相关论文: Learning with Cross-Kernels and Ideal PCA

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…

Due to the complexity of cancer, clustering algorithms have been used to disentangle the observed heterogeneity and identify cancer subtypes that can be treated specifically. While kernel based clustering approaches allow the use of more…

Principal component analysis (PCA) is often used for analyzing data in the most diverse areas. In this work, we report an integrated approach to several theoretical and practical aspects of PCA. We start by providing, in an intuitive and…

Point clouds are sets of points in two or three dimensions. Most kernel methods for learning on sets of points have not yet dealt with the specific geometrical invariances and practical constraints associated with point clouds in computer…

Linear principal component analysis (PCA) can be extended to a nonlinear PCA by using artificial neural networks. But the benefit of curved components requires a careful control of the model complexity. Moreover, standard techniques for…

Transfer learning refers to the process of adapting a model trained on a source task to a target task. While kernel methods are conceptually and computationally simple machine learning models that are competitive on a variety of tasks, it…

We consider the problem of learning a mixture of Random Utility Models (RUMs). Despite the success of RUMs in various domains and the versatility of mixture RUMs to capture the heterogeneity in preferences, there has been only limited…

The kernel matrix used in kernel methods encodes all the information required for solving complex nonlinear problems defined on data representations in the input space using simple, but implicitly defined, solutions. Spectral analysis on…

The rapidly growing field of single-cell transcriptomic sequencing (scRNAseq) presents challenges for data analysis due to its massive datasets. A common method in manifold learning consists in hypothesizing that datasets lie on a lower…

Kernel and Multiple Kernel Canonical Correlation Analysis (CCA) are employed to classify schizophrenic and healthy patients based on their SNPs, DNA Methylation and fMRI data. Kernel and Multiple Kernel CCA are popular methods for finding…

Machine learning and deep learning have been used extensively to classify physical surfaces through images and time-series contact data. However, these methods rely on human expertise and entail the time-consuming processes of data and…

Recent work has sought to understand the behavior of neural networks by comparing representations between layers and between different trained models. We examine methods for comparing neural network representations based on canonical…

Feature learning in neural networks is crucial for their expressive power and inductive biases, motivating various theoretical approaches. Some approaches describe network behavior after training through a change in kernel scale from…

For supervised and unsupervised learning, positive definite kernels allow to use large and potentially infinite dimensional feature spaces with a computational cost that only depends on the number of observations. This is usually done…

A low-rank transformation learning framework for subspace clustering and classification is here proposed. Many high-dimensional data, such as face images and motion sequences, approximately lie in a union of low-dimensional subspaces. The…

We present a simple picture of the training process of joint embedding self-supervised learning methods. We find that these methods learn their high-dimensional embeddings one dimension at a time in a sequence of discrete, well-separated…

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…

Deep learning is renowned for its theory-practice gap, whereby principled theory typically fails to provide much beneficial guidance for implementation in practice. This has been highlighted recently by the benign overfitting phenomenon:…

Metric learning for classification has been intensively studied over the last decade. The idea is to learn a metric space induced from a normed vector space on which data from different classes are well separated. Different measures of the…

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…