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