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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…

Constructing the adjacency graph is fundamental to graph-based clustering. Graph learning in kernel space has shown impressive performance on a number of benchmark data sets. However, its performance is largely determined by the chosen…

This work proposes an algorithm for explicitly constructing a pair of neural networks that linearize and reconstruct an embedded submanifold, from finite samples of this manifold. Our such-generated neural networks, called Flattening…

Kernel methods provide a theoretically grounded framework for non-linear and non-parametric learning, with strong analytic foundations and statistical guarantees. Yet, their scalability has long been limited by prohibitive time and memory…

Unified understanding of neuro networks (NNs) gets the users into great trouble because they have been puzzled by what kind of rules should be obeyed to optimize the internal structure of NNs. Considering the potential capability of random…

There exist many high-dimensional data in real-world applications such as biology, computer vision, and social networks. Feature selection approaches are devised to confront with high-dimensional data challenges with the aim of efficient…

We propose a new technique for constructing low-rank approximations of matrices that arise in kernel methods for machine learning. Our approach pairs a novel automatically constructed analytic expansion of the underlying kernel function…

One of the main computational bottlenecks when working with kernel based learning is dealing with the large and typically dense kernel matrix. Techniques dealing with fast approximations of the matrix vector product for these kernel…

Despite the great success of convolutional neural networks (CNN) for the image classification task on datasets like Cifar and ImageNet, CNN's representation power is still somewhat limited in dealing with object images that have large…

Can neural networks learn to compare graphs without feature engineering? In this paper, we show that it is possible to learn representations for graph similarity with neither domain knowledge nor supervision (i.e.\ feature engineering or…

Quantum kernel method is a machine learning model exploiting quantum computers to calculate the quantum kernels (QKs) that measure the similarity between data. Despite the potential quantum advantage of the method, the commonly used…

Kernel methods are widespread in machine learning; however, they are limited by the quadratic complexity of the construction, application, and storage of kernel matrices. Low-rank matrix approximation algorithms are widely used to address…

Nonnegative Matrix Factorization (NMF) has been continuously evolving in several areas like pattern recognition and information retrieval methods. It factorizes a matrix into a product of 2 low-rank non-negative matrices that will define…

Value approximation using deep neural networks is at the heart of off-policy deep reinforcement learning, and is often the primary module that provides learning signals to the rest of the algorithm. While multi-layer perceptron networks are…

Understanding feature representation for deep neural networks (DNNs) remains an open question within the general field of explainable AI. We use principal component analysis (PCA) to study the performance of a k-nearest neighbors classifier…

We consider supervised learning problems within the positive-definite kernel framework, such as kernel ridge regression, kernel logistic regression or the support vector machine. With kernels leading to infinite-dimensional feature spaces,…

Semi-supervised learning algorithms typically construct a weighted graph of data points to represent a manifold. However, an explicit graph representation is problematic for neural networks operating in the online setting. Here, we propose…

We propose a kernelized classification layer for deep networks. Although conventional deep networks introduce an abundance of nonlinearity for representation (feature) learning, they almost universally use a linear classifier on the learned…

Research in both machine learning and psychology suggests that salient examples can help humans to interpret learning models. To this end, we take a novel look at black box interpretation of test predictions in terms of training examples.…

In machine learning it is common to interpret each data point as a vector in Euclidean space. However the data may actually be functional i.e.\ each data point is a function of some variable such as time and the function is discretely…