# The analysis of proximities: Multidimensional scaling with an unknown distance function. I.

@article{Shepard1962TheAO, title={The analysis of proximities: Multidimensional scaling with an unknown distance function. I.}, author={Roger N. Shepard}, journal={Psychometrika}, year={1962}, volume={27}, pages={125-140} }

A computer program is described that is designed to reconstruct the metric configuration of a set of points in Euclidean space on the basis of essentially nonmetric information about that configuration. A minimum set of Cartesian coordinates for the points is determined when the only available information specifies for each pair of those points—not the distance between them—but some unknown, fixed monotonic function of that distance. The program is proposed as a tool for reductively analyzing…

## 1,201 Citations

…. Computer Abstracts

- 1978

DESCRIPTION: Nonmetric multidimensional scaling (MOS) or, as it is called more appropriately, monotone distance analysis, has become one of the most useful research tools in the social sciences. It…

Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis

- Mathematics
- 1964

Multidimensional scaling is the problem of representingn objects geometrically byn points, so that the interpoint distances correspond in some sense to experimental dissimilarities between objects.…

Generalized Non-metric Multidimensional Scaling

- Mathematics, Computer ScienceAISTATS
- 2007

It is argued that this setting is more natural in some experimental settings and proposed algorithm based on convex optimization techniques to solve the non-metric multidimensional scaling problem in which only a set of order relations of the form dij < dkl are provided is provided.

Multidimensional scaling: An introduction

- Mathematics
- 2017

A. MDS produces a geometric model of proximities data 1. Start with data on similarities (or dissimilarities) among a set of stimulus objects. 2. MDS represents each stimulus as a point within a…

Nearest neighbor analysis of psychological spaces.

- Mathematics
- 1986

Geometric models impose an upper bound on the number of points that can share the same nearest neighbor. A much more restrictive bound is implied by the assumption that the data points represent a…

Subspace Least Squares Multidimensional Scaling

- Computer ScienceSSVM
- 2017

This work casts the least squares variant of MDS (LS-MDS) in the spectral domain and uncovers a multiresolution property of distance scaling which speeds up the optimization by a significant amount, while producing comparable, and sometimes even better, embeddings.

A MAXIMUM LIKELIHOOD METHOD FOR NONMETRIC MULTIDIMENSIONAL SCALING: I . THE CASE IN WHICH ALL EMPIRICAL PAIRWISE ORDERINGS ARE INDEPENDENT-THEORY

- 2011

A maximum likelihood estimation procedure is developed for nonmetric multidimensional scaling (MDS) which applies to the situation in which all empirical pairwise orderings of dissimilarities are…

Methods for Binary Multidimensional Scaling

- Mathematics, Computer ScienceNeural Computation
- 2002

Several methods for performing approximately optimized binary MDS into a low-dimensional discrete space are introduced and analyzed.

Multidimensional Scaling

- 1980

Multidimensional scaling (MDS) is a technique that creates a map displaying the relative positions of a number of objects, given only a table of the distances between them. The map may consist of…

Multidimensional scaling.

- MedicineAnnual review of psychology
- 1980

A large class of these nonspatial models can still be characterized as dimensional modelsmbut with discrete rather than continuously valued dimensions, as this chapter demonstrates.