2021

Topological Analysis of Transneuronal Spreading Mechanisms in Neurodegenerative Diseases by Persistent Homology

In the light of new advancements in algebraic topology, we give an introductory exhibition on the usage of simplicial complexes and persistent homology in the analysis of spatiotemporal patterns in the physiological deterioration caused by Alzheimer's disease and its precursor, mild cognitive impairment.

Revisiting Deep Learning based Classification Methods of
Diabetic Retinopathy and Macular Edema in 2D Fundus Photography

We provide a glimpse into the ongoing research of retinal image classification with deep learning methods in medical literature. Specifically, we provide a meta-analysis of new techniques towards the classification of retinal disorders such as diabetic retinopathy and macular edema.

A Category-Theoretic Perspective of Information Theory

We present an axiomatization of Claude Shannon's work "A mathematical theory of communication" from a categorical point of view using Categories, natural transformations, functors, morphisms, etc.

2019

Punctuation Restoration in Unsegmented Text with Deep Convolutional Neural Networks

In this work we suggest an approach to predict marks of punctuation for unsegmented text corpora. A Deep Convolutional Neural Network (DCNN) model is implemented to determine if a punctuation mark should be inserted in a word window of lenght 30. The goal is to find the optimal weights \(W\) and biases \(b\) within cost function \(C\): $$ \underset{W, b}{\arg \min } C=\frac{1}{2 N} \sum_{i=1}^{N}\left\|\hat{Y}_{i}-Y_{i}\right\|^{2}+\frac{\lambda}{2} \sum_{l=1}^{L-1}\left\|W_{l}\right\|_{F}^{2}$$ We empirically show the effectiveness of our proposed architecture outperforming previous state-of-the-art solutions.

Predicting Most Important Passages in YouTube Tech
Talks with Unsupervised Graph-Based Ranking Models

Visualizing importance predictions (colored in red) over the time axis which are smoothened by Weierstrass Transform.

Word Embeddings (WE) have recently imposed themselves as a standard for representing word meaning in NLP. In this work, we propose the unsupervised application of graph-based ranking models to video speech captions, building a graph that interconnects words represented by GloVe embeddings. For a sentence \(V_{i}\), the weighted rank is defined as: $$ W S\left(V_{i}\right)=(1-d)+d * \sum_{V_{j} \in I n\left(V_{i}\right)} \frac{w_{j i}}{\sum_{V_{k} \in O u t\left(V_{j}\right)} w_{j k}} W S\left(V_{j}\right) $$

2017

Food Image Recognition System for Cooking Recipe Retrieval

We propose a novel approach for food image retrieval by combining Deep Convolutional Neural Network (DCNN) and Approximate Nearest Neighbor (ANN) scores. In our re-ranking scheme, we retrieve the best candidates first using only the CNN scores and then re-rank the top K results using the ANN scores, giving the model additional performance improvement.

2016

Genetic Algorithm for Self-Referential Image Approximation

Mona Lisa after 120'000 generations approximated with 260 individuals.

We propose an approach to solve the image matching problem with some stochastic optimization approach, in which the search for the optimal solution involves randomness in some constructive way. If \(\mathcal{S}\) denotes the (finite) set of all possible solutions, the task we consider is to maximize or minimize the objective function \(f : \mathcal{S} \rightarrow \mathbb{R}\). In the case of maximization, on which we focus here, the problem is to find a configuration \(x_{o p t} \in \mathcal{S}\) which satisfies $$ f\left(x_{o p t}\right) \geq f(x) \text { for all } x \in \mathcal{S} $$

2015

Discrete Optimization Algorithm for Converting an Image to a Connected Graph of Strings

Face approximated by 6000 lines to linked string graph using discrete optimization.

By using ordinary linear least squares for the optimization task, defined by $$ \min _{x}\|A x-y\|_{2}^{2} \quad \text { with } \quad A : \mathbb{R}^{n} \rightarrow \mathbb{R}^{m} $$ we propose an algorithm which takes a normal image as input and turns it into a linked string graph that best attempts to re-assemble the image input.