- Haley D., Kamalinejad E., Zhong F., "IsoClustering: A Generalized Framework for Local Data Clustering", 2016, submitted
- Kamalinejad E., "On local well-posedness of the thin-film equation via the Wasserstein gradient flow", 2015, Springer: Calculus of Variations and Partial Differential Equations, Volume 52, Issue 3, pp 547–564
- Kamalinejad E., Moradifam A., "Radial Symmetry of Large Solutions of Semilinear Elliptic Equations with Convection",2014, Proceedings of the Royal Society of Edinburgh: Section A Mathematics, Volume 144, Issue 1, pp. 139-147
- Kamalinejad E., "An Optimal Transport Approach to Nonlinear Evolution Equations", 2012, University of Toronto PhD Thesis
- AlNabulsiy S., Kamalinejad E., Meskasx J., Wang J., Yink K., Downton J., "Azimuthal Elastic Inversion for Fracture Characterization", 2012, IMA Preprint Series # 2399
- Kamalinejad E., "Analysis of Natural Framing of Knots", 2007, Shahid Beheshti University, MSc Thesis

Publications

We started this project with Thomas Laurent and Kevin Costello at UC Riverside. In this project, we proposed the newly developed method of graph sparcification based on NI-forest sampling as a preprocessing step for L1 Cheeger cut clustering. We showed that this approach results in a competitively fast yet very accurate clustering algorithm. This project is a work in progress. You can find some preliminary results that we presented at American Mathematical Society Sectional Conference here.

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Projects

Graph Sparsification for L1 Clustering

We are working on this project with Fay Zhong, and David Haley. In this project, we proposed a new method of unsupervised classification based on geometric ideas borrowed from properties of smooth surfaces. The first phase of the project is done and resulted in a fast parallelizable algorithm that can handle overlapping clusters. The corresponding paper is submitted. We are working on the second phase of the project which deals with overlapping clusters.

A Geometric Approach to Unsupervised Classifications

This is a tutorial developed for my machine learning course. In this tutorial, we build a feed forward neural network from scratch. This tutorial show all of the steps in building a feed forward neural network. We also provide some functions to visualize the evolution of the learning process to help understand how it works. Here is the tutorial code in Python (Jupyter Notebook).

Multilayer Neural Networks with Visualization

This is a tutorial developed for my mathematical modeling course. In this tutorial, we study all of the steps involved in developing a robust scientific model for 2D waves. The project studies efficient scientific modeling both from theoretical and practical points of view. The implementation allows for the computations to be deployed on a cluster/GPU. Hence this could be used as a guide for similar modeling problems with heavy computations.

Here is the tutorial code in Python (Jupyter Notebook).

Parallel Computation for Solving 2D Wave Equation

In this project, we are studying the problem of object recognition when the input has different modes (e.g. visual and sound data). In the first phase of the project, we used data captured from the Microsoft HoloLens headset to do a real-time face recognition. In this setting, we are using visual and depth sensors of the headset. In the future, we want to expand this project to include more modes in the input and attack more challenging setups in object recognition.

Multimodal Object Recognition