84 citations · 697 across the 67 of their papers we have counts for
25 papers · 1 filter
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…
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…
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…
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…
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…
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…
Reproducing Kernel Hilbert Space, Mercer's Theorem, Eigenfunctions, Nyström Method, and Use of Kernels in Machine Learning: Tutorial and Survey
Benyamin Ghojogh, Ali Ghodsi, Fakhri Karray +1
This is a tutorial and survey paper on kernels, kernel methods, and related fields. We start with reviewing the history of kernels in functional analysis and machine learning. Then…
Unified Framework for Spectral Dimensionality Reduction, Maximum Variance Unfolding, and Kernel Learning By Semidefinite Programming: Tutorial and Survey
Benyamin Ghojogh, Ali Ghodsi, Fakhri Karray +1
This is a tutorial and survey paper on unification of spectral dimensionality reduction methods, kernel learning by Semidefinite Programming (SDP), Maximum Variance Unfolding (MVU)…
Laplacian-Based Dimensionality Reduction Including Spectral Clustering, Laplacian Eigenmap, Locality Preserving Projection, Graph Embedding, and Diffusion Map: Tutorial and Survey
Benyamin Ghojogh, Ali Ghodsi, Fakhri Karray +1
This is a tutorial and survey paper for nonlinear dimensionality and feature extraction methods which are based on the Laplacian of graph of data. We first introduce adjacency matr…
Generative Locally Linear Embedding
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…
Factor Analysis, Probabilistic Principal Component Analysis, Variational Inference, and Variational Autoencoder: Tutorial and Survey
Benyamin Ghojogh, Ali Ghodsi, Fakhri Karray +1
This is a tutorial and survey paper on factor analysis, probabilistic Principal Component Analysis (PCA), variational inference, and Variational Autoencoder (VAE). These methods, w…
Locally Linear Embedding and its Variants: Tutorial and Survey
Benyamin Ghojogh, Ali Ghodsi, Fakhri Karray +1
This is a tutorial and survey paper for Locally Linear Embedding (LLE) and its variants. The idea of LLE is fitting the local structure of manifold in the embedding space. In this…
Multidimensional Scaling, Sammon Mapping, and Isomap: Tutorial and Survey
Benyamin Ghojogh, Ali Ghodsi, Fakhri Karray +1
Multidimensional Scaling (MDS) is one of the first fundamental manifold learning methods. It can be categorized into several methods, i.e., classical MDS, kernel classical MDS, met…
Stochastic Neighbor Embedding with Gaussian and Student-t Distributions: Tutorial and Survey
Benyamin Ghojogh, Ali Ghodsi, Fakhri Karray +1
Stochastic Neighbor Embedding (SNE) is a manifold learning and dimensionality reduction method with a probabilistic approach. In SNE, every point is consider to be the neighbor of…
Batch-Incremental Triplet Sampling for Training Triplet Networks Using Bayesian Updating Theorem
Milad Sikaroudi, Benyamin Ghojogh, Fakhri Karray +2
Variants of Triplet networks are robust entities for learning a discriminative embedding subspace. There exist different triplet mining approaches for selecting the most suitable t…
Quantile-Quantile Embedding for Distribution Transformation and Manifold Embedding with Ability to Choose the Embedding Distribution
Benyamin Ghojogh, Fakhri Karray, Mark Crowley
We propose a new embedding method, named Quantile-Quantile Embedding (QQE), for distribution transformation and manifold embedding with the ability to choose the embedding distribu…
Weighted Fisher Discriminant Analysis in the Input and Feature Spaces
Benyamin Ghojogh, Milad Sikaroudi, H. R. Tizhoosh +2
Fisher Discriminant Analysis (FDA) is a subspace learning method which minimizes and maximizes the intra- and inter-class scatters of data, respectively. Although, in FDA, all the…
Roweis Discriminant Analysis: A Generalized Subspace Learning Method
Benyamin Ghojogh, Fakhri Karray, Mark Crowley
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…
Quantized Fisher Discriminant Analysis
Benyamin Ghojogh, Ali Saheb Pasand, Fakhri Karray +1
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…
Locally Linear Image Structural Embedding for Image Structure Manifold Learning
Benyamin Ghojogh, Fakhri Karray, Mark Crowley
Most of existing manifold learning methods rely on Mean Squared Error (MSE) or norm. However, for the problem of image quality assessment, these are not promising measure.…
Fisher and Kernel Fisher Discriminant Analysis: Tutorial
Benyamin Ghojogh, Fakhri Karray, Mark Crowley
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-dimensiona…
Unsupervised and Supervised Principal Component Analysis: Tutorial
Benyamin Ghojogh, Mark Crowley
This is a detailed tutorial paper which explains the Principal Component Analysis (PCA), Supervised PCA (SPCA), kernel PCA, and kernel SPCA. We start with projection, PCA with eige…
Linear and Quadratic Discriminant Analysis: Tutorial
Benyamin Ghojogh, Mark Crowley
This tutorial explains Linear Discriminant Analysis (LDA) and Quadratic Discriminant Analysis (QDA) as two fundamental classification methods in statistical and probabilistic learn…
The Theory Behind Overfitting, Cross Validation, Regularization, Bagging, and Boosting: Tutorial
Benyamin Ghojogh, Mark Crowley
In this tutorial paper, we first define mean squared error, variance, covariance, and bias of both random variables and classification/predictor models. Then, we formulate the true…