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We propose a decentralized subspace algorithm for identification of large-scale, interconnected systems that are described by sparse (multi) banded state-space matrices. First, we prove that the state of a local subsystem can be…
Euler's elastica model has been extensively studied and applied to image processing tasks. However, due to the high nonlinearity and nonconvexity of the involved curvature term, conventional algorithms suffer from slow convergence and high…
Gaussian Processes are widely used for regression tasks. A known limitation in the application of Gaussian Processes to regression tasks is that the computation of the solution requires performing a matrix inversion. The solution also…
Clustering in image analysis is a central technique that allows to classify elements of an image. We describe a simple clustering technique that uses the method of similarity matrices. We expand upon recent results in spectral analysis for…
Subspace clustering refers to the task of finding a multi-subspace representation that best fits a collection of points taken from a high-dimensional space. This paper introduces an algorithm inspired by sparse subspace clustering (SSC) [In…
Blur is an image degradation that is difficult to remove. Invariants with respect to blur offer an alternative way of a~description and recognition of blurred images without any deblurring. In this paper, we present an original unified…
In this paper, we aim to design and analyze distributed Bayesian estimation algorithms for sensor networks. The challenges we address are to (i) derive a distributed provably-correct algorithm in the functional space of probability…
We propose a probabilistic model for refining coarse-grained spatial data by utilizing auxiliary spatial data sets. Existing methods require that the spatial granularities of the auxiliary data sets are the same as the desired granularity…
Bi-clustering is a technique that allows for the simultaneous clustering of observations and features in a dataset. This technique is often used in bioinformatics, text mining, and time series analysis. An important advantage of…
Data mining techniques, including clustering and classification tasks, for the automatic information extraction from large datasets are increasingly demanded in several scientific fields. In particular, in the astrophysical field, large…
Sampling techniques are used in many fields, including design of experiments, image processing, and graphics. The techniques in each field are designed to meet the constraints specific to that field such as uniform coverage of the range of…
Finding a suitable data representation for a specific task has been shown to be crucial in many applications. The success of subspace clustering depends on the assumption that the data can be separated into different subspaces. However,…
This paper develops a high-accuracy algorithm for time fractional wave problems, which employs a spectral method in the temporal discretization and a finite element method in the spatial discretization. Moreover, stability and convergence…
The problem of automatically clustering data is an age old problem. People have created numerous algorithms to tackle this problem. The execution time of any of this algorithm grows with the number of input points and the number of cluster…
Spectral clustering is a novel clustering method which can detect complex shapes of data clusters. However, it requires the eigen decomposition of the graph Laplacian matrix, which is proportion to $O(n^3)$ and thus is not suitable for…
A novel elastic time distance for sparse multivariate functional data is proposed and used to develop a robust distance-based two-layer partition clustering method. With this proposed distance, the new approach not only can detect correct…
Sampling-based algorithms are classical approaches to perform Bayesian inference in inverse problems. They provide estimators with the associated credibility intervals to quantify the uncertainty on the estimators. Although these methods…
In this paper we present a locally and dimension-adaptive sparse grid method for interpolation and integration of high-dimensional functions with discontinuities. The proposed algorithm combines the strengths of the generalised sparse grid…
As climate change intensifies, the shift to cleaner energy sources becomes increasingly urgent. With wind energy production set to accelerate, reliable wind probabilistic forecasts are essential to ensure its efficient use. However, since…
3D Gaussian splatting models, as a novel explicit 3D representation, have been applied in many domains recently, such as explicit geometric editing and geometry generation. Progress has been rapid. However, due to their mixed scales and…