In this paper we investigate a new framework for graph partitioning using decision trees to search for sub-graphs within a graph adjacency matrix. Graph partitioning by a decision tree seeks to optimize a specified graph partitioning index such as ratio cut by recursively applying decision rules found within nodes of the graph. Key advantages of tree models for graph partitioning are they provi...

The transductive SVM is a semi-supervised learning algorithm that searches for a large margin hyperplane in feature space. By withholding the training labels and adding a constraint that favors balanced clusters, it can be turned into a clustering algorithm. The Normalized Cuts clustering algorithm of Shi and Malik, although originally presented as spectral relaxation of a graph cut problem, ca...

This paper presents a subword normalized cut (N-cut) approach to automatic story segmentation of Chinese broadcast news (BN). We represent a speech recognition transcript using a weighted undirected graph, where the nodes correspond to sentences and the weights of edges describe inter-sentence similarities. Story segmentation is formalized as a graph-partitioning problem under the N-cut criteri...

Sum of Squares Error and Normalized Cut are two widely used clustering functional. It is known their minimum values are monotone with respect to the input number of clusters and this monotonicity does not allow for a simple automatic selection of a correct number of clusters. Here we study monotonicity not just on the minimizers but on the entire clustering lattice. We show the value of Sum of ...

We propose a normalized-cut model for the problem of aligning a known hierarchical browsing structure, e.g., electronic slides of lecture recordings, with the sequential transcripts of the corresponding spoken documents, with the aim to help index and access the latter. This model optimizes a normalizedcut graph-partitioning criterion and considers local tree constraints at the same time. The e...

The incidence of thyroid nodule is very high and generally increases with the age. Thyroid nodule may presage the emergence of thyroid cancer. Most thyroid nodules are asymptomatic which makes thyroid cancer different from other cancers. The thyroid nodule can be completely cured if detected early. Therefore, it is necessary to correctly classify the thyroid nodule to be benign or malignant. Fi...

In the first part of this paper, we survey results that are associated with three types of Laplacian matrices:difference, normalized, and signless. We derive eigenvalue and eigenvector formulaes for paths and cycles using circulant matrices and present an alternative proof for finding eigenvalues of the adjacency matrix of paths and cycles using Chebyshev polynomials. Even though each results i...

The study highlights a novel method to segment single trees in 3D from dense airborne full waveform LIDAR data using the normalized cut segmentation. The key idea is to subdivide the tree area in a voxel space and to setup a bipartite graph which is formed by the voxels and similarity measures between the voxels. The normalized cut segmentation divides the graph hierarchically into segments whi...