We compare two weakly supervised graph-based classification algorithms: spectral partitioning and tripartite updating. We provide results from empirical tests on the problem of number classification. Our results indicate (a) that both methods require minimal labeled data, (b) that both methods scale well with the number of unlabeled examples, and (c) that tripartite updating outperforms spectra...

Three graph theoretical statistics are considered for the problem of estimating the intrinsic dimension of a data set. The first is the ‘‘reach’’ statistic, r j,k, proposed in Brito et al. (2002) [4] for the problem of identification of Euclidean dimension. The second,Mn, is the sample average of squared degrees in the minimum spanning tree of the data, while the third statistic, Uk n , is base...

The question of generating realistic graphs has always been a topic of huge interests. This topic has gained huge attention over the past few years with the advent of massive real-world network data that re generated by large software companies like Facebook and Google, along with the increase in the computation power that makes anyone capable of processing them. With real graphs at massive sca...

Attempts to solve the famous Four Color Problem led to fruitful discoveries and rich coloring theories. In this talk, some old and some recent applications of tools from topology to graph coloring problems will be presented. In particular, the following subjects will be treated: The use of Euler’s formula and local planarity conditions, Kempe equivalence, homotopy, winding number and its higher...

This paper introduces an unsupervised graph-based method that selects textual labels for automatically generated topics. Our approach uses the topic keywords to query a search engine and generate a graph from the words contained in the results. PageRank is then used to weigh the words in the graph and score the candidate labels. The state-of-the-art method for this task is supervised (Lau et al...

This paper is a tutorial on the application of graph theoretic techniques in classical coding theory. A fundamental problem in coding theory is to determine the maximum size of a code satisfying a given minimum Hamming distance. This problem is thought to be extremely hard and still not completely solved. In addition to a number of closed form expressions for special cases and some numerical re...

Hyperspectral imagery is a challenging modality due to the dimension of the pixels which can range from hundreds to over a thousand frequencies depending on the sensor. Most methods in the literature reduce the dimension of the data using a method such as principal component analysis, however this procedure can lose information. More recently methods have been developed to address classificatio...

The management of large databases of hierarchical (e.g., multi-scale or multilevel) image features is a common problem in object recognition. Such structures are often represented as trees or directed acyclic graphs (DAGs), where nodes represent image feature abstractions and arcs represent spatial relations, mappings across resolution levels, component parts, etc. Object recognition consists o...

Computing the product of the (binary) adjacency matrix of a large graph with a real-valued vector is an important operation that lies at the heart of various graph analysis tasks, such as computing PageRank. In this paper we show that some well-known Web and social graph compression formats are computation-friendly, in the sense that they allow boosting the computation. In particular, we show t...