SPSS command: SPSS RBF

Radial basis function (RBF) network in your browser

A radial basis function network predicts a categorical or scale target from a layer of Gaussian units, each centred on a cluster of similar training cases.

Run Radial Basis Function Network in your browser All SPSS procedures

Free · No account · Files stay on your device · Updated 18 October 2026

What it tells you

Crosstabs follows the SPSS RBF procedure on your device: TwoStep clustering places the hidden units, output weights are fitted by least squares, and the number of units is chosen by testing error or BIC — no iterative training, so the same partition always gives the same network.

How well the target is predicted on cases not used for fitting: relative error for a scale target, percent incorrect for a categorical one.
How many hidden units the data support, from the testing error (or BIC) at each candidate number of units.
Where each basis function sits and how wide it is, in the hidden-layer parameter estimates.
Which predictors drive the predictions, from sensitivity-based importance, plus ROC, gains and lift for categorical targets.

When to use it

Use it when

A smooth nonlinear relation — saturation, a peak, a threshold — between a few predictors and an outcome.
You want a fast, reproducible network without tuning learning rates or training steps.
Comparing against a multilayer perceptron on the same partition.

Use something else when

Many predictors: Gaussian units cover the input space poorly in high dimensions; reduce predictors first or use a multilayer perceptron.
You need interpretable coefficients and tests: use linear or logistic regression.
Very small training samples: the number of hidden units cannot exceed the number of training cases.
Survey weights must be applied: results are unweighted.

How to run it in Crosstabs

01
Open your data
Open the file in the workspace and switch to Statistics mode.
02
Choose Radial basis function
In the Machine learning group, pick Radial basis function.
03
Set target and predictors
Under Variables choose the Target measurement, the Target, Factors and Covariates, and the Rescaling of covariates (and of a scale target).
04
Set the partitions
Under Partitions set Training, Testing and Holdout (relative) and a Random seed. With a testing sample the number of units is chosen by testing error; without one, by BIC.
05
Choose the architecture and run
Pick the Activation function for hidden layer (Normalized or Ordinary radial basis function) and the Number of units: Best number within an automatically computed range, Best number within a range (Minimum and Maximum hidden units) or Specified number. Optionally set the Overlap among hidden units, then click Run.

Run Radial Basis Function Network in your browser

Worked example

Computed by the Crosstabs engine from the synthetic data below when this page was built — not typed in.

Data

160 synthetic store-weeks with weekly ad spend and shelf price as covariates and unit sales as a scale target. Sales rise with ad spend but saturate, and peak at a mid price, so the relation is smooth but clearly nonlinear. A seeded partition splits cases 7 : 3 into training and testing. Normalized radial basis function, number of units chosen within the automatically computed range, default overlap.

Model Summary

Statistic	Value
Training — Sum of Squares Error	14.520
Training — Relative Error	0.266
Testing — Sum of Squares Error	5.572
Testing — Relative Error	0.385

Errors are computed on the rescaled target.

Selection of the Number of Hidden Units

Hidden units	Testing error
2	13.806
3	11.266
4	7.137
5	6.237
6	6.032
7	6.262
8	6.793
9	5.572
10	6.056

TwoStep found 3 clusters automatically; the searched range is 2 to 10 units. The model with the smallest testing error is chosen.

Independent Variable Importance

Predictor	Importance	Normalized Importance
ad_spend	0.606	100.0%
price	0.394	65.0%

Sensitivity analysis on the combined training and testing samples.

How to read it

The search over 2–10 hidden units picked 9 Gaussian basis functions, the count with the lowest testing error. Their relative error on the 50 testing weeks is 0.385, so the network explains about 61.5% of the variance in rescaled sales on unseen cases and captures the main shape but leaves visible error. ad_spend carries 100.0% of the normalized importance and price 65.0%. Because the output weights are a least-squares fit rather than iterative training, rerunning on the same partition gives the same network.

Output tables explained

Network Information: Input units and rescaling, the number of hidden units, the hidden activation (softmax for normalized units, exponential for ordinary ones), the overlap factor h, and the identity output with sum-of-squares error.
Model Summary: Sum of squares error and relative error (scale) or percent incorrect predictions (categorical) for training, testing and holdout.
Selection of the Number of Hidden Units: Testing error or BIC at each candidate number of units; the footnote gives TwoStep's automatic cluster count and the searched range.
Classification: Observed by predicted counts per partition for a categorical target, with ROC, area under the curve, gains and lift charts.
Independent Variable Importance: Sensitivity-based importance and normalized importance of each predictor.
Parameter Estimates: Hidden layer: each basis function's centre in rescaled input units and its width. Output layer: the least-squares weight from each unit (and a bias for ordinary units).

Assumptions and notes

Similar inputs give similar outputs: each Gaussian unit summarises one cluster of training cases, with a spherical width scaled by the overlap factor (1 + 0.1 × inputs by default).
Covariates are rescaled on the training cases so no predictor dominates the distances; factors are one-of-c coded.
Cases with missing values, and testing or holdout cases with a category unseen in training, are excluded.
The automatic range runs from min(K, R) — at least 2 for normalized units — to max(10, 2K, R), where K is TwoStep's automatic cluster count and R the number of output units, capped at the number of training cases.

How the results are validated

RBF is checked against an independent NumPy implementation of the SPSS RBF chapter that takes cluster assignments from the repository's separate TwoStep reference, places centres and widths from the clusters and fits output weights with numpy.linalg.lstsq; ROC areas come from scikit-learn. Across four configurations (ordinary and normalized units, categorical and scale targets, automatic, range and fixed unit counts, testing-error and BIC selection, a holdout sample and a custom overlap) the TwoStep cluster count and the candidate sequence are identical, testing errors and BIC agree to 1e-8, centres and widths to 1e-10, partition errors to 1e-8, relative errors to 1e-9, importance to 1e-9 and AUC to 1e-12. Validation evidence

Questions

How is an RBF network different from a multilayer perceptron?

An RBF network places its hidden units by clustering and solves the output weights in one least-squares step, so it is fast and deterministic. A multilayer perceptron learns all weights iteratively from a random start, which is slower but often more flexible with many predictors.

Normalized or ordinary radial basis function?

Normalized units divide each activation by their sum (a softmax), so every input gets a full set of weights even far from any centre; this is the default. Ordinary units use the raw Gaussian values plus a bias and can fade to the bias far from the data.

How is the number of hidden units chosen?

Each candidate number is fitted with TwoStep clusters of that size; the one with the lowest testing error wins, or the lowest BIC when there is no testing sample. Choose Specified number to fix it yourself.

What does the overlap factor do?

It widens or narrows every Gaussian unit. Larger values give smoother predictions that blend neighbouring clusters; smaller values make each unit more local. Leave it blank for the default 1 + 0.1 × the number of input units.

Is my data uploaded?

No. Clustering and fitting run in a Web Worker in your browser.

Run Radial Basis Function Network on your own data

Open a .sav, CSV or Excel file. Everything runs in your browser; the file never leaves your device.

Open the workspace

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