Related papers: NNK-Means: Data summarization using dictionary lea…
In this paper we present a new approach of incorporating kernels into dictionary learning. The kernel K-SVD algorithm (KKSVD), which has been introduced recently, shows an improvement in classification performance, with relation to its…
In this paper we present new algorithms for training reduced-size nonlinear representations in the Kernel Dictionary Learning (KDL) problem. Standard KDL has the drawback of a large size of the kernel matrix when the data set is large.…
Modern machine learning systems are increasingly trained on large amounts of data embedded in high-dimensional spaces. Often this is done without analyzing the structure of the dataset. In this work, we propose a framework to study the…
In the last decade, a considerable research effort has been devoted to developing adaptive algorithms based on kernel functions. One of the main features of these algorithms is that they form a family of universal approximation techniques,…
This work proposes kernel transform learning. The idea of dictionary learning is well known; it is a synthesis formulation where a basis is learnt along with the coefficients so as to generate or synthesize the data. Transform learning is…
Multi-kernel learning (MKL) has been widely used in function approximation tasks. The key problem of MKL is to combine kernels in a prescribed dictionary. Inclusion of irrelevant kernels in the dictionary can deteriorate accuracy of MKL,…
Natural language processing often involves computations with semantic or syntactic graphs to facilitate sophisticated reasoning based on structural relationships. While convolution kernels provide a powerful tool for comparing graph…
Data-driven neighborhood definitions and graph constructions are often used in machine learning and signal processing applications. k-nearest neighbor~(kNN) and $\epsilon$-neighborhood methods are among the most common methods used for…
In this paper we present a new classification method based on Dictionary Learning (DL). The main contribution consists of a kernel version of incoherent DL, derived from its standard linear counterpart. We also propose an improvement of the…
Asymmetric data naturally exist in real life, such as directed graphs. Different from the common kernel methods requiring Mercer kernels, this paper tackles the asymmetric kernel-based learning problem. We describe a nonlinear extension of…
Kernel methods are ubiquitous tools in machine learning. However, there is often little reason for the common practice of selecting a kernel a priori. Even if a universal approximating kernel is selected, the quality of the finite sample…
Graph Neural Networks (GNNs) have become a standard approach for learning from graph-structured data. However, their reliance on parametric classifiers (most often linear softmax layers) limits interpretability and sometimes hinders…
In recent years, deep learning has revolutionized natural language processing (NLP) by enabling the development of models that can learn complex representations of language data, leading to significant improvements in performance across a…
Successful applications of deep learning (DL) requires large amount of annotated data. This often restricts the benefits of employing DL to businesses and individuals with large budgets for data-collection and computation. Summarization…
Graphs are useful to interpret widely used image processing methods, e.g., bilateral filtering, or to develop new ones, e.g., kernel based techniques. However, simple graph constructions are often used, where edge weight and connectivity…
Kernel $k$-means clustering is a powerful tool for unsupervised learning of non-linearly separable data. Since the earliest attempts, researchers have noted that such algorithms often become trapped by local minima arising from…
Acquiring labels are often costly, whereas unlabeled data are usually easy to obtain in modern machine learning applications. Semi-supervised learning provides a principled machine learning framework to address such situations, and has been…
In this paper, we propose supervised dictionary learning (SDL) by incorporating information on class labels into the learning of the dictionary. To this end, we propose to learn the dictionary in a space where the dependency between the…
Research in modern data-driven dynamical systems is typically focused on the three key challenges of high dimensionality, unknown dynamics, and nonlinearity. The dynamic mode decomposition (DMD) has emerged as a cornerstone for modeling…
Adaptive algorithms based on kernel structures have been a topic of significant research over the past few years. The main advantage is that they form a family of universal approximators, offering an elegant solution to problems with…