Construction of embedded fMRI resting state functional connectivity networks using manifold learning

We construct embedded functional connectivity networks (FCN) from benchmark resting-state functional magnetic resonance imaging (rsfMRI) data acquired from patients with schizophrenia and healthy controls based on linear and nonlinear manifold learning algorithms, namely, Multidimensional Scaling (MDS), Isometric Feature Mapping (ISOMAP) and Diffusion Maps. Furthermore, based on key global graph-theoretical properties of the embedded FCN, we compare their classification potential using machine learning techniques. We also assess the performance of two metrics that are widely used for the construction of FCN from fMRI, namely the Euclidean distance and the lagged cross-correlation metric. We show that the FCN constructed with Diffusion Maps and the lagged cross-correlation metric outperform the other combinations

Hyperbolic Geometry in Computer Vision: A Novel Framework for Convolutional Neural Networks

Real-world visual data exhibit intrinsic hierarchical structures that can be represented effectively in hyperbolic spaces. Hyperbolic neural networks (HNNs) are a promising approach for learning feature representations in such spaces. However, current methods in computer vision rely on Euclidean backbones and only project features to the hyperbolic space in the task heads, limiting their ability to fully leverage the benefits of hyperbolic geometry. To address this, we present HCNN, the first fully hyperbolic convolutional neural network (CNN) designed for computer vision tasks. Based on the Lorentz model, we generalize fundamental components of CNNs and propose novel formulations of the convolutional layer, batch normalization, and multinomial logistic regression (MLR). Experimentation on standard vision tasks demonstrates the effectiveness of our HCNN framework and the Lorentz model in both hybrid and fully hyperbolic settings. Overall, we aim to pave the way for future research in hyperbolic computer vision by offering a new paradigm for interpreting and analyzing visual data. Our code is publicly available at https://github.com/kschwethelm/HyperbolicCV

Exact heat kernel on a hypersphere and its applications in kernel SVM

Many contemporary statistical learning methods assume a Euclidean feature space. This paper presents a method for defining similarity based on hyperspherical geometry and shows that it often improves the performance of support vector machine compared to other competing similarity measures. Specifically, the idea of using heat diffusion on a hypersphere to measure similarity has been previously proposed, demonstrating promising results based on a heuristic heat kernel obtained from the zeroth order parametrix expansion; however, how well this heuristic kernel agrees with the exact hyperspherical heat kernel remains unknown. This paper presents a higher order parametrix expansion of the heat kernel on a unit hypersphere and discusses several problems associated with this expansion method. We then compare the heuristic kernel with an exact form of the heat kernel expressed in terms of a uniformly and absolutely convergent series in high-dimensional angular momentum eigenmodes. Being a natural measure of similarity between sample points dwelling on a hypersphere, the exact kernel often shows superior performance in kernel SVM classifications applied to text mining, tumor somatic mutation imputation, and stock market analysis

Robust Large-Margin Learning in Hyperbolic Space

Recently, there has been a surge of interest in representation learning in hyperbolic spaces, driven by their ability to represent hierarchical data with significantly fewer dimensions than standard Euclidean spaces. However, the viability and benefits of hyperbolic spaces for downstream machine learning tasks have received less attention. In this paper, we present, to our knowledge, the first theoretical guarantees for learning a classifier in hyperbolic rather than Euclidean space. Specifically, we consider the problem of learning a large-margin classifier for data possessing a hierarchical structure. Our first contribution is a hyperbolic perceptron algorithm, which provably converges to a separating hyperplane. We then provide an algorithm to efficiently learn a large-margin hyperplane, relying on the careful injection of adversarial examples. Finally, we prove that for hierarchical data that embeds well into hyperbolic space, the low embedding dimension ensures superior guarantees when learning the classifier directly in hyperbolic space.Comment: Accepted to NeurIPS 202

Automated classification of web contents in B2B marketing

Recent growth in digitization has affected how customers seek the information they need to make a purchase decision. This trend of customers making their purchase decision based on the information they collect online is increasing. To accommodate this change in purchase behavior, companies tend to share as much information about themselves and their products online, which in turn drives the amount of unstructured data produced. To get value for this huge amount of data being produced, the unstructured data needs to be processed before being used in digital marketing applications. When it comes to the companies serving business to customers (B2C), plenty of research exists on how the digital content could be used for marketing, but for the companies serving business to business (B2B) a huge research gap presides. B2C marketing and B2B marketing might share some analytical concepts but they are different domains. Not much research has been done in the field of using machine learning in B2B digital marketing. The lack of availability of labeled text data from the B2B domain makes it challenging for researchers to experiment on text classification models, while several methods have been proposed and used to classify unstructured text data in marketing and other domains. This thesis studies previous works done in the field of text classification in general, in the marketing domain, and compares those methods across the dataset available for this research. Text classification methods such as Random Forest, Linear SVM, KNN, Multinomial Naïve Bayes, and Multinomial Logistic Regression dominates the research field, hence these methods are tested in this research. In the used dataset surprisingly, Random Forest Classifier performed best with an average accuracy of 0.85 in the designed five-class classification task

Axiomatic geometries for text documents

High-dimensional structured data such as text and images is often poorly understood and misrepresented in statistical modelling. Typical approaches to modelling such data involve, either explicitly or implicitly, arbitrary geometric assumptions. In this chapter, we consider statistical modelling of non-Euclidean data whose geometry is obtained by embedding the data in a statistical manifold. The resulting models perform better than their Euclidean counterparts on real world data and draw an interesting connection betweenČencov and Campbell's axiomatic characterisation of the Fisher information and the recently proposed diffusion kernels and square root embedding

Evaluating classification accuracy for modern learning approaches

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/149333/1/sim8103_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/149333/2/sim8103.pd

Machine Learning and Job Posting Classification: A Comparative Study

In this paper, we investigated multiple machine learning classifiers which are, Multinomial Naive Bayes, Support Vector Machine, Decision Tree, K Nearest Neighbors, and Random Forest in a text classification problem. The data we used contains real and fake job posts. We cleaned and pre-processed our data, then we applied TF-IDF for feature extraction. After we implemented the classifiers, we trained and evaluated them. Evaluation metrics used are precision, recall, f-measure, and accuracy. For each classifier, results were summarized and compared with others