Graph-based Methods for Visualization and Clustering
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In many fields, the computation of an output depending on a field variable is of great interest. If the field variable depends on a high-dimensional parameter, the computational cost involved can be huge. Hence, it is necessary to find efficient and reliab ...
Machine learning is a broad discipline that comprises a variety of techniques for extracting meaningful information and patterns from data. It draws on knowledge and "know-how" from various scientific areas such as statistics, graph theory, linear algebra, ...
When examining complex problems, such as the folding of proteins, coarse grained descriptions of the system drive our investigation and help us to rationalize the results. Oftentimes collective variables (CVs), derived through some chemical intuition about ...
In this paper, we present a novel semi-supervised dimensionality reduction technique to address the problems of inefficient learning and costly computation in coping with high-dimensional data. Our method named the dual subspace projections (DSP) embeds hi ...
Two subsets of vertices in a graph are called homometric if the multisets of distances determined by them are the same. Let h(n) denote the largest number h such that any connected graph of n vertices contains two disjoint homometric subsets of size h. It ...
In this study we investigated the effect of medial temporal lobe epilepsy (MTLE) on the global characteristics of brain connectivity estimated by topological measures. We used DSI (Diffusion Spectrum Imaging) to construct a connectivity matrix where the no ...
The goal of transductive learning is to find a way to recover the labels of lots of data with only a few known samples. In this work, we will work on graphs for two reasons. First, it’s possible to construct a graph from a given dataset with features. The ...
It has been shown recently that a Macroscopic Fundamental Diagram (MFD) exists in urban transportation networks under certain conditions. However, MFD is not universally expected. Previous research demonstrates the existence of MFDs in homogeneous networks ...
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Clustering on graphs has been studied extensively for years due to its numerous applications. However, in contrast to the classic problems, clustering in mobile and online social networks brings new challenges. In these scenarios, it is common that observa ...
Locality-Sensitive Hashing (LSH) approximates nearest neighbors in high dimensions by projecting original data into low-dimensional subspaces. The basic idea is to hash data samples to ensure that the probability of collision is much higher for samples tha ...
