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

Multidimensional approximation of nonlinear dynamical systems

A key task in the field of modeling and analyzing nonlinear dynamical systems is the recovery of unknown governing equations from measurement data only. There is a wide range of application areas for this important instance of system identification, ranging from industrial engineering and acoustic signal processing to stock market models. In order to find appropriate representations of underlying dynamical systems, various data-driven methods have been proposed by different communities. However, if the given data sets are high-dimensional, then these methods typically suffer from the curse of dimensionality. To significantly reduce the computational costs and storage consumption, we propose the method multidimensional approximation of nonlinear dynamical systems (MANDy) which combines data-driven methods with tensor network decompositions. The efficiency of the introduced approach will be illustrated with the aid of several high-dimensional nonlinear dynamical systems

A virtual workspace for hybrid multidimensional scaling algorithms

In visualising multidimensional data, it is well known that different types of algorithms to process them. Data sets might be distinguished according to volume, variable types and distribution, and each of these characteristics imposes constraints upon the choice of applicable algorithms for their visualization. Previous work has shown that a hybrid algorithmic approach can be successful in addressing the impact of data volume on the feasibility of multidimensional scaling (MDS). This suggests that hybrid combinations of appropriate algorithms might also successfully address other characteristics of data. This paper presents a system and framework in which a user can easily explore hybrid algorithms and the data flowing through them. Visual programming and a novel algorithmic architecture let the user semi-automatically define data flows and the co-ordination of multiple views

Exploring a Multidimensional Representation of Documents and Queries (extended version)

In Information Retrieval (IR), whether implicitly or explicitly, queries and documents are often represented as vectors. However, it may be more beneficial to consider documents and/or queries as multidimensional objects. Our belief is this would allow building "truly" interactive IR systems, i.e., where interaction is fully incorporated in the IR framework. The probabilistic formalism of quantum physics represents events and densities as multidimensional objects. This paper presents our first step towards building an interactive IR framework upon this formalism, by stating how the first interaction of the retrieval process, when the user types a query, can be formalised. Our framework depends on a number of parameters affecting the final document ranking. In this paper we experimentally investigate the effect of these parameters, showing that the proposed representation of documents and queries as multidimensional objects can compete with standard approaches, with the additional prospect to be applied to interactive retrieval

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

An overview of the proper generalized decomposition with applications in computational rheology

We review the foundations and applications of the proper generalized decomposition (PGD), a powerful model reduction technique that computes a priori by means of successive enrichment a separated representation of the unknown field. The computational complexity of the PGD scales linearly with the dimension of the space wherein the model is defined, which is in marked contrast with the exponential scaling of standard grid-based methods. First introduced in the context of computational rheology by Ammar et al. [3] and [4], the PGD has since been further developed and applied in a variety of applications ranging from the solution of the Schrödinger equation of quantum mechanics to the analysis of laminate composites. In this paper, we illustrate the use of the PGD in four problem categories related to computational rheology: (i) the direct solution of the Fokker-Planck equation for complex fluids in configuration spaces of high dimension, (ii) the development of very efficient non-incremental algorithms for transient problems, (iii) the fully three-dimensional solution of problems defined in degenerate plate or shell-like domains often encountered in polymer processing or composites manufacturing, and finally (iv) the solution of multidimensional parametric models obtained by introducing various sources of problem variability as additional coordinates

A visual workspace for constructing hybrid MDS algorithms and coordinating multiple views

Data can be distinguished according to volume, variable types and distribution, and each of these characteristics imposes constraints upon the choice of applicable algorithms for their visualisation. This has led to an abundance of often disparate algorithmic techniques. Previous work has shown that a hybrid algorithmic approach can be successful in addressing the impact of data volume on the feasibility of multidimensional scaling (MDS). This paper presents a system and framework in which a user can easily explore algorithms as well as their hybrid conjunctions and the data flowing through them. Visual programming and a novel algorithmic architecture let the user semi-automatically define data flows and the co-ordination of multiple views of algorithmic and visualisation components. We propose that our approach has two main benefits: significant improvements in run times of MDS algorithms can be achieved, and intermediate views of the data and the visualisation program structure can provide greater insight and control over the visualisation process

Blending the physical and the digital through conceptual spaces

The rise of the Internet facilitates an ever increasing growth of virtual, i.e. digital spaces which co-exist with the physical environment, i.e. the physical space. In that, the question arises, how physical and digital space can interact synchronously. While sensors provide a means to continuously observe the physical space, several issues arise with respect to mapping sensor data streams to digital spaces, for instance, structured linked data, formally represented through symbolic Semantic Web (SW) standards such as OWL or RDF. The challenge is to bridge between symbolic knowledge representations and the measured data collected by sensors. In particular, one needs to map a given set of arbitrary sensor data to a particular set of symbolic knowledge representations, e.g. ontology instances. This task is particularly challenging due to the vast variety of possible sensor measurements. Conceptual Spaces (CS) provide a means to represent knowledge in geometrical vector spaces in order to enable computation of similarities between knowledge entities by means of distance metrics. We propose an approach which allows to refine symbolic concepts as CS and to ground ontology instances to so-called prototypical members which are vectors in the CS. By computing similarities in terms of spatial distances between a given set of sensor measurements and a finite set of CS members, the most similar instance can be identified. In that, we provide a means to bridge between the physical space, as observed by sensors, and the digital space made up of symbolic representations