Proximity Mapping

This documentation guides users through the specification of input data, model selection, transformation functions, dimensionality settings, and the inclusion of attributes and properties in Proximity Mapping.

Proximity mapping is a visualization technique that is used to reduce the dimensionality of multivariate data and to display relationships among objects (cases, items, or other entities) in a spatial configuration. Originally developed under the name, multidimensional scaling (MDS) in psychology, the method uses proximities (similarities, dissimilarities, or distances) to position objects so that their spatial arrangement reflects the structure in the data. Similar objects appear near each other; dissimilar ones are placed farther apart. Proximity mapping supports interpretation and pattern recognition by transforming complex relational data into intuitive two or three-dimensional plots.

In IBM® SPSS® Statistics, proximity mapping is implemented through the PROXMAP procedure. Unlike PROXSCAL, which is limited to analyzing proximity matrices, PROXMAP accepts multiple forms of input and provides greater flexibility. It supports multiple proximity sources, incorporates additional variables (attributes and properties), and offers a wide range of transformation and restriction options. These features make PROXMAP a powerful tool for exploring multivariate structure and integrating diverse types of data into a unified spatial representation.

When proximity information is available from multiple sources, either directly specified or derived from multivariate data, PROXMAP can fit several models of individual differences in addition to the default identity model. Available models include the Weighted Identity (Dilation) model, the Weighted Euclidean (Diagonal) model, and the Generalized Euclidean model with optional rank restrictions.

Compared to traditional dimension-reduction techniques such as Principal Components Analysis (PCA) and Classical MDS, PROXMAP provides a more direct and flexible representation of proximities. Classical MDS can be used to initialize the configuration. When applied to multivariate data, Classical MDS is equivalent to principal coordinates analysis, a variant of PCA.

PROXMAP accepts the following types of input.

Input type	Description
Raw proximities and derived proximities	Derived proximities are computed from numeric, ordinal, or nominal variables. Both types of proximities are optionally transformed using monotonic functions (For example, ordinal or spline-based), before approximated by distances.
Attributes	Variables that constrain the configuration and appear as directions in the joint space (supervised mapping).
Properties	Supplementary variables used for interpretation; these are displayed in the space but do not influence the configuration (unsupervised mapping).

A unique feature of PROXMAP is the ability to use the same set of variables across different roles:

As the basis for proximity derivation
As attributes that shape the configuration
As properties that support interpretation

Alternatively, distinct sets of variables can be assigned to each role.

In addition to linear transformation, PROXMAP provides various transformation options (including ordinal, monotonic spline, nonmonotonic spline, and nominal transformations) for both attributes and properties. For proximities, transformations must be monotonic and also include power transformations. Output includes graphical diagnostics such as stress plots, minimum spanning trees, and neighborhood graphs to assist with interpretation and evaluation.

Example

Proximity Mapping can be widely applied across disciplines, including Psychology and Behavioral Sciences (perception, memory, preferences), Marketing (brand mapping, segmentation), Sociology (ideology mapping, social networks), Education and Psychometrics (test diagnostics, skill profiling), Linguistics (semantic similarity, dialect mapping), Geography (perceived distances, ecological spatial analysis), Genomics and Bioinformatics (expression patterns, population structure, single-cell expression heterogeneity exploration), Chemoinformatics (molecular similarity), Computer Science (embedding visualization), Anthropology and Archaeology (artifact similarity, cranial data).

Data

The data to be analyzed includes variables that either represent a proximity matrix (or matrices), or represent multivariate data that is converted into proximity matrix or matrices.

For multivariate data, the variables can be a mixture of scale, ordinal, and nominal measurement level variables. The minimum number of variables needed is 3

For proximity data, provide the same number of variables as the number of cases.

For both proximity data and multivariate data, the minimum number of cases needed is 3.

The output includes spatial configurations, various diagnostic plots, and fit statistics. Biplots display objects alongside variables, attributes, and properties in a common space.

To start PROXMAP analysis, click Analyze > Mapping > Proximity Mapping.

This procedure pastes PROXMAP command syntax.