ShapDBM: Exploring Decision Boundary Maps in Shapley Space

Luke Watkin; Daniel Archambault; Alex Telea

cs.HCMar 23, 2026

ShapDBM: Exploring Decision Boundary Maps in Shapley Space

Authors: Luke Watkin, Daniel Archambault, Alex Telea

Organizations: School of Computing, Newcastle University, UK · Department of Information and Computing Science, Utrecht University, Netherlands

Abstract

Decision Boundary Maps (DBMs) are an effective tool for visualising machine learning classification boundaries. Yet, DBM quality strongly depends on the dimensionality reduction (DR) technique and high dimensional space used for the data points. For complex ML data, DR can create many mixed classes which yield DBMs that are hard to use or even misleading. We propose a new technique to compute DBMs by transforming data space into Shapley space and computing DR on it. Compared to DBMs computed directly from data, our maps have similar or higher quality metric values and visibly more compact, easier to explore, decision zones that better agree with measured model performance.

Figures & tables

	Model			Data			Shapley
Dataset	Acc	AP	AR	MA	MP	MR	MA	MP	MR
MNIST	99.6	.996	.995	96.8	.97(.0001)	.97(.0003)	91.8	.93(.01)	.92(.004)
SVHN	95.3	.950	.949	25.3	.27(.02)	.22(.02)	85.4	.86(.005)	.83(.005)
CIFAR-4	89.9	.899	.899	49.4	.51(.002)	.49(.06)	44.4	.63(.08)	.44(.13)

Table 1: Model accuracy (Acc), average precision (AP), average recall (AR). Maps average accuracy (MA), average precision (MP), and average recall (MR) scores, variance shown in brackets.

Figure 1: Data space projections $P(D)$ and DBMs (a,c) and Shapley space projection $P(S)$ and DBMs (b,d), MNIST and CIFAR-4.

Figure 2: Shapley DBM for SVHN with samples A-E from classes having multiple decision zones. A region R is marked where boundaries strongly differ from what the projection plot (Fig. b) conveys.

Figure 3: Samples from MNIST dataset (top) and reconstructed samples based on projections using NNInv trained on data space projections (middle) or projected Shapley values (bottom)

Figure 4: SVHN and CIFAR-4 samples reconstructed using NNInv from data space and Shapley space projections.

Panel of Figure 5 — Figure 5: (a) Samples taken from the SVHN dataset used in our case study (note that the samples are resized to 28 pixels instead of 32) and (b) a variant of our SVHN case study created by passing samples of classes 3 and 7 through a Sobel filter.

Dataset	$N$	$N_{train}$	$n$	Estimation Time (hours)
MNIST	70k	60k	784	16
SVHN	99k	73k	2352	21
CIFAR-4	24k	20k	2352	5

Table 2: Computation times for Shapley values for all case study datasets, in relation to the size of the dataset (N), the size of their training sets on which Shapley values are calculated (

N_{train}

) and dimensionality (n).

Panel of Figure 6 — Figure 6: Scatterplots and DBMs for a 10k subset of SVHN using (a) Data space projections $P(D)$ . (b) Shapley space projections $P(S)$ .

Panel of Figure 7 — Figure 7: Scatterplots and DBMs for MNIST using UMAP. (a) Data space projections $P(D)$ . (b) Shapley space projections $P(S)$ .

Panel of Figure 8 — Figure 8: Scatterplots and DBMs for SVHN using UMAP. (a) Data space projections $P(D)$ . (b) Shapley space projections $P(S)$ .

Panel of Figure 9 — Figure 9: Scatterplots and DBMs for CIFAR-4 using UMAP. (a) Data space projections $P(D)$ . (b) Shapley space projections $P(S)$ .

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Sep 25, 2026J/K move · Enter open · S save

LandscapeSHAP: Which Persistent Homology Class Gets the Credit?

Nikola Milićević

Shapley Value Attribution Topological Data Analysis Persistent Homology

Open paper AskPDF arXiv

Shapley values, a solution concept from cooperative game theory, have recently become a standard tool for feature credit allocation in machine learning. They provide an axiomatically justified method to fairly distribute a model's prediction among the data features. Shapley values have not yet been applied to explain machine learning models trained on features from topological data analysis. We develop what we believe is the first such approach, focusing on the persistence landscape featurization of persistence diagrams. Because each landscape coordinate is a rank statistic, crediting a model's prediction back to individual persistent homology classes (persistence diagram points) is nontrivial. We introduce LandscapeSHAP, a method for fair credit allocation to persistence diagram points based on a model's prediction. For linear models on persistence landscapes, LandscapeSHAP has a closed form expression that gives the exact Shapley value of every persistence diagram point. In particular, there is no coalition sampling required. We further prove that the four Shapley "fairness" axioms uniquely characterize this credit allocation for any model, not only linear ones. For a general nonlinear model, this unique value can only be calculated exactly from its defining coalition averaging formula, which requires considering all

2^N

many coalitions, where

N

is the number of points in the persistence diagram. This is computationally intractable for persistence diagrams of realistic size. We complement the exact linear model result with an efficient Monte Carlo sampling of persistence diagram coalitions. We give convergence rates in terms of number of samples needed to approximate to a desired degree of accuracy. We also prove stability results for the LandscapeSHAP credit allocation, for any model.

Abstract

Decision Boundary Analysis

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