activity
20172026
most citedLinear and Quadratic Discriminant Analysis: Tutorial

84 citations · 697 across the 67 of their papers we have counts for

collaborators

67 papers

cs.CV2026

LoRSA: Toward Generalizable Parameter-Efficient Fine-Tuning for Biomedical Downstream Tasks

Saed Moradi, Benyamin Ghojogh, M. Hadi Sepanj +2

Parameter-efficient fine-tuning enables the adaptation of vision foundation models to biomedical tasks under limited computational resources, but a single low-rank update can const…

stat.ML2026

Data Evolution by Wittgenstein's Rule Following

Aydin Ghojogh, Benyamin Ghojogh

This paper introduces Wittgenstein's Rule Following (WRF) data evolution, a framework in philomatics for evolving or generating a new dataset from a sequence of previously observed…

math.DG2026

Foundations of Riemannian Geometry for Riemannian Optimization: A Monograph with Detailed Derivations

Benyamin Ghojogh

Riemannian geometry provides the fundamental framework for optimization on nonlinear spaces such as matrix manifolds, which arise in machine learning, signal processing, and roboti…

math.RA2026

Similarity Algebra: A Framework for Approximate Algebraic and Lie Structures with Collapse to Classical Algebra

Benyamin Ghojogh, Golbahar Amanpour

Classical algebraic structures require exact satisfaction of their defining axioms. We propose similarity algebra, a framework extending algebraic and Lie structures to settings wh…

cs.LG2026

On the Relation of State Space Models and Hidden Markov Models

Aydin Ghojogh, M. Hadi Sepanj, Benyamin Ghojogh

State Space Models (SSMs) and Hidden Markov Models (HMMs) are foundational frameworks for modeling sequential data with latent variables and are widely used in signal processing, c…

cs.LG2026

Wittgenstein's Family Resemblance Clustering Algorithm

Golbahar Amanpour, Benyamin Ghojogh

This paper, introducing a novel method in philomatics, draws on Wittgenstein's concept of family resemblance from analytic philosophy to develop a clustering algorithm for machine…

cs.LG2025

Self-Supervised Learning by Curvature Alignment

Benyamin Ghojogh, M. Hadi Sepanj, Paul Fieguth

Self-supervised learning (SSL) has recently advanced through non-contrastive methods that couple an invariance term with variance, covariance, or redundancy-reduction penalties. Wh…

stat.ML2025

Kernel VICReg for Self-Supervised Learning in Reproducing Kernel Hilbert Space

M. Hadi Sepanj, Benyamin Ghojogh, Saed Moradi +1

Self-supervised learning (SSL) has emerged as a powerful paradigm for representation learning by optimizing geometric objectives, such as invariance to augmentations, variance pres…

cs.LG2025★ 4 cited

Self-Supervised Learning Using Nonlinear Dependence

M. Hadi Sepanj, Benyamin Ghojogh, Paul Fieguth

Self-supervised learning has gained significant attention in contemporary applications, particularly due to the scarcity of labeled data. While existing SSL methodologies primarily…

cs.LG2025

An Optimal Cascade Feature-Level Spatiotemporal Fusion Strategy for Anomaly Detection in CAN Bus

Mohammad Fatahi, Danial Sadrian Zadeh, Benyamin Ghojogh +2

Intelligent transportation systems (ITS) play a pivotal role in modern infrastructure but face security risks due to the broadcast-based nature of the in-vehicle Controller Area Ne…

stat.ML2023

Probabilistic Classification by Density Estimation Using Gaussian Mixture Model and Masked Autoregressive Flow

Benyamin Ghojogh, Milad Amir Toutounchian

Density estimation, which estimates the distribution of data, is an important category of probabilistic machine learning. A family of density estimators is mixture models, such as…

math.HO2023

On Philomatics and Psychomatics for Combining Philosophy and Psychology with Mathematics

Benyamin Ghojogh, Morteza Babaie

We propose the concepts of philomatics and psychomatics as hybrid combinations of philosophy and psychology with mathematics. We explain four motivations for this combination which…

cs.LG2023★ 17 cited

Recurrent Neural Networks and Long Short-Term Memory Networks: Tutorial and Survey

