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Graph spectral clustering algorithms have been shown to be effective in finding clusters and generally outperform traditional clustering algorithms, such as k-means. However, they have scalibility issues in both memory usage and computational time. To overcome these limitations, the common approaches sparsify the similarity matrix by zeroing out some of its elements. They generally consider local...
In this paper, we propose a novel entropic signature for graphs, where we probe the graphs by means of continuous-time quantum walks. More precisely, we characterise the structure of a graph through its average mixing matrix. The average mixing matrix is a doubly-stochastic matrix that encapsulates the time-averaged behaviour of a continuous-time quantum walk on the graph, i.e., the ij-th element...
In multiview image stitching, the colors of images in a scene might vary when images are taken under different illumination or camera settings. A common way to produce a seamless stitched image is to transform the colors of a target image to match that of a source image. In this paper we present a color transfer method based on two premises: first, pixels in the generated image should have similar...
Reconstruction of skulls from defective models is a very important and challenging task in craniofacial surgery, forensics, and anthropology. Existing methods typically reconstruct approximating surfaces that regard corresponding points on the target skull as soft constraints, thus incurring non-zero error even for non-defective parts and high overall reconstruction error. This paper proposes a novel...
Subspace clustering refers to the task of clustering a collection of points drawn from a high-dimensional space into a union of multiple subspaces that best fits them. State-of-the-art approaches have been proposed for tackling this clustering problem by using the low-rank or sparse optimization techniques. However, most of the traditional subspace clustering methods are developed for single-view...
The emerging field of graph signal processing requires a solid design of downsampling operation for graph signals to extend pattern recognition, machine learning and signal processing techniques into the graph setting. The state-of-the-art downsampling method is constructed upon the maximum spanning trees of the graphs. However, under the framework of this method, unbalanced downsampling often occurs...
Real-world datasets consist of data representations (views) from different sources which often provide information complementary to each other. Multi-view learning algorithms aim at exploiting the complementary information present in different views for clustering and classification tasks. Several multi-view clustering methods that aim at partitioning objects into clusters based on multiple representations...
One of the widely used algorithms for graph-based semi-supervised learning (SSL) is the Local and Global Consistency (LGC). Such an algorithm can be viewed as a convex optimization problem that balances fitness on labeled examples and smoothness on the graph using a graph Laplacian. In this paper, we provide a novel graph-based SSL algorithm incorporating two normalization constraints into the regularization...
In this paper, we present a novel thermodynamic framework for graphs that can be used to analyze time evolving networks, relating the thermodynamics variables to macroscopic changes in network topology, and linking major structural transition to phase changes in the thermodynamic picture. We start from a recent quantum-mechanical characterization of the structure of a network relating the graph Laplacian...
In this paper, we introduce a nonlinear dimensionality reduction (NLDR) technique that can construct a low-dimensional embedding efficiently and accurately with low embedding distortions. The key idea is to divide NLDR into nonlinearity reduction and linear dimensionality reduction, which simplifies the overall NLDR process. Nonlinearity reduction is based on the elastic shell model that measures...
Feature extraction, one kind of dimensionality reduction methodology, has aroused considerable research interests during the last few decades. Traditional graph embedding methods construct a fixed graph with original data to fulfill the aim of feature extraction. The lack of the graph learning mechanism leaves room for the improvement of their performances. In this paper, we propose a novel framework,...
Here, we turn our attention to barycentric embeddings and examine their utility for semi-supervised image labelling tasks. To this end, we view the pixels in the image as vertices in a graph and their pairwise affinities as weights of the edges between them. Abstracted in this manner, we can pose the semi-supervised labelling problem into a graph theoretic setting where the labels are assigned based...
Tracking shots have posed a significant challenge for salient region detection due to the presence of highly competing background motion. In this paper, we propose a computationally efficient technique to detect salient objects in a tracking shot. We first separate the tracked foreground pixels from the background by accounting for the variability of the pixels in a set of frames. The focus of the...
We present a novel approach to the computation of dense correspondence maps between shapes in a non-rigid setting. The problem is defined in terms of functional correspondences. We deal with the non-injectivity of the solution of the functional map framework due to the under-determinedness of the original problem. Key to our approach is the injectivity constraint plugged directly into the problem...
In this paper, we use the Maxwell-Boltzmann partition function to compute network entropy. The partition function is used to model the energy level population statistics where the network is in thermodynamic equilibrium with a heat-bath. Here the network Hamiltonian operator defines a set of energy levels occupied by particles in thermal equilibrium. These energy levels are given by the eigenvalues...
Many text segmentation methods are elaborate and thus are not suitable to real-time implementation on mobile devices. Having an efficient and effective method, robust to noise, blur, or uneven illumination, is interesting due to the increasing number of mobile applications needing text extraction. We propose a hierarchical image representation, based on the morphological Laplace operator, which is...
Visualization helps us to understand single-label and multi-label classification problems. In this paper, we show several standard techniques for simultaneous visualization of samples, features and multi-classes on the basis of linear regression and matrix factorization. The experiment with two real-life multi-label datasets showed that such techniques are effective to know how labels are correlated...
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