26 research outputs found
Relations Between Adjacency and Modularity Graph Partitioning
In this paper the exact linear relation between the leading eigenvector of
the unnormalized modularity matrix and the eigenvectors of the adjacency matrix
is developed. Based on this analysis a method to approximate the leading
eigenvector of the modularity matrix is given, and the relative error of the
approximation is derived. A complete proof of the equivalence between
normalized modularity clustering and normalized adjacency clustering is also
given. Some applications and experiments are given to illustrate and
corroborate the points that are made in the theoretical development.Comment: 11 page
Fast Incremental SVDD Learning Algorithm with the Gaussian Kernel
Support vector data description (SVDD) is a machine learning technique that
is used for single-class classification and outlier detection. The idea of SVDD
is to find a set of support vectors that defines a boundary around data. When
dealing with online or large data, existing batch SVDD methods have to be rerun
in each iteration. We propose an incremental learning algorithm for SVDD that
uses the Gaussian kernel. This algorithm builds on the observation that all
support vectors on the boundary have the same distance to the center of sphere
in a higher-dimensional feature space as mapped by the Gaussian kernel
function. Each iteration involves only the existing support vectors and the new
data point. Moreover, the algorithm is based solely on matrix manipulations;
the support vectors and their corresponding Lagrange multiplier 's
are automatically selected and determined in each iteration. It can be seen
that the complexity of our algorithm in each iteration is only , where
is the number of support vectors. Experimental results on some real data
sets indicate that FISVDD demonstrates significant gains in efficiency with
almost no loss in either outlier detection accuracy or objective function
value.Comment: 18 pages, 1 table, 4 figure
Peak Criterion for Choosing Gaussian Kernel Bandwidth in Support Vector Data Description
Support Vector Data Description (SVDD) is a machine-learning technique used
for single class classification and outlier detection. SVDD formulation with
kernel function provides a flexible boundary around data. The value of kernel
function parameters affects the nature of the data boundary. For example, it is
observed that with a Gaussian kernel, as the value of kernel bandwidth is
lowered, the data boundary changes from spherical to wiggly. The spherical data
boundary leads to underfitting, and an extremely wiggly data boundary leads to
overfitting. In this paper, we propose empirical criterion to obtain good
values of the Gaussian kernel bandwidth parameter. This criterion provides a
smooth boundary that captures the essential geometric features of the data
Feasibility of Multiple Repeat Gamma Knife Radiosurgeries for Trigeminal Neuralgia: A Case Report and Review of the Literature
Treatment options for trigeminal neuralgia (TN) must be customized for the individual patient, and physicians must be aware of the medical, surgical, and radiation treatment modalities to prescribe optimal treatment courses for specific patients. The following case illustrates the potential for gamma knife radiosurgery (GKRS) to be repeated multiple times for the purpose of achieving facial pain control in cases of TN that have been refractory to other medical and surgical options, as well as prior GKRS. The patient described failed to achieve pain control with initial GKRS, as well as medical and surgical treatments, but experienced significant pain relief for a period of time with a second GKRS procedure and later underwent a third procedure. Only a small subset of patients have reportedly undergone more than two GKRS for TN; thus, further research and long-term clinical followup will be valuable in determining its usefulness in specific clinical situations