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We studied university curricula (from computer science, stats and business schools). The top contenders are linear programming, regression, clustering, Neural networks and SVM.
Then we looked at the peer groups. Obviously, the top 10 algos are published once in 4 years I guess. The current list is C5.0, KNN, SVM, EM, K-means, Pagerank, CART, Naive Bayes and a few more. We also looked at competition sites like Kaggle and found the winning algos. Singular value decomposition, Restricted boltzman machines, random forests, spectral methods seem to be the leaders there.
Lastly, we asked industry practitioners. As expected the focus was on data engineering, feature engineering, cleaning and visualization with modeling sort of not much emphasis!
Personally, they suggested they would also add genetic algorithms to this list as a very important technique. They almost always use it for optimization.
While developing the curriculum of INSOFE programs, they spent a lot of time pondering about this.