Many algorithms for determining properties of real algebraic or semi-algebraic sets rely upon the ability to compute smooth points. In this paper, we present a procedure based on computing critical points some well-chosen function that guarantees computation in each bounded connected component (real) atomic set. Our technique is intuitive principal, performs well previously difficult examples, ...

We propose a transformation method to circumvent the problems with high dimensional data. For each object in the data, we create an itemset of the k-nearest neighbors of that object, not just for one of the dimensions, but for many views of the data. On the resulting collection of sets, we can mine frequent itemsets; that is, sets of points that are frequently seen together in some of the views...