Benyamin Ghojogh, Ali Ghodsi

This is a tutorial paper on Recurrent Neural Network (RNN), Long Short-Term Memory Network (LSTM), and their variants. We start with a dynamical system and backpropagation through…

cs.LG2022★ 1 cited

Gravitational Dimensionality Reduction Using Newtonian Gravity and Einstein's General Relativity

Benyamin Ghojogh, Smriti Sharma

Due to the effectiveness of using machine learning in physics, it has been widely received increased attention in the literature. However, the notion of applying physics in machine…

cs.LG2022★ 1 cited

Affective Manifolds: Modeling Machine's Mind to Like, Dislike, Enjoy, Suffer, Worry, Fear, and Feel Like A Human

Benyamin Ghojogh

After the development of different machine learning and manifold learning algorithms, it may be a good time to put them together to make a powerful mind for machine. In this work,…

stat.ML2022★ 2 cited

Theoretical Connection between Locally Linear Embedding, Factor Analysis, and Probabilistic PCA

Benyamin Ghojogh, Ali Ghodsi, Fakhri Karray +1

Locally Linear Embedding (LLE) is a nonlinear spectral dimensionality reduction and manifold learning method. It has two main steps which are linear reconstruction and linear embed…

cs.LG2022

On Manifold Hypothesis: Hypersurface Submanifold Embedding Using Osculating Hyperspheres

Benyamin Ghojogh, Fakhri Karray, Mark Crowley

Consider a set of data points in the Euclidean space . This set is called dataset in machine learning and data science. Manifold hypothesis states that the datase…

stat.ML2022★ 14 cited

Spectral, Probabilistic, and Deep Metric Learning: Tutorial and Survey

Benyamin Ghojogh, Ali Ghodsi, Fakhri Karray +1

This is a tutorial and survey paper on metric learning. Algorithms are divided into spectral, probabilistic, and deep metric learning. We first start with the definition of distanc…

cs.LG2021★ 2 cited

Generative Adversarial Networks and Adversarial Autoencoders: Tutorial and Survey

Benyamin Ghojogh, Ali Ghodsi, Fakhri Karray +1

This is a tutorial and survey paper on Generative Adversarial Network (GAN), adversarial autoencoders, and their variants. We start with explaining adversarial learning and the van…

stat.ME2021

Sufficient Dimension Reduction for High-Dimensional Regression and Low-Dimensional Embedding: Tutorial and Survey

Benyamin Ghojogh, Ali Ghodsi, Fakhri Karray +1

This is a tutorial and survey paper on various methods for Sufficient Dimension Reduction (SDR). We cover these methods with both statistical high-dimensional regression perspectiv…

math.OC2021★ 20 cited

KKT Conditions, First-Order and Second-Order Optimization, and Distributed Optimization: Tutorial and Survey

Benyamin Ghojogh, Ali Ghodsi, Fakhri Karray +1

This is a tutorial and survey paper on Karush-Kuhn-Tucker (KKT) conditions, first-order and second-order numerical optimization, and distributed optimization. After a brief review…

cs.HC2021★ 37 cited

Uniform Manifold Approximation and Projection (UMAP) and its Variants: Tutorial and Survey

Benyamin Ghojogh, Ali Ghodsi, Fakhri Karray +1

Uniform Manifold Approximation and Projection (UMAP) is one of the state-of-the-art methods for dimensionality reduction and data visualization. This is a tutorial and survey paper…

stat.ML2021★ 4 cited

Johnson-Lindenstrauss Lemma, Linear and Nonlinear Random Projections, Random Fourier Features, and Random Kitchen Sinks: Tutorial and Survey

Benyamin Ghojogh, Ali Ghodsi, Fakhri Karray +1

This is a tutorial and survey paper on the Johnson-Lindenstrauss (JL) lemma and linear and nonlinear random projections. We start with linear random projection and then justify its…

math.OC2021

Vector Transport Free Riemannian LBFGS for Optimization on Symmetric Positive Definite Matrix Manifolds

Reza Godaz, Benyamin Ghojogh, Reshad Hosseini +3

This work concentrates on optimization on Riemannian manifolds. The Limited-memory Broyden-Fletcher-Goldfarb-Shanno (LBFGS) algorithm is a commonly used quasi-Newton method for num…