Is this a kind of “sketching”?

Say one is given a matrix (assume real and symmetric if necessary) and its n−dimensional columns be say v1,v2,..,vn. Now is it possible to find a set of d<n lower dimensional vectors (w1,..,wd) such that they form a d×d matrix B (assume real and symmetric) with either of these properties, That the d eigenvalues of … Read more

Different properties of Heavy-Hitters and Count-Min Sketch algorithms?

I’m currently using the Heavy-Hitters algorithm as described here and I’m wondering what if any space, time, accuracy, or real-world performance differences I would see if I were to switch to an implementation of Count-min Sketch plus a linked list to store the “heavy hitters” instead? As far as I can tell, both require O(k) … Read more

Is this a known question in matrix sketching?

Say one has a D×n matrix A all of whose entries are non-zero. One wants a method which will look at each of the columns of A one by one and create new m≪D dimensional columns and stack them up as a matrix A′ of dimension m×n such that ‖ for some given \epsilon. Is … Read more

Integer set disjointness query on sketches with something like homomorphic hashing

Suppose I have two sets of integers A and B and I have a sketch data structure described by a function sketchn:P(Z)→2n that returns a bitstring of size n. These sketches can be checked for disjointness with a function disjointn:2n×2n→2, where if disjointn(sketchn(A),sketchn(B))=1, then A∩B=∅ (but A∩B=∅ may also be true when disjoint returns 0, … Read more

What is the correct way to determine the width and depth of a count-min sketch?

The width (number of registers) and depth (number of hash functions) of a Count-Min sketch determine the accuracy of counts retrieved. I’ve found two different methods for calculating the width (w) and depth (d). First Method The clearest example I’ve found is from a 2011 paper by the original Count-Min authors: Suppose we want an … Read more

Can you in some way design a “sketch” illustration theme for Google Maps?

Is there any way to make Google Maps like this? This is promising, but not for Google Maps. This doesn’t look promising 🙂 Answer Google Maps offers a very extensive API for style customisation. You can customise almost any element. This is done through a Javascript API: the styles are saved in a JSON structure … Read more