A combined measure for quantifying and qualifying the topology preservation of growing self-organizing maps

The Self-OrganizingMap (SOM) is a neural network model that performs an ordered projection of a high dimensional input space in a low-dimensional topological structure. The process in which such mapping is formed is defined by the SOM algorithm, which is a competitive, unsupervised and nonparametric method, since it does not make any assumption about the input data distribution. The feature maps provided by this algorithm have been successfully applied for vector quantization, clustering and high dimensional data visualization processes. However, the initialization of the network topology and the selection of the SOM training parameters are two difficult tasks caused by the unknown distribution of the input signals. A misconfiguration of these parameters can generate a feature map of low-quality, so it is necessary to have some measure of the degree of adaptation of the SOM network to the input data model. The topologypreservation is the most common concept used to implement this measure. Several qualitative and quantitative methods have been proposed for measuring the degree of SOM topologypreservation, particularly using Kohonen's model. In this work, two methods for measuring the topologypreservation of the Growing Cell Structures (GCSs) model are proposed: the topographic function and the topology preserving ma

DIMAL: Deep Isometric Manifold Learning Using Sparse Geodesic Sampling

This paper explores a fully unsupervised deep learning approach for computing distance-preserving maps that generate low-dimensional embeddings for a certain class of manifolds. We use the Siamese configuration to train a neural network to solve the problem of least squares multidimensional scaling for generating maps that approximately preserve geodesic distances. By training with only a few landmarks, we show a significantly improved local and nonlocal generalization of the isometric mapping as compared to analogous non-parametric counterparts. Importantly, the combination of a deep-learning framework with a multidimensional scaling objective enables a numerical analysis of network architectures to aid in understanding their representation power. This provides a geometric perspective to the generalizability of deep learning.Comment: 10 pages, 11 Figure

Anisotropic Radial Layout for Visualizing Centrality and Structure in Graphs

This paper presents a novel method for layout of undirected graphs, where nodes (vertices) are constrained to lie on a set of nested, simple, closed curves. Such a layout is useful to simultaneously display the structural centrality and vertex distance information for graphs in many domains, including social networks. Closed curves are a more general constraint than the previously proposed circles, and afford our method more flexibility to preserve vertex relationships compared to existing radial layout methods. The proposed approach modifies the multidimensional scaling (MDS) stress to include the estimation of a vertex depth or centrality field as well as a term that penalizes discord between structural centrality of vertices and their alignment with this carefully estimated field. We also propose a visualization strategy for the proposed layout and demonstrate its effectiveness using three social network datasets.Comment: Appears in the Proceedings of the 25th International Symposium on Graph Drawing and Network Visualization (GD 2017

A review of data visualization: opportunities in manufacturing sequence management.

Data visualization now benefits from developments in technologies that offer innovative ways of presenting complex data. Potentially these have widespread application in communicating the complex information domains typical of manufacturing sequence management environments for global enterprises. In this paper the authors review the visualization functionalities, techniques and applications reported in literature, map these to manufacturing sequence information presentation requirements and identify the opportunities available and likely development paths. Current leading-edge practice in dynamic updating and communication with suppliers is not being exploited in manufacturing sequence management; it could provide significant benefits to manufacturing business. In the context of global manufacturing operations and broad-based user communities with differing needs served by common data sets, tool functionality is generally ahead of user application

VizRank: Data Visualization Guided by Machine Learning

Data visualization plays a crucial role in identifying interesting patterns in exploratory data analysis. Its use is, however, made difficult by the large number of possible data projections showing different attribute subsets that must be evaluated by the data analyst. In this paper, we introduce a method called VizRank, which is applied on classified data to automatically select the most useful data projections. VizRank can be used with any visualization method that maps attribute values to points in a two-dimensional visualization space. It assesses possible data projections and ranks them by their ability to visually discriminate between classes. The quality of class separation is estimated by computing the predictive accuracy of k-nearest neighbor classifier on the data set consisting of x and y positions of the projected data points and their class information. The paper introduces the method and presents experimental results which show that VizRank's ranking of projections highly agrees with subjective rankings by data analysts. The practical use of VizRank is also demonstrated by an application in the field of functional genomics