A common way for researchers to model or graphically portray spatial knowledge of a large environment is by applying multidimensional scaling (MDS) to a set of pairwise distance estimations. We introduce two MDS-like techniques that incorporate people's knowledge of directions instead of (or in addition to) their knowledge of distances. Maps of a familiar environment derived from these procedur...

Multidimensional-scaling (MDS) is a dimensionality reduction tool used for information analysis, data visualization and manifold learning. Most MDS procedures find embedding of data points in low dimensional Euclidean (flat) domains, such that distances between the points are as close as possible to given interpoints dissimilarities. We present an efficient solver for Classical Scaling, a speci...

In this study we show that humans form very similar perceptual spaces when they explore parametrically-defined shell-shaped objects visually or haptically. A physical object space was generated by varying three shape parameters. Sighted participants explored pictures of these objects while blindfolded participants haptically explored 3D printouts of the objects. Similarity ratings were performe...

One of the most important issues that have absorbed the public opinion and expert community during the recent years, is the qualitative and quantitative aspects of the housing. There are several challenges related to this topic that includes the contexts of the construction, manufacturing, planning to social aspects, cultural, physical and architectural design. The thing that has a significant ...

Multidimensional scaling (MDS) methods are designed to establish a one-to-one correspondence of input-output relationships. While the input may be given as high-dimensional data items or as adjacency matrix characterizing data relations, the output space is usually chosen as low-dimensional Euclidean, ready for visualization. MDSLocalize, an existing method, is reformulated in terms of Sanger’s...

Distances matrices are traditionally analyzed with statistical methods that represent distances as maps such as Metric Multidimensional Scaling (MDS), Generalized Procrustes Analysis (GPA), Individual Differences Scaling (INDSCAL), and DISTATIS. MDS analyzes only one distance matrix at a time while GPA, INDSCAL and DISTATIS extract similarities between several distance matrices. However, none o...

Classical multidimensional scaling (MDS) is a method for visualizing high-dimensional point clouds by mapping to low-dimensional Euclidean space. This mapping is defined in terms of eigenfunctions of a matrix of interpoint proximities. In this paper we analyze in detail multidimensional scaling applied to a specific dataset: the 2005 United States House of Representatives roll call votes. MDS a...

Multidimensional scaling (MDS) is a statistical tool for constructing a low-dimension configuration to represent the relationships among objects. In order to extend the conventional MDS analysis to consider the situation of uncertainty under group decision making, in this paper the interval-valued data is considered to represent the dissimilarity matrix in MDS and the rough sets concept is used...

Multidimensional Scaling (MDS) is one of the most popular methods for dimensionality reduction and visualization of high dimensional data. Apart from these tasks, it also found applications in the field of geometry processing for the analysis and reconstruction of non-rigid shapes. In this regard, MDS can be thought of as a shape from metric algorithm, consisting of finding a configuration of p...

Manifold learning techniques are used to preserve the original geometry of dataset after reduction by preserving the distance among data points. MDS (Multidimensional Scaling), ISOMAP (Isometric Feature Mapping), LLE (Locally Linear Embedding) are some of the geometrical structure preserving dimension reduction methods. In this paper, we have compared MDS and ISOMAP and considered similarity as...