Extracting Knowledge from the Geometric Shape of Social Network Data Using Topological Data Analysis

Topological data analysis is a noble approach to extract meaningful information from high-dimensional data and is robust to noise. It is based on topology, which aims to study the geometric shape of data. In order to apply topological data analysis, an algorithm called mapper is adopted. The output from mapper is a simplicial complex that represents a set of connected clusters of data points. In this paper, we explore the feasibility of topological data analysis for mining social network data by addressing the problem of image popularity. We randomly crawl images from Instagram and analyze the effects of social context and image content on an image’s popularity using mapper. Mapper clusters the images using each feature, and the ratio of popularity in each cluster is computed to determine the clusters with a high or low possibility of popularity. Then, the popularity of images are predicted to evaluate the accuracy of topological data analysis. This approach is further compared with traditional clustering algorithms, including k-means and hierarchical clustering, in terms of accuracy, and the results show that topological data analysis outperforms the others. Moreover, topological data analysis provides meaningful information based on the connectivity between the clusters.https://doi.org/10.3390/e1907036

Geometric deep learning: going beyond Euclidean data

Many scientific fields study data with an underlying structure that is a non-Euclidean space. Some examples include social networks in computational social sciences, sensor networks in communications, functional networks in brain imaging, regulatory networks in genetics, and meshed surfaces in computer graphics. In many applications, such geometric data are large and complex (in the case of social networks, on the scale of billions), and are natural targets for machine learning techniques. In particular, we would like to use deep neural networks, which have recently proven to be powerful tools for a broad range of problems from computer vision, natural language processing, and audio analysis. However, these tools have been most successful on data with an underlying Euclidean or grid-like structure, and in cases where the invariances of these structures are built into networks used to model them. Geometric deep learning is an umbrella term for emerging techniques attempting to generalize (structured) deep neural models to non-Euclidean domains such as graphs and manifolds. The purpose of this paper is to overview different examples of geometric deep learning problems and present available solutions, key difficulties, applications, and future research directions in this nascent field

Methodology and Algorithms for Pedestrian Network Construction

With the advanced capabilities of mobile devices and the success of car navigation systems, interest in pedestrian navigation systems is on the rise. A critical component of any navigation system is a map database which represents a network (e.g., road networks in car navigation systems) and supports key functionality such as map display, geocoding, and routing. Road networks, mainly due to the popularity of car navigation systems, are well defined and publicly available. However, in pedestrian navigation systems, as well as other applications including urban planning and physical activities studies, road networks do not adequately represent the paths that pedestrians usually travel. Currently, there are no techniques to automatically construct pedestrian networks, impeding research and development of applications requiring pedestrian data. This coupled with the increased demand for pedestrian networks is the prime motivation for this dissertation which is focused on development of a methodology and algorithms that can construct pedestrian networks automatically. A methodology, which involves three independent approaches, network buffering (using existing road networks), collaborative mapping (using GPS traces collected by volunteers), and image processing (using high-resolution satellite and laser imageries) was developed. Experiments were conducted to evaluate the pedestrian networks constructed by these approaches with a pedestrian network baseline as a ground truth. The results of the experiments indicate that these three approaches, while differing in complexity and outcome, are viable for automatically constructing pedestrian networks

Analyze Large Multidimensional Datasets Using Algebraic Topology

This paper presents an efficient algorithm to extract knowledge from high-dimensionality, high- complexity datasets using algebraic topology, namely simplicial complexes. Based on concept of isomorphism of relations, our method turn a relational table into a geometric object (a simplicial complex is a polyhedron). So, conceptually association rule searching is turned into a geometric traversal problem. By leveraging on the core concepts behind Simplicial Complex, we use a new technique (in computer science) that improves the performance over existing methods and uses far less memory. It was designed and developed with a strong emphasis on scalability, reliability, and extensibility. This paper also investigate the possibility of Hadoop integration and the challenges that come with the framework