Sensitivity and robustness in MDS configurations for mixed-type data: a study of the economic crisis impact on socially vulnerable Spanish people

Multidimensional scaling (MDS) techniques are initially proposed to produce pictorial representations of distance, dissimilarity or proximity data. Sensitivity and robustness assessment of multivariate methods is essential if inferences are to be drawn from the analysis. To our knowledge, the literature related to MDS for mixed-type data, including variables measured at continuous level besides categorical ones, is quite scarce. The main motivation of this work was to analyze the stability and robustness of MDS configurations as an extension of a previous study on a real data set, coming from a panel-type analysis designed to assess the economic crisis impact on Spanish people who were in situations of high risk of being socially excluded. The main contributions of the paper on the treatment of MDS configurations for mixed-type data are: (i) to propose a joint metric based on distance matrices computed for continuous, multi-scale categorical and/or binary variables, (ii) to introduce a systematic analysis on the sensitivity of MDS configurations and (iii) to present a systematic search for robustness and identification of outliers through a new procedure based on geometric variability notions.Gower distance, MDS configurations, Mixed-type data, Outliers identification, Related metric scaling, Survey data

Human response to vibration in residential environments (NANR209), Technical report 6 : determination of exposure-response relationships

This technical report presents the development of exposure-response relationships for the human response to vibration in residential environments. The data used to formulate the relationships presented in this report are those which were collected for the Defra funded project “NANR209: Human response to vibration in residential environments”, the main aim of which was the development of exposure-response relationships. Vibration caused by railway traffic, construction work, and internal sources outside of the residents’ control were considered. Response data was collected via face to face interviews with residents in their own homes. The questionnaire was presented as a neighbourhood satisfaction survey and gathered information on, among other things, annoyance caused by vibration and noise exposure. Development and implementation of the questionnaire used for the collection of response data is discussed in Technical Report 2 and Technical Report 5. Vibration exposure was determined via measurement and prediction in such a way that, where possible, an estimation of internal vibration exposure was established for each residence in which a questionnaire was completed. The measurement procedures and methods employed to estimate vibration exposure are detailed in Technical Report 1 and Technical Report 3. Estimations of noise exposure were also derived for each residence using the methods detailed in Technical Report 4

Personality Assessment, Forced-Choice.

Instead of responding to questionnaire items one at a time, respondents may be forced to make a choice between two or more items measuring the same or different traits. The forced-choice format eliminates uniform response biases, although the research on its effectiveness in reducing the effects of impression management is inconclusive. Until recently, forced-choice questionnaires were scaled in relation to person means (ipsative data), providing information for intra-individual assessments only. Item response modeling enabled proper scaling of forced-choice data, so that inter-individual comparisons may be made. New forced-choice applications in personality assessment and directions for future research are discussed

Multidimensional Scaling on Multiple Input Distance Matrices

Multidimensional Scaling (MDS) is a classic technique that seeks vectorial representations for data points, given the pairwise distances between them. However, in recent years, data are usually collected from diverse sources or have multiple heterogeneous representations. How to do multidimensional scaling on multiple input distance matrices is still unsolved to our best knowledge. In this paper, we first define this new task formally. Then, we propose a new algorithm called Multi-View Multidimensional Scaling (MVMDS) by considering each input distance matrix as one view. Our algorithm is able to learn the weights of views (i.e., distance matrices) automatically by exploring the consensus information and complementary nature of views. Experimental results on synthetic as well as real datasets demonstrate the effectiveness of MVMDS. We hope that our work encourages a wider consideration in many domains where MDS is needed

BOOL-AN: A method for comparative sequence analysis and phylogenetic reconstruction

A novel discrete mathematical approach is proposed as an additional tool for molecular systematics which does not require prior statistical assumptions concerning the evolutionary process. The method is based on algorithms generating mathematical representations directly from DNA/RNA or protein sequences, followed by the output of numerical (scalar or vector) and visual characteristics (graphs). The binary encoded sequence information is transformed into a compact analytical form, called the Iterative Canonical Form (or ICF) of Boolean functions, which can then be used as a generalized molecular descriptor. The method provides raw vector data for calculating different distance matrices, which in turn can be analyzed by neighbor-joining or UPGMA to derive a phylogenetic tree, or by principal coordinates analysis to get an ordination scattergram. The new method and the associated software for inferring phylogenetic trees are called the Boolean analysis or BOOL-AN

Pattern vectors from algebraic graph theory

Graphstructures have proven computationally cumbersome for pattern analysis. The reason for this is that, before graphs can be converted to pattern vectors, correspondences must be established between the nodes of structures which are potentially of different size. To overcome this problem, in this paper, we turn to the spectral decomposition of the Laplacian matrix. We show how the elements of the spectral matrix for the Laplacian can be used to construct symmetric polynomials that are permutation invariants. The coefficients of these polynomials can be used as graph features which can be encoded in a vectorial manner. We extend this representation to graphs in which there are unary attributes on the nodes and binary attributes on the edges by using the spectral decomposition of a Hermitian property matrix that can be viewed as a complex analogue of the Laplacian. To embed the graphs in a pattern space, we explore whether the vectors of invariants can be embedded in a low- dimensional space using a number of alternative strategies, including principal components analysis ( PCA), multidimensional scaling ( MDS), and locality preserving projection ( LPP). Experimentally, we demonstrate that the embeddings result in well- defined graph clusters. Our experiments with the spectral representation involve both synthetic and real- world data. The experiments with synthetic data demonstrate that the distances between spectral feature vectors can be used to discriminate between graphs on the basis of their structure. The real- world experiments show that the method can be used to locate clusters of graphs