相关论文: Fisher and Kernel Fisher Discriminant Analysis: Tu…

Deep kernel learning provides an elegant and principled framework for combining the structural properties of deep learning algorithms with the flexibility of kernel methods. By means of a deep neural network, we learn a parametrized kernel…

We present a new method which generalizes subspace learning based on eigenvalue and generalized eigenvalue problems. This method, Roweis Discriminant Analysis (RDA), is named after Sam Roweis to whom the field of subspace learning owes…

Convolutional neural networks (CNNs) have been successful in representing the fully-connected inferencing ability perceived to be seen in the human brain: they take full advantage of the hierarchy-style patterns commonly seen in complex…

Linear discriminant analysis improves class separability but struggles with non-linearly separable data. To overcome this, we introduce Deep Discriminant Analysis (DDA), which directly optimizes the Fisher criterion utilizing deep networks.…

In this paper, we propose a novel approach named by Discriminative Principal Component Analysis which is abbreviated as Discriminative PCA in order to enhance separability of PCA by Linear Discriminant Analysis (LDA). The proposed method…

In this paper we show how specific families of positive definite kernels serve as powerful tools in analyses of iteration algorithms for multiple layer feedforward Neural Network models. Our focus is on particular kernels that adapt well to…

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…

With the advance of modern technology, more and more data are being recorded continuously during a time interval or intermittently at several discrete time points. They are both examples of "functional data", which have become a prevailing…

This paper addresses an important problem of ranking the pre-trained deep neural networks and screening the most transferable ones for downstream tasks. It is challenging because the ground-truth model ranking for each task can only be…

In this work we explore how the architecture proposed in [8], which expresses the processing steps of the classical Fisher vector pipeline approaches, i.e. dimensionality reduction by principal component analysis (PCA) projection, Gaussian…

In this thesis we examined several multimodal feature extraction and learning methods for retrieval and classification purposes. We reread briefly some theoretical results of learning in Section 2 and reviewed several generative and…

Algebraic topology methods have recently played an important role for statistical analysis with complicated geometric structured data such as shapes, linked twist maps, and material data. Among them, \textit{persistent homology} is a…

We present a general architecture of deep differentiable forest and its sparse attention mechanism. The differentiable forest has the advantages of both trees and neural networks. Its structure is a simple binary tree, easy to use and…

Data matrix centering is an ever-present yet under-examined aspect of data analysis. Functional data analysis (FDA) often operates with a default of centering such that the vectors in one dimension have mean zero. We find that centering…

Classification is an important tool with many useful applications. Among the many classification methods, Fisher's Linear Discriminant Analysis (LDA) is a traditional model-based approach which makes use of the covariance information.…

Functional Data Analysis (FDA) is an extension of traditional data analysis to functional data, for example spectra, temporal series, spatio-temporal images, gesture recognition data, etc. Functional data are rarely known in practice;…

Accurate prediction of Drug-Target Affinity (DTA) is crucial for reducing experimental costs and accelerating early screening in computational drug discovery. While sequence-based deep learning methods avoid reliance on costly 3D…

Principal component analysis (PCA) is a popular tool for linear dimensionality reduction and feature extraction. Kernel PCA is the nonlinear form of PCA, which better exploits the complicated spatial structure of high-dimensional features.…

Deep neural networks have become essential for numerous applications due to their strong empirical performance such as vision, RL, and classification. Unfortunately, these networks are quite difficult to interpret, and this limits their…

Fisher information matrices and neural tangent kernels (NTK) for 2-layer ReLU networks with random hidden weight are argued. We discuss the relation between both notions as a linear transformation and show that spectral decomposition of NTK…