Batch kernel SOM and related Laplacian methods for social network analysis

Large graphs are natural mathematical models for describing the structure of the data in a wide variety of fields, such as web mining, social networks, information retrieval, biological networks, etc. For all these applications, automatic tools are required to get a synthetic view of the graph and to reach a good understanding of the underlying problem. In particular, discovering groups of tightly connected vertices and understanding the relations between those groups is very important in practice. This paper shows how a kernel version of the batch Self Organizing Map can be used to achieve these goals via kernels derived from the Laplacian matrix of the graph, especially when it is used in conjunction with more classical methods based on the spectral analysis of the graph. The proposed method is used to explore the structure of a medieval social network modeled through a weighted graph that has been directly built from a large corpus of agrarian contracts

Mining a medieval social network by kernel SOM and related methods

This paper briefly presents several ways to understand the organization of a large social network (several hundreds of persons). We compare approaches coming from data mining for clustering the vertices of a graph (spectral clustering, self-organizing algorithms. . .) and provide methods for representing the graph from these analysis. All these methods are illustrated on a medieval social network and the way they can help to understand its organization is underlined

Overlap Removal of Dimensionality Reduction Scatterplot Layouts

Dimensionality Reduction (DR) scatterplot layouts have become a ubiquitous visualization tool for analyzing multidimensional data items with presence in different areas. Despite its popularity, scatterplots suffer from occlusion, especially when markers convey information, making it troublesome for users to estimate items' groups' sizes and, more importantly, potentially obfuscating critical items for the analysis under execution. Different strategies have been devised to address this issue, either producing overlap-free layouts, lacking the powerful capabilities of contemporary DR techniques in uncover interesting data patterns, or eliminating overlaps as a post-processing strategy. Despite the good results of post-processing techniques, the best methods typically expand or distort the scatterplot area, thus reducing markers' size (sometimes) to unreadable dimensions, defeating the purpose of removing overlaps. This paper presents a novel post-processing strategy to remove DR layouts' overlaps that faithfully preserves the original layout's characteristics and markers' sizes. We show that the proposed strategy surpasses the state-of-the-art in overlap removal through an extensive comparative evaluation considering multiple different metrics while it is 2 or 3 orders of magnitude faster for large datasets.Comment: 11 pages and 9 figure

Characteristics of networks generated by kernel growing neural gas

This research aims to develop kernel GNG, a kernelized version of the growing neural gas (GNG) algorithm, and to investigate the features of the networks generated by the kernel GNG. The GNG is an unsupervised artificial neural network that can transform a dataset into an undirected graph, thereby extracting the features of the dataset as a graph. The GNG is widely used in vector quantization, clustering, and 3D graphics. Kernel methods are often used to map a dataset to feature space, with support vector machines being the most prominent application. This paper introduces the kernel GNG approach and explores the characteristics of the networks generated by kernel GNG. Five kernels, including Gaussian, Laplacian, Cauchy, inverse multiquadric, and log kernels, are used in this study

A self-organizing world: special issue of the 13th edition of the workshop on self-organizing maps and learning vector quantization, clustering and data visualization, WSOM¿+¿2019

Postprint (author's final draft

Urban Land Cover Classification with Missing Data Modalities Using Deep Convolutional Neural Networks

Automatic urban land cover classification is a fundamental problem in remote sensing, e.g. for environmental monitoring. The problem is highly challenging, as classes generally have high inter-class and low intra-class variance. Techniques to improve urban land cover classification performance in remote sensing include fusion of data from different sensors with different data modalities. However, such techniques require all modalities to be available to the classifier in the decision-making process, i.e. at test time, as well as in training. If a data modality is missing at test time, current state-of-the-art approaches have in general no procedure available for exploiting information from these modalities. This represents a waste of potentially useful information. We propose as a remedy a convolutional neural network (CNN) architecture for urban land cover classification which is able to embed all available training modalities in a so-called hallucination network. The network will in effect replace missing data modalities in the test phase, enabling fusion capabilities even when data modalities are missing in testing. We demonstrate the method using two datasets consisting of optical and digital surface model (DSM) images. We simulate missing modalities by assuming that DSM images are missing during testing. Our method outperforms both standard CNNs trained only on optical images as well as an ensemble of two standard CNNs. We further evaluate the potential of our method to handle situations where only some DSM images are missing during testing. Overall, we show that we can clearly exploit training time information of the missing modality during testing