Related papers: Kernel Spectral Curvature Clustering (KSCC)
As quantum computers become increasingly practical, so does the prospect of using quantum computation to improve upon traditional algorithms. Kernel methods in machine learning is one area where such improvements could be realized in the…
Quantum kernel methods, i.e., kernel methods with quantum kernels, offer distinct advantages as a hybrid quantum-classical approach to quantum machine learning (QML), including applicability to Noisy Intermediate-Scale Quantum (NISQ)…
This paper generalizes recent advances on quadratic manifold (QM) dimensionality reduction by developing kernel methods-based nonlinear-augmentation dimensionality reduction. QMs, and more generally feature map-based nonlinear corrections,…
We propose and show the efficacy of a new method to address generic inverse problems. Inverse modeling is the task whereby one seeks to determine the control parameters of a natural system that produce a given set of observed measurements.…
Support vector machines (SVMs) are a well-established classifier effectively deployed in an array of classification tasks. In this work, we consider extending classical SVMs with quantum kernels and applying them to satellite data analysis.…
Data sites selected from modeling high-dimensional problems often appear scattered in non-paternalistic ways. Except for sporadic clustering at some spots, they become relatively far apart as the dimension of the ambient space grows. These…
Spectral clustering is a leading and popular technique in unsupervised data analysis. Two of its major limitations are scalability and generalization of the spectral embedding (i.e., out-of-sample-extension). In this paper we introduce a…
Unsupervised semantic segmentation is a long-standing challenge in computer vision with great significance. Spectral clustering is a theoretically grounded solution to it where the spectral embeddings for pixels are computed to construct…
Despite the fundamental importance of clustering, to this day, much of the relevant research is still based on ambiguous foundations, leading to an unclear understanding of whether or how the various clustering methods are connected with…
To cluster data that are not linearly separable in the original feature space, $k$-means clustering was extended to the kernel version. However, the performance of kernel $k$-means clustering largely depends on the choice of kernel…
In this paper, we consider data acquired by multimodal sensors capturing complementary aspects and features of a measured phenomenon. We focus on a scenario in which the measurements share mutual sources of variability but might also be…
An improved version of the sparse multiway kernel spectral clustering (KSC) is presented in this brief. The original algorithm is derived from weighted kernel principal component (KPCA) analysis formulated within the primal-dual…
Combining information from various image features has become a standard technique in concept recognition tasks. However, the optimal way of fusing the resulting kernel functions is usually unknown in practical applications. Multiple kernel…
Kernel method is a very powerful tool in machine learning. The trick of kernel has been effectively and extensively applied in many areas of machine learning, such as support vector machine (SVM) and kernel principal component analysis…
The K-means algorithm is among the most commonly used data clustering methods. However, the regular K-means can only be applied in the input space and it is applicable when clusters are linearly separable. The kernel K-means, which extends…
Clustering is a fundamental task in data analysis, and spectral clustering has been recognized as a promising approach to it. Given a graph describing the relationship between data, spectral clustering explores the underlying cluster…
Computer model calibration involves using partial and imperfect observations of the real world to learn which values of a model's input parameters lead to outputs that are consistent with real-world observations. When calibrating models…
One of the fundamental problems in network analysis is detecting community structure in multi-layer networks, of which each layer represents one type of edge information among the nodes. We propose integrative spectral clustering approaches…
In Computer Vision, problem of identifying or classifying the objects present in an image is called Object Categorization. It is a challenging problem, especially when the images have clutter background, occlusions or different lighting…
With the advent of kernel methods, automating the task of specifying a suitable kernel has become increasingly important. In this context, the Multiple Kernel Learning (MKL) problem of finding a combination of pre-specified base kernels…