdinalClassClassifier.java, which is the result of this research:

• Eibe Frank and Mark Hall, A simple approach to ordinal classification. In Proceedings of the 12th European Conference on Machine Learning, 2001, pp. 145-156.

If you don't need a pre-made approach, then these references (in addition to doug's note about the Yahoo SVM paper) might be useful:

• W Chu and Z Ghahramani, Gaussian processes for ordinal regression. Journal of Machine Learning Research, 2006.
• Wei Chu and S. Sathiya Keerthi, New approaches to support vector ordinal regression. In Proceedings of the 22nd international conference on Machine Learning, 2005, 145-152.

Answer 3

The problems that dough has raised are all valid. Let me add another one. You didn't say how you would like to measure the agreement between the classification and the "gold standard". You have to formulate the answer to that question as soon as possible, as this will have a huge impact on your next step. In my experience, the most problematic part of any (ok, not any, most) optimization task is the score function. Try asking yourself whether all errors equal? Does miss-classifying the "3" as being "4" has the same impact as classifying "4" as "3"? What about "1" vs "5". Can mistakenly missing one case have disastrous consequences (miss HIV diagnosis, activate pilot ejection in a plane)

The simplest way to measure the agreement between categorical classifiers is Cohen's Kappa. More complicated methods are described in the following links here, here, here, and here

Having said that, sometimes picking a solution that "just works", instead of "the right one" is faster and easier. If I were you I would pick a machine learning library (R, Weka, I personally love Orange) and see what I get. Only if you don't have reasonably good results with that, look for more complex solutions

Answer 4

If not interested in fancy statistics a one hidden layer back propagation neural network with 3 or 5 output nodes will probably do the trick if the training data is sufficiently large. Most NN classifiers try to minimize the mean squared error which is not always desired. Support Vector Machines mentioned earlier is a good alternative. FANN is a good library for back propagation NNs, it also has some tools to assist in training of the network.