Clustering with Target Encodings

• Clustering-based strategy using target encodings is a machine learning approach that transforms categorical variables into statistical embeddings for informed grouping.
• It leverages conditional means and standard deviations to create dissimilarity matrices for hierarchical clustering, optimizing group assignments with measures like the Silhouette coefficient.
• Integration into kernel methods and applications in online learning, privacy-preserving tasks, and algorithm selection demonstrate its robustness and computational efficiency.

A clustering-based strategy using target encodings refers to a set of methodologies in machine learning where target or response information is used to define representations or metrics for clustering, ultimately supporting improved modeling, classification, regression, or representation learning. Instead of clustering solely on raw feature similarity, these strategies leverage statistical summaries or probabilistic encodings of the target variable—typically categorical or continuous outcomes—to inform grouping. This paradigm is particularly effective when the structure over categorical variables is unknown, target relationships are complex or evolving, or when domain adaptation or privacy requirements are present.

1. Target Encoding Foundations and Statistical Summaries

Target encoding transforms each categorical input level into a numerical vector summarizing its relationship with the target variable. For a categorical input $z$ with levels $c \in \{1, \ldots, C\}$ and associated outcomes $y^{(i)}$, standard practice is to compute for each level $c$:

• The conditional mean $\mu_c = \frac{1}{|I_c|} \sum_{i \in I_c} y^{(i)}$
• The conditional standard deviation $$\sigma_c = \sqrt{\frac{1}{|I_c|} \sum_{i \in I_c} (y^{(i)} - \mu_c)^2}$$

where $I_c = \{i: z^{(i)} = c\}$. This $2$-vector encoding $\psi(c) = (\mu_c, \sigma_c)$ provides a concise yet informative embedding of the categorical level in the space of target outcomes. The intuition is that levels producing similar mean and spread in the target induce similar functional effects and can be grouped together for downstream modeling (Perez et al., 2 Oct 2025).

2. Level Dissimilarity and Clustering

Given the target-based embeddings, a pairwise dissimilarity matrix across categorical levels is constructed, typically using the Euclidean distance:

$d(c, c') = \|\psi(c) - \psi(c')\|$

Alternative metrics, such as statistical divergences (e.g., Wasserstein), are theoretically feasible, but for moderate levels and small sample sizes per level, mean and variance summary statistics remain most practical. The dissimilarity matrix $D$ serves as input to a hierarchical clustering algorithm (e.g., agglomerative clustering), yielding $Q$ groups that summarize the level structure. Selection of $Q$ is automated by maximizing a clustering quality measure such as the average Silhouette coefficient, which is defined for each level as the contrast between within-cluster and nearest out-of-cluster dissimilarity (Perez et al., 2 Oct 2025).

3. Integration into Kernel Methods: Nested Group Kernels

Post-clustering, the categorical variable's levels are replaced by group assignments, enabling the use of "nested" or group kernels within Gaussian process regression or similar frameworks. The kernel is block-structured:

$$T = \begin{bmatrix} W_1 & B_{1,2} & \cdots \ B_{2,1} & W_2 & \cdots \ \vdots & \vdots & \ddots \end{bmatrix}$$

with block $W_l$ for within-group covariances and block $B_{l,l'}$ (constant) for between-group covariances. All kernel parameters are estimated alongside other hyperparameters by maximizing marginal likelihood. This effectively models prior similarity among grouped levels discovered solely from target outcomes, making the approach robust even in the absence of domain-specific group knowledge (Perez et al., 2 Oct 2025).

4. Performance and Computational Considerations

Extensive experiments demonstrate that target-encoding-based clustering is highly competitive:

• On datasets lacking a priori group structure, nested kernels with target-encoded clusters ("MSD"—mean, standard deviation) generally outperform one-hot encoding as well as kernels built on latent variable Gaussian process (LVGP) pre-training.
• When the real group structure is recoverable from target statistics (as in the beam bending dataset with 9+ samples per level), clustering via mean-variance encoding approaches the gold-standard performance of kernels built with known groups. With sparse observations, clustering may only partially reconstruct groups, but performance still exceeds naive or under-parameterized kernels.
• The computational expense of summarizing levels and hierarchically clustering them is minimal compared to learning LVGP mappings or cross-validating all possible group assignments—making target encoding strategies well-suited for settings demanding low overhead (Perez et al., 2 Oct 2025).

The efficacy of this approach is evaluated with performance profiles: cumulative distribution functions $p_i(\tau)$ of the fraction of tasks where a method's relative error is within the top $\tau\%$ of best errors, and associated area under the curve (AUC) metrics. Pareto front analyses identify the best accuracy/runtime trade-off among all methods assessed.

5. Broader Methodological Implications

This strategy generalizes across machine learning tasks and modalities:

• In neural networks, encoding categorical information by combining target-encoding and clustering has been used to define error-correcting output codes and robust classification targets, leveraging similarity in label space and boosting convergence and robustness (Rodríguez et al., 2018, Jaiswal et al., 2019).
• In bandit and online learning, adaptive clustering of contexts linked to learned encoders allows target-aware grouping and dynamically refined representations for policy selection (Lin et al., 2018).
• In privacy-preserving, distributed, or concept-drift scenarios, target encoding combined with clustering supports consensus labeling and updated trust assignment among classifiers and clusterers, accommodating shifts in distribution and decentralizing computation (Acharya et al., 2012).
• For algorithm selection in mixed-variable optimization, target encoding enables the mapping of categorical variables into continuous landscape features, essential for algorithm selector models; further hybridization with local (context-dependent) encoding such as SHAP (Shapley Additive Explanations) enhances performance by mixing global and local perspectives (Dietrich et al., 10 Jul 2024).

6. Comparative Advantages and Limitations

The target-encoding-based clustering approach shows robustness to unknown group structure, high predictive performance, and low computational overhead compared to alternatives:

• Direct one-hot or integer encodings ignore level effect similarities, leading to reduced statistical efficiency and potential overfitting in high-cardinality settings (Pargent et al., 2021).
• Latent variable kernel approaches require model pre-training and hyperparameter tuning, increasing complexity and computational cost.
• Cross-validating all possible groupings is intractable in moderate- to high-cardinality settings. The data-driven nature of target encoding allows group discovery to adapt as new data and outcome patterns emerge, making the strategy especially relevant in online, streaming, or dynamically shifting contexts (Perez et al., 2 Oct 2025, Lorasdagi