In recent data mining research, the graph clustering methods, such as normalized cut and ratio cut, have been well studied and applied to solve many unsupervised learning applications. The original graph clustering methods are NP-hard problems. Traditional approaches used spectral relaxation to solve the graph clustering problems. The main disadvantage of these approaches is that the obtained s...

Clustering, particularly hierarchical clustering, is an important method for understanding and analysing data across a wide variety of knowledge domains with notable utility in systems where the data can be classified in an evolutionary context. This paper introduces a new hierarchical clustering problem defined by a novel objective function we call the arithmetic-harmonic cut. We show that the...

A brain tumor is a mass of unnecessary cells growing in the brain. Brain tissue classification from magnetic resonance images (MRI) is of great importance for research and clinical studies of the normal and diseased human brain. In just a few decades, the use of magnetic resonance imaging (MRI) scanners has grown enormously. An MRI scan is the best way to see inside the human body without cutti...

Results of a recent comparative experimental assessment of methods for network community detection applied to benchmark graphs indicate that the two best methods use different objective functions but a similar local search-based optimization (LSO) procedure. This observation motivates the following research question: Given the LSO optimization procedure, how much does the choice of the objectiv...

Digital image processing is the fastest growing computer-based technology. It plays a vital role in computer vision and image processing tasks and is generally used for various purposes like medical diagnosis, robotics, remote sensing, industrial inspection etc... Some major operations performed on an image to extract some useful information that corresponds to the key stages in the digital ima...

Consider a neighborhood graph, for example a k-nearest neighbor graph, that is constructed on sample points drawn according to some density p. Our goal is to re-weight the graph’s edges such that all cuts and volumes behave as if the graph was built on a different sample drawn from an alternative density p. We introduce the f -adjusted graph and prove that it provides the correct cuts and volum...

Normalized Cuts has successfully been applied to a wide range of tasks in computer vision, it is indisputably one of the most popular segmentation algorithms in use today. A number of extensions to this approach have also been proposed, ones that can deal with multiple classes or that can incorporate a priori information in the form of grouping constraints. It was recently shown how a general l...

We generalize the notion of quasirandom which concerns a class of equivalent properties that random graphs satisfy. We show that the convergence of a graph sequence under the spectral distance is equivalent to the convergence using the (normalized) cut distance. The resulting graph limit is called graphlets. We then consider several families of graphlets and, in particular, we characterize quas...