This could be a good overview of recommender systems even though I haven't seen all of it myself: http://www.slideshare.net/xamat/recommender-systems-machine-learning-summer-school-2014-cmu

http://www.slideshare.net/xamat/recommender-systems-machine-learning-summer-school-2014-cmu

 The naive Bayes classifier is designed for use when predictors are independent of one another within each class, but it appears to work well in practice even when that independence assumption is not valid hence its important you use Nearest neihbour to pull the associativity between students.use nearest classifier rule Cross-Validation Multiedit Algorithm should be helpful.over to you.

I will propose an ad-hoc solution.

If you have 70 students, this means you have at most 70 4-elective combinations.

If you store these as cluster centers and find the (hamming) distance between the student's chosen courses and cluster centers, you can find the most similar cluster and recommend the complementary elective. If there are more than one cluster with the same distance, complementary courses can be chosen based on their frequencies. This method does not only work to find the fourth, but can be used even the user only chooses one elective and needs recommendation for the second elective.

In the future, clusters may be modified by expert knowledge to help students choose better combinations. By modifying the distance function, distances between similar electives can be set to less than 1.

If possible you should explore all the major ML algorithms.check which is performing well to your needs with respect to the optimal feature set.Hopefully I understood your problem.Correct me if I am wrong.

For recommender system, you can use Singularity-based Approach. Here, i am going to attach a file related to that... Just go through it.

Standing back a bit: The fact that historically, certain previous students willingly took certain electives or were coerced into taking those choices should not influence the choice of the next cohort of students.  This is particularly important for a fast changing market like computer science.

 I feel that that electives should be chosen (and thus recommended) according to

1.       The interests of the student (to keep the student motivated)

2.       A plan that is not so narrow that the student specializes too soon or too broad that the student becomes an expert in nothing.

3.       A plan that permits the student to graduate with a coherent set of subjects without any major gaps.

4.       The talents of the available lecturers and the quality of contents of the course.

5.       A plan that permits the student to graduate with a coherent set of subjects, which suit an existing or groundbreaking potential job in the market-place.

 It seems to me that you have found a hammer, and now every screw looks like a nail.

 Case-based reasoning (CBR) is a technique that can be attempted in this situation.

How come and you don't mention in your choices the "de-facto standard" collaborative filtering (CF) approaches, including user-based as well as item-based k-NN CF algorithms? From your description, these algorithms (or even better, an ensemble thereof) would be an excellent fit for your project. In fact, you may also use the grades the previous students obtained to further improve your recommendations: based on the current transaction record of a student, your recommender can easily obtain an estimate -that should likely be pretty accurate- on the grade the student will likely get on each elective course, and use that estimate to sort items to propose to them. Solving "change of interests" and other such issues, in case they appear to be significant, is easy: simply use a sliding window, say use only the last two or three years of student classes to train your recommenders against. In general, item-based classifiers work much faster (and consume less memory) than user-based CF approaches. Further, if your data is too large (in the order of tens of GB, which doesn't seem to be the case here), you can use SVD-based approaches, however, SVD trades speed (and memory footprint) for quality, so unless you work with really large datasets, you shouldn't do it.

As I said before, ensembles of recommenders in most domains work better than a single recommender, in all standard quality metrics (Recall-at-n, precision, F1, you name it...), but of course, the offline training process takes more time to complete.

PS1: You can try the LensKit from the University of Minnesota which has very good implementations of the algorithms mentioned above. Older versions of the Apache Mahout project used to implement the above features, but their implementation wasn't very good, and they dropped them from the latest versions. For the other ML algorithms you mention, I would go with WEKA (from the Univ. of Waikato).

PS2: I just noticed how small your training set is. With only 70 prior student histories (each taking ~4 electives), I am not sure how well any recommender algorithm will perform. It would be well worth the effort to see if you can get data from more students to build your training set (say, have at least 400-500 student records). Also, with such small dataset, the grades of the students could prove to be a strong differentiating factor, in that the grades of the students in the mandatory classes could provide a strong feature to predict the grades in the elective courses.

I think there is a lot more involved in this than the 280 selections. I agree with Ian Kennedy that the system needs to make more personalized recommendations. Ioannis, how about a hybrid approach (CF + Content Based). I like the graph based solutions for the recommender problem, students, subjects, subject attributes, student attributes are represented as nodes. You can then do a random walk from a student to find the top-k page ranked subjects (which becomes your recommendation set). In terms of personalization, is it possible to find out how the 70 students rate their selections now and how they performed, if they did well does that mean it was a good selection? Also, are there any suggested electives for certain career paths i.e. if you want to become a Project Manager, do you need to take Compiler Theory as an elective - please keep in mind that I completed my bachelor degree in the 90s. Please see the link to a paper on graph based solutions.

http://link.springer.com/chapter/10.1007/978-3-319-26350-2_12

@Alphan: Well, since you mention it, in an industrial project, we have done just that: see attached link. The problem with content-based recommenders is that you need to implement them yourself, and they are quite problem-domain-specific; I am not sure if Katrin and her team would want to go that far. Also, in my experience, content-based recommenders will indeed increase the performance of the overall ensemble, but if taken on their own, they perform much worse than the CF approaches in most datasets; so they are useful only as a "performance booster" tool. BTW, Karypis (Minnesota)  has recently published some very nice work on Top-K item recommenders. But even his much earlier work, the SUGGEST library (in C) is very useful.

PS: Regarding grades, clearly, how well you do on a course does does not imply that your selection was a good one. However, since it is unlikely to have data that directly answer the question "How good was the "Compiler Theory" course for you?", -after all, there may be no answer to this question- the best you can do with the data you are likely to have at your disposal is to estimate the grade the students will get, and explicitly state in your recommendations that the proposals are based on an estimate of the student's likely grade. And in a statistical sense, indeed, students will fare better on classes they like more, but this is not absolute.

In any case, that's how I would approach the problem... others will have different approaches.

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Beware. High marks may be caused by having very intelligent or hard-working students; interesting lectures or from too-easy exams being set.