4,358 research outputs found
The notions of the SMARANDACHE GROUP and the SMARANDACHE BOOLEAN RING
The notions of the Snmarandache group and the Smarandache Boolean ring are introduced here with the help of group action and ring action i.e. module respectively. The centre of the Smarandache groupoid is determined. These are very important for the study of Algebraic structures
Lattices of Smarandache Groupoid
Smarandache groupoid is not partly ordered under Smarandache inclusion relation but it contains some partly ordered sets, which are lattices under Smarandache union and intersection. We propose to establish the complemented and distributive lattices of Smarandache groupoid. Some properties of these lattices are discussed here
Scaling Graph-based Semi Supervised Learning to Large Number of Labels Using Count-Min Sketch
Graph-based Semi-supervised learning (SSL) algorithms have been successfully
used in a large number of applications. These methods classify initially
unlabeled nodes by propagating label information over the structure of graph
starting from seed nodes. Graph-based SSL algorithms usually scale linearly
with the number of distinct labels (m), and require O(m) space on each node.
Unfortunately, there exist many applications of practical significance with
very large m over large graphs, demanding better space and time complexity. In
this paper, we propose MAD-SKETCH, a novel graph-based SSL algorithm which
compactly stores label distribution on each node using Count-min Sketch, a
randomized data structure. We present theoretical analysis showing that under
mild conditions, MAD-SKETCH can reduce space complexity at each node from O(m)
to O(log m), and achieve similar savings in time complexity as well. We support
our analysis through experiments on multiple real world datasets. We observe
that MAD-SKETCH achieves similar performance as existing state-of-the-art
graph- based SSL algorithms, while requiring smaller memory footprint and at
the same time achieving up to 10x speedup. We find that MAD-SKETCH is able to
scale to datasets with one million labels, which is beyond the scope of
existing graph- based SSL algorithms.Comment: 9 page
- …