A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
A new method improves few-shot learning by combining ProtoNet with LFD.
Extends Fisher's Discriminant Analysis for interval-valued data.
Paper introduces new loss functions for Siamese networks using FDA.
Survey of spectral, probabilistic, and deep metric learning methods.
This paper proposes a new subspace learning method, named Quantized Fisher Discriminant Analysis (QFDA), which makes use of both machine learning and information theory. There is a lack of literature for combination of machine learning and information theory and this paper tries to tackle this gap. QFDA finds a subspac…
This is a detailed tutorial paper which explains the Fisher discriminant Analysis (FDA) and kernel FDA. We start with projection and reconstruction. Then, one- and multi-dimensional FDA subspaces are covered. Scatters in two- and then multi-classes are explained in FDA. Then, we discuss on the rank of the scatters and …
New framework assesses neural sensitivity to small perturbations.
This paper discusses a new type of discriminant analysis based on the orthogonal projection of data onto a generalized difference subspace (GDS). In our previous work, we have demonstrated that GDS projection works as the quasi-orthogonalization of class subspaces, which is an effective feature extraction for subspace …
We propose to investigate test statistics for testing homogeneity in reproducing kernel Hilbert spaces. Asymptotic null distributions under null hypothesis are derived, and consistency against fixed and local alternatives is assessed. Finally, experimental evidence of the performance of the proposed approach on both ar…
A new weighted FDA method improves face recognition accuracy.
A new classification rule for FDA improves classification performance by accounting for unequal covariance matrices.
Fisher discriminant analysis (FDA) is a widely used method for classification and dimensionality reduction. When the number of predictor variables greatly exceeds the number of observations, one of the alternatives for conventional FDA is regularized Fisher discriminant analysis (RFDA). In this paper, we present a simp…
Unified analysis of multilabel Fisher discriminants with improved dimensionality and robustness.
Unified analysis of multilabel Fisher discriminants with improved dimensionality and robustness.
Section 1.3 was incorrect, and 2.1 will be removed from further submissions. A rewritten version will be posted in the future.
A new QDA classifier for high-dimensional data with spiked covariance.
We propose a Bayesian framework of Gaussian process in order to extend Fisher's discriminant to classify functional data such as spectra and images. The probability structure for our extended Fisher's discriminant is explicitly formulated, and we utilize the smoothness assumptions of functional data as prior probabilit…
This tutorial explains Linear Discriminant Analysis (LDA) and Quadratic Discriminant Analysis (QDA) as two fundamental classification methods in statistical and probabilistic learning. We start with the optimization of decision boundary on which the posteriors are equal. Then, LDA and QDA are derived for binary and mul…
Fisher's linear discriminant analysis (FLDA) is an important dimension reduction method in statistical pattern recognition. It has been shown that FLDA is asymptotically Bayes optimal under the homoscedastic Gaussian assumption. However, this classical result has the following two major limitations: 1) it holds only fo…
A new algorithm improves Wasserstein discriminant analysis for better data classification.
SQFA learns features maximizing Fisher-Rao distance for better classification.
Kernel discriminant analysis uses nonlinear embeddings to improve classification.
Linear Discriminant Analysis (LDA) is a well-known method for dimensionality reduction and classification. Previous studies have also extended the binary-class case into multi-classes. However, many applications, such as object detection and keyframe extraction cannot provide consistent instance-label pairs, while LDA …
Optimal domain adaptation model using Fisher's Linear Discriminant.
We examine Generative Adversarial Networks (GANs) through the lens of deep Energy Based Models (EBMs), with the goal of exploiting the density model that follows from this formulation. In contrast to a traditional view where the discriminator learns a constant function when reaching convergence, here we show that it ca…
Tandem mass spectrometry (MS/MS) is a high-throughput technology used toidentify the proteins in a complex biological sample, such as a drop of blood. A collection of spectra is generated at the output of the process, each spectrum of which is representative of a peptide (protein subsequence) present in the original co…
Fisher loss improves deep domain adaptation by learning discriminative within-class compact and between-class separable representations.
Adaptive classifier optimizes high-dimensional data with spiked covariance structure.
Generative models of eye gaze help identify viewers from images.
Survey of Locally Linear Embedding and its variants.
Paper improves matrix-valued data classification using nonparametric LDA.
This paper is a tutorial for eigenvalue and generalized eigenvalue problems. We first introduce eigenvalue problem, eigen-decomposition (spectral decomposition), and generalized eigenvalue problem. Then, we mention the optimization problems which yield to the eigenvalue and generalized eigenvalue problems. We also prov…
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 significantly. RDA is a family of infinite number of algorithms where Principal Comp…
Clustering in high-dimensional spaces is nowadays a recurrent problem in many scientific domains but remains a difficult task from both the clustering accuracy and the result understanding points of view. This paper presents a discriminative latent mixture (DLM) model which fits the data in a latent orthonormal discrim…
Researchers use information geometry to analyze and improve DRWs for node classification.
For high-dimensional classification, it is well known that naively performing the Fisher discriminant rule leads to poor results due to diverging spectra and noise accumulation. Therefore, researchers proposed independence rules to circumvent the diverse spectra, and sparse independence rules to mitigate the issue of n…
The paper solves optimal bounds for separating data points in high dimensions.
We study the problem of inferring readers' identities and estimating their level of text comprehension from observations of their eye movements during reading. We develop a generative model of individual gaze patterns (scanpaths) that makes use of lexical features of the fixated words. Using this generative model, we d…
A framework compares image representations based on local geometry.
LDA improves image classification accuracy with fewer features.
New method speeds up solving orthogonality constrained problems.
New tensor framework connects Fisher information, hypergraphs, and multi-observable correlations.
Study local convergence of GDA for training GANs with kernel-based discriminators.
It is well known that in a supervised classification setting when the number of features is smaller than the number of observations, Fisher's linear discriminant rule is asymptotically Bayes. However, there are numerous modern applications where classification is needed in the high-dimensional setting. Naive implementa…
Data processing inequalities link Fisher information to local differential privacy constraints.
Multivariate Pattern (MVP) classification can map different cognitive states to the brain tasks. One of the main challenges in MVP analysis is validating the generated results across subjects. However, analyzing multi-subject fMRI data requires accurate functional alignments between neuronal activities of different sub…
We present local discriminative Gaussian (LDG) dimensionality reduction, a supervised dimensionality reduction technique for classification. The LDG objective function is an approximation to the leave-one-out training error of a local quadratic discriminant analysis classifier, and thus acts locally to each training po…
In this paper, we propose a method for image-set classification based on convex cone models, focusing on the effectiveness of convolutional neural network (CNN) features as inputs. CNN features have non-negative values when using the rectified linear unit as an activation function. This naturally leads us to model a se…