New discriminant analysis using GDS projection improves face recognition.
problem Improving face recognition accuracy with limited data.
method GDS projection onto generalized difference subspace, simplified Fisher criterion, normalization.
result GDS projection and gFDA are equivalent, inheriting FDA's discriminant ability.
PBN combines generative and discriminative capabilities in a neural network.
problem Combining generative and discriminative capabilities in neural networks.
method Convolutional PBN, sharing FF-NN embodiment, combining generative and discriminative qualities.
result PBN shows excellent qualities from either generative or discriminative viewpoint.
End-to-end CCA optimizes both discriminative and latent space projections for multi-view learning.
problem Lack of class label information in CCA for multi-view learning tasks.
method Simultaneously optimizes a CCA-based and a task objective in an end-to-end manner to learn a non-linear CCA projection.
result Significant improvement in cross-view classification, regularization with a second view, and semi-supervised learning.
The lack of proper class discrimination among the Hyperspectral (HS) data points poses a potential challenge in HS classification. To address this issue, this paper proposes an optimal geometry-aware transformation for enhancing the classification accuracy. The underlying idea of this method is to obtain a linear proje…
The paper analyzes an ensemble of randomly projected linear discriminants for high-dimensional data.
problem Classification issues in small samples of high-dimensional data.
method Asymptotic analysis using random matrix theory.
result The ensemble offers a performance advantage under certain conditions.
Study infinite Euclidean distance discriminants of algebraic varieties.
problem Understanding the structure of data points with infinitely many critical points in Euclidean distance correspondence.
method Developed computer code to compute discriminants and proved properties of fibers.
result Infinite Euclidean distance discriminants contain all data points with infinitely many critical points for the nearest-point problem.
Paper proposes a method to reduce sensor drift in electronic noses.
problem Sensor drift in electronic noses.
method Discriminative subspace projection approach.
result The method minimizes within-class variance and maximizes between-class variance using label information.
Unified framework for multi-view learning with orthogonal projections.
problem Learning individual orthogonal projections for multiple views.
method Successive approximations via eigenvectors, iterative Krylov subspace method.
result Consistently competitive and often better than existing methods.
MILDA uses unlabelled data to compute LDA projections.
problem Training LDA models with unlabelled data.
method Minimal prior information to compute LDA projection vector.
result MILDA closely matches supervised LDA performance and adapts to non-stationary data.
We describe topologically the discriminant locus of a smooth cubic surface in the complex projective space CP3 that contains 5 fibres of the projection CP3⟶S4.
We propose a novel, projection based way to incorporate the conditional information into the discriminator of GANs that respects the role of the conditional information in the underlining probabilistic model. This approach is in contrast with most frameworks of conditional GANs used in application today, which use the …
The study classifies points on ruled surfaces in 4-space based on geometric properties.
problem Characterizing points on smooth ruled surfaces in 4-space.
method Contact with transverse planes, binary differential equations, and projective transformations.
result Parabolic points on ruled surfaces in 4-space can be classified as butterfly hyperbolic, parabolic, or elliptic based on the discriminant of a binary differential equation.
A variety of real-world tasks involve the classification of images into pre-determined categories. Designing image classification algorithms that exhibit robustness to acquisition noise and image distortions, particularly when the available training data are insufficient to learn accurate models, is a significant chall…
Improves deep learning with less labeled data using unsupervised projection.
problem Lack of labeled data for deep learning models.
method Modified unsupervised discriminant projection as a regularization term for semi-supervised learning.
result Proposes an algorithm that enhances classification performance with minimal labeled data.
We study the problem of supervised linear dimensionality reduction, taking an information-theoretic viewpoint. The linear projection matrix is designed by maximizing the mutual information between the projected signal and the class label (based on a Shannon entropy measure). By harnessing a recent theoretical result on…
Wasserstein Discriminant Analysis (WDA) is a new supervised method that can improve classification of high-dimensional data by computing a suitable linear map onto a lower dimensional subspace. Following the blueprint of classical Linear Discriminant Analysis (LDA), WDA selects the projection matrix that maximizes the …
Develops MGQDA for multi-group classification with theoretical guarantees and practical applications.
problem Complex multi-group classification problems with nonlinear decision boundaries and group-specific covariance patterns.
method MGQDA, a method based on quadratic discriminant analysis that projects predictors onto a lower-dimensional subspace.
result MGQDA achieves competitive or improved predictive performance compared to existing methods.
Kernel discriminant analysis uses nonlinear embeddings to improve classification.
problem Limited effectiveness of linear discriminant analysis in capturing nonlinear features.
method Study of nonlinear embeddings in kernel discriminant analysis using polynomial and Gaussian kernels, solving generalized eigenvalue problems.
result Polynomial and Gaussian discriminants capture class differences through population moments and randomized projections.
VPFD uses vocoder features for adversarial training in VC.
problem Adversarial training on waveform data is time-consuming and memory-intensive.
method VPFD employs vocoder features for adversarial training.
result VPFD achieves VC performance comparable to waveform discriminators with reduced training time and memory.
Torsion objects of von Neumann categories describe the phenomen "spectrum near zero" discovered by S. Novikov and M. Shubin. In this paper we classify Hermitian forms on torsion objects of a finite von Neumann category. We prove that any such form can be represented as a discriminant form of a degenerate Hermitian form…
A new algorithm interprets DR dimensions and selects features.
problem Lack of interpretability in DR algorithms.
method I-KDR algorithm that maps data to a lower dimensional space with interpretable dimensions and feature selection.
result I-KDR provides better interpretations and higher discriminative performance.
The paper develops a method for optimal projection selection in high-dimensional classification.
problem High-dimensional classification with latent variable structure.
method Formulates a latent-variable model and proposes a computationally efficient classifier.
result Explicit rates of convergence for excess risk of the proposed classifier are derived and shown to be optimal.
New method studies discriminantal loci of algebraic varieties.
problem Understanding discriminantal loci of algebraic varieties.
method Efficient use of groupoids to describe monodromy.
result New insights into discriminantal loci of hypersurfaces.
FairUDT uses uplift decision trees to detect and mitigate discrimination in training data.
problem Bias in machine learning classifiers due to historical discrimination or underrepresentation of minority groups.
method Integrates uplift modeling with decision trees and introduces a modified leaf relabeling approach for fairness.
result Achieves an acceptable accuracy-discrimination tradeoff while maintaining interpretability.
Proposes KMvDA for object recognition from multi-view data.
problem Recognizing objects from different views, even when views are heterogeneous.
method Introduces kernel multi-view discriminant analysis (KMvDA) and uses random Fourier features (RFF) for large-scale learning.
result KMvDA and RFF approximation improve object recognition from multi-view data.
Paper analyzes null space for class-specific discriminant learning.
problem Improving discriminant learning for class-specific problems.
method Null space analysis for Class-Specific Discriminant Analysis (CSDA).
result Proposed solutions outperform standard CSDA methods.
Explains Fisher and Kernel Fisher Discriminant Analysis with examples and comparisons.
problem Classifying data with different features and dimensions.
method Projection and reconstruction, scatters analysis, PCA comparison, Fisher forest.
result Equivalence of Fisher and Linear Discriminant Analysis, effectiveness of Fisher forest.
Semi-supervised model learns multi-view data representations.
problem Learning discriminative representations with limited labeled data.
method Multi-view Discriminative Neural Network (MDNN) with coupled deep networks.
result MDNN effectively separates and clusters samples from different and same classes.
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…
Neural networks use their hidden layers to transform input data into linearly separable data clusters, with a linear or a perceptron type output layer making the final projection on the line perpendicular to the discriminating hyperplane. For complex data with multimodal distributions this transformation is difficult t…
SDSPCAAN combines supervised and local data structures for better dimensionality reduction.
problem Preserving both global and local data structures for noisy high-dimensional data.
method Supervised discriminative sparse PCA with adaptive neighbors (SDSPCAAN).
result SDSPCAAN improves classification accuracy on high-dimensional datasets.
Improves conditional GANs' robustness to noisy labels.
problem Learning conditional generators from noisy labeled samples.
method Introduces Robust Conditional GAN (RCGAN) and RCGAN-U architectures.
result Improves quality and accuracy of generated samples from noisy labels.
SONA improves conditional generation by balancing authenticity and alignment.
problem Challenges in balancing authenticity and conditional alignment in conditional generative models.
method SONA integrates unconditional discrimination, matching-aware supervision, and adaptive weighting to balance authenticity and alignment.
result SONA achieves superior sample quality and conditional alignment compared to state-of-the-art methods.
Faster reconstruction of compressed signals using conditional GAN and NPGD.
problem Recovering compressed signals from measurements.
method Network-based projected gradient descent (NPGD) combined with measurement-conditional generative adversarial networks (GANs/BEGANs).
result Significant speed-up in reconstruction (up to 140-175 times faster).
Simple fine-tuning of GANs with frozen discriminator outperforms existing methods.
problem Fine-tuning GANs requires numerous data and heavy computation.
method Freeze lower layers of the discriminator for fine-tuning.
result FreezeD significantly outperforms previous techniques on various datasets.
Recent work has shown that state-of-the-art models are highly vulnerable to adversarial perturbations of the input. We propose cowboy, an approach to detecting and defending against adversarial attacks by using both the discriminator and generator of a GAN trained on the same dataset. We show that the discriminator con…
Study shows special Kähler geometry on base of holomorphic Lagrangian fibrations implies projective space.
problem Understanding the geometry of holomorphic Lagrangian fibrations.
method Using special Kähler geometry and parallel splitting of tangent bundles.
result Holomorphic Lagrangian fibrations over non-projective spaces are impossible.
Proposes a new layer for efficient 3D shape discrimination.
problem Irregular structure and redundancy in 3D point clouds hinder efficient inter-class discrimination.
method Integrates Blended Convolution and Synthesis layer that projects and synthesizes 3D point clouds, followed by 3D convolution in the unit ball.
result End-to-end architecture achieves compelling results on 3D shape recognition and retrieval.
A new adaptive kNN classifier outperforms Random Forests.
problem Improving classification accuracy using nearest neighbors.
method Finding discriminant subspaces for efficient nearest neighbor classification, leveraging bagging for diversity.
result The proposed method outperforms Random Forests and other nearest neighbors ensembles.
This paper studies global webs on the projective plane with vanishing curvature. The study is based on an interplay of local and global arguments. The main local ingredient is a criterium for the regularity of the curvature at the neighborhood of a generic point of the discriminant. The main global ingredient, the Lege…
Structure-preserving GANs learn distributions with group symmetry efficiently.
problem Learning distributions with group symmetry efficiently.
method Developed structure-preserving GANs by reducing the discriminator space and designing structured generators.
result Significantly improved sample fidelity and diversity in small data regimes.
A Longitudinal Attribute-Conditioned Neural Network (LANTERN) framework for modeling health-state transition probabilities in irregular longitudinal data.
problem Estimating long-term care transition probabilities in irregular longitudinal health data.
method A neural network that learns from individual health history, incorporates time elapsed, and conditions on demographic and socioeconomic attributes.
result Improves severe disability discrimination and maintains strong calibration.
Random Projection (RP) technique has been widely applied in many scenarios because it can reduce high-dimensional features into low-dimensional space within short time and meet the need of real-time analysis of massive data. There is an urgent need of dimensionality reduction with fast increase of big genomics data. Ho…
A new algorithm improves Wasserstein discriminant analysis for better data classification.
problem Improving data classification in machine learning.
method Bi-level nonlinear eigenvector algorithm (WDA-nepv) for optimal transport and trace ratio optimizations.
result WDA-nepv enhances classification accuracy and scalability.
G-PATE generates private data with high utility using teacher-discriminator aggregation.
problem Privacy concerns in large-scale data sharing for machine learning.
method Generative adversarial nets combined with private gradient aggregation among discriminators.
result Significantly improves privacy budget efficiency and data utility.
EAGC boosts GCD by regulating gradient entanglement, improving known and novel category separability.
problem Gradient entanglement distorts supervised gradients and overlaps known and novel class representations.
method EAGC uses AGA and EEP to align and project gradients, reducing entanglement and overlap.
result EAGC consistently boosts GCD performance, setting new state-of-the-art results.
Novel L1-norm and L2-norm LDA methods improve discriminant analysis.
problem Improving linear discriminant analysis for robustness and adaptability.
method Proposes L1BLDA and L2BLDA using Bhattacharyya error bound, maximizing between-class scatters and minimizing within-class scatters.
result Proposed methods avoid SSS and have no rank limit, demonstrating robust performance and effectiveness.
This paper is devoted to the classification of connected components of Prym eigenform loci in the strata H(2,2)^odd and H(1,1,2) in the Abelian differentials bundle in genus 3. These loci, discovered by McMullen are GL^+(2,R)-invariant submanifolds (of complex dimension 3) that project to the locus of Riemann surfaces …