PROJECT TITLE :

Fully Dynamic k-Center Clustering with Improved Memory Efficiency

ABSTRACT:

Any machine learning library worth its salt will include both static and dynamic clustering algorithms as core components. The sliding window model, along with other, more simplistic models, has been the primary focus of the majority of the work that has been done to develop dynamic machine learning and data mining algorithms. However, in many applications that are used in the real world, it is possible that one will be required to deal with arbitrary deletions and insertions. For instance, one may need to remove data items that are not necessarily the oldest ones because they have been flagged as containing inappropriate content or due to privacy concerns. This may require one to remove data items that are not necessarily the most recent ones. It's possible that clustering data on trajectory will require you to deal with more general update operations as well. We develop a (2+)-approximation algorithm for the k-center clustering problem with a "small" amortized cost under the fully dynamic adversarial model. This algorithm's goal is to minimize the total amount of money spent on the problem. In such a model, it is possible to arbitrarily add or remove points, provided that the opponent does not have access to the random choices that our algorithm generates. When the ratio between the maximum and minimum distance between any two points in input is bounded by a polynomial, while k and are constant, the amortized cost of our algorithm is poly-logarithmic. This is the case when the ratio between the maximum and minimum distance between any two points in input. In addition, we were able to significantly reduce the amount of memory that our fully dynamic algorithm required, but this came at the expense of the algorithm's ability to approximate the ratio 4+. Our theoretical findings are supported by an extensive experimental evaluation conducted on dynamic data taken from Twitter and Flickr, in addition to trajectory data, which demonstrates the efficiency of our methodology.