Although prototype-based explanations provide a human-understandable way of representing model predictions they often fail to direct user attention to the most relevant features. We propose a novel approach to identify the most informative features within prototypes, termed alike parts. Using feature importance scores derived from an agnostic explanation method, it emphasizes the most relevant overlapping features between an instance and its nearest prototype. Furthermore, the feature importance score is incorporated into the objective function of the prototype selection algorithms to promote global prototypes diversity. Through experiments on six benchmark datasets, we demonstrate that the proposed approach improves user comprehension while maintaining or even increasing predictive accuracy.
Research on explaining black-box machine learning methods, which have been intensively developing in
recent years, has led to the introduction of a great number of various explanation methods; see, e.g. [
Although in general prototypes can be applied to diferent types of data, in this paper we focus on
tabular data, i.e., the description of examples in the form of vectors of (feature , value) pairs. However,
their interpretation may be a challenge, especially when there are too many features [
Recall that similar expectations have been examined for other data modalities. For images,
prototypical parts networks were introduced to identify characteristic patches instead of complete images [
Our approach uses feature importance in two ways. First, we identify alike parts by highlighting the most informative overlapping features between an instance and its nearest prototype, directing the user’s attention to a limited number of key features when interpreting a model prediction. Second, we incorporate feature importance into the prototype selection objective function to promote diversity, which aids in identifying alike parts. These strategies balance interpretability and diversity, enhancing both local explanations and prototype selection. The methods are evaluated on benchmark datasets, with source code available on GitHub1.
A dataset consists of instances (learning examples), expressed as = (x, )=1, where each x ∈ X represents a dimensional feature vector, and ∈ denotes its corresponding label. In this work, we consider tabular data in a feature-value format. We assume the presence of a classifier ℎ trained in , which serves as a black-box model to make predictions. The classifier ℎ maps an input instance x to a predicted label : ℎ(x) ↦→ ^.
From our perspective, a prototype is a representative instance selected from the dataset, i.e., an element (x , ^ ), where ^ denotes the class assignment of the instance made by the classifier ℎ. Typically, the set of prototypes, denoted as , is a subset of , such that = {(x , )}=1, where ≪ ( ⊂ ), ensuring that the number of prototypes is much smaller than the total size of the training dataset.
Some prototype selection methods use kernel functions and vector quantization [
More recent proposals mitigate these distance limitations by considering the proximity of instances in
the new space, referring to predictions of the black-box model; see the tree-space prototypes developed
for explaining ensembles. The first algorithm, SM-A, introduced in [
Although numerous methods have been proposed to assess feature influence for black-box model
predictions, they have not been widely applied in conjunction with prototype-based explanations.
Popular techniques such as SHAP [
Despite multiple studies on prototypes for tabular data, only a few papers discuss how prototypes
should be presented to end users. In [
In Section 3.1 we will first present our proposal to support the local explanation of the example predication by the nearest prototype. Then, in Section 3.2 we will generalize it to create a diverse global set of prototypes.
Following [
Finding alike parts for the instance and its prototype from Apple Quality dataset. The first two rows present the feature importance values for the instance and its prototype, respectively. The third row shows the computed weights, obtained as the element-wise product of normalized feature importance scores (Formula 2). The bottom row indicates the binary mask, which selects the most relevant shared features-those with weights above the mean - denoted by ’1’
Instance Prototype Weights Mask
Size -2.77 -0.97 0.18 1 -1.08 -0.20 0.02
0 Weight Sweetness
Crunchiness Juiciness
Ripeness
Acidity -1.72 -3.07 0.27 1 1.38 0.00 0.00 0 0.19 -0.52 0.00 0 3.65 3.16 0.51 1 0.31 -0.52 0.00 0
Therefore, we propose a method that identifies the most informative features shared between an instance and its prototype, guiding the user’s attention to a concise subset of features. Further, we refer to them as alike parts, where the importance of features within the alike part is similarly high in both the instance and its nearest prototype.
To explain the instance x by its nearest prototype p , we first identify the alike parts by computing
feature importance scores for each feature ∈ 1, . . . , in the classification of
classifier ℎ, denoted as (ℎ, x) and (ℎ, p ), respectively. We use the SHAP method [
((ℎ, x))2 ∑︀ =1((ℎ, x))2 , ^(ℎ, p ) =
((ℎ, p ))2 ∑︀ =1((ℎ, p))2
The prototype selection algorithms discussed in this paper, such as [
︃( = ⊮ > 1 ∑︁ =1
)︃ () = ∑︁ || =1 p∈
min (x, p ) ,
where the notation || refers to the cardinality of the training set. The choice of the distance function
varies between diferent algorithms. In neural network-based approaches, it can be a dot product
between trainable embeddings [
To strengthen diversification in feature importance, we propose extending the objective function by including an additional feature importance component defined as the product of normalized feature importance of -th feature of instance x and its nearest prototype p :
(x, p ) = ∑︁ =1
((ℎ, x))2 ((ℎ, p ))2 ∑︀=1((ℎ, x))2 · ∑︀=1((ℎ, p))2 .
The scores can be calculated once for all x prior to optimization and cached for eficiency. The revised function incorporates both the minimization of the distance between each instance and its nearest prototype and an additional term weighted by to account for the feature importance score. The first term promotes that each instance in the dataset is well represented by a prototype, promoting compact coverage of by assigning each instance to its closest prototype, while the second encourages diversification in the feature importance across prototypes. The revised function is formally defined as: || () = ∑︁ min ( (x, p ) + · (x, p )) ,
=1 p∈
This modification enables a more nuanced global prototype selection, with balancing distance and
feature importance. The updated formulation improves prototype selection for identifying alike parts.
The proposed method is robust to missing values, assuming that the selected components can handle
them. In this paper, we used prototype selection algorithms [
As discussed in Section 3.2, the proposed optimization method can be adapted to various algorithms. We
applied this modification to prototype selection algorithms optimizing tree distance: A-PETE, SM-A, and
G-KM [
The experiments are organized as follows: Section 4.1 presents examples of alike parts identification on real data and how extending the optimized function improves this process. Section 4.2 aims to quantify the quality of the proposed improvements by comparing our modified with the original prototype selection methods, highlighting the impact of our changes. Section 4.3 presents an ablation study that analyzes the contribution of the factor to algorithm performance.
Finding alike parts on real data is shown in Table 1, illustrating how feature importance for both the
instance and prototype is used to compute weights. Table 2 compares how alike parts of an instance
and its nearest prototype are selected using the original (raw) and FI-informed versions of the A-Pete
for the Diabetes dataset. Incorporating feature importance into A-Pete’s optimization led to diferent
selections than the raw algorithm when generating prototypes from black-box RF [
For example, when using the prototype from raw A-PETE, only the Glucose is highlighted as the
feature important for both the instance and prototype. Meanwhile, the FI-informed algorithm also
highlights Diabetes Pedigree Function, and Age which aligns with established medical knowledge on
diabetes risk factors [
A visual comparison of the globally generated sets of prototypes and selected important attributes for the Diabetes dataset is presented as Figure 1. The figure contrasts prototypes generated using the original (raw) A-Pete algorithm with those generated using the FI-informed approach. The figure demonstrates that the FI-informed algorithm yields more diversified prototypes that highlight parts varying between prototypes – the sixth feature was selected as important only when FI was included in the target function. A similar phenomenon was observed for Australia Rain and Breast Cancer – certain features were considered significant only when using the FI-informed version of the algorithm.
The proposed approach was validated on the test subset of each dataset to quantitatively compare the frequency of features identified as important. In the Figure 2, presenting results, one can observe that the frequency of highlighting each feature difers between the original and FI-informed strategies. This diference is especially noticeable for the G-KM algorithm: when prototypes are selected using the FI-informed strategy, certain features are highlighted that were not emphasized by the raw algorithm.
3https://www.kaggle.com/datasets/rahmasleam/breast-cancer 4https://www.kaggle.com/datasets/mathchi/diabetes-data-set 5https://www.kaggle.com/datasets/teejmahal20/airline-passenger-satisfaction 6https://www.kaggle.com/datasets/nelgiriyewithana/apple-quality 7https://www.kaggle.com/datasets/taweilo/wine-quality-dataset-balanced-classification
This section compares the accuracy achieved by a surrogate model based on prototypes, as it was
done in [
Figure 3 illustrates how algorithm-specific hyperparameters and the weighting factor influence prototype selection and consequently impact accuracy, with controlling the extent to which feature importance is incorporated into the optimization function. The results show that the modified approach maintains or improves predictive performance with respect to main parameters. Similar information is presented in Table 3 where the values corresponding to the accuracy optima found are presented for the original and the FI-incorporated algorithms.
Here, we analyze the impact of the parameter on the selection of the prototype by examining how it influences the alikeness between an explained instance and its prototype. Figure 4 shows how mean feature importance and alike-part length vary with . The results indicate that as increases, the mean feature importance similarity tends to rise, suggesting that high encourages the selection of prototypes that align more closely with important features of the explained instance. However, this trend is not strictly monotonic and careful tuning is required, with ≤ 2.0 often providing a good balance, although the optimal value depends on the dataset. To determine the optimal value of , grid search or Bayesian optimization can be used to tune and other algorithm-specific parameters, aiming to maximize the accuracy of a surrogate 1-NN model.
This work introduces an innovative approach to prototype-based explanations, enhancing their interpretability by directing user attention to the most important features of both the prototype and the classified instance, the so-called alike parts. By incorporating feature importance into the prototype selection, our proposal bridges a gap in the literature where these two aspects were previously considered separately. The experimental results suggest that this integration improves the clarity of the explanation while preserving and, in some cases, even improving the predictive accuracy (see Section 4.2). Incorporating feature importance leads to selecting prototypes with diferent, often more meaningful, alike parts. This was shown with the Diabetes dataset, where our method identified features such as Age and Pedigree Function as crucial, aligning with established medical knowledge (see Section 4.1). Moreover, it can extend beyond the tested algorithms, G-KM, SM-A, A-PETE, and a black-box RF. Importantly, Section 4.3 shows that adjusting the weighting factor fine-tunes the balance between feature importance and distance minimization, highlighting adaptability to diferent tasks. Future research should explore its efectiveness from the user perspective, assessing whether these explanations enhance human understanding of model decisions. Furthermore, evaluating the approach on non-tabular modalities, such as images and text, is necessary to assess its broader applicability.
This research was funded in part by National Science Centre, Poland OPUS grant no. 2023/51/B/ST6/00545 and in part by PUT SBAD 0311/SBAD/0752 grant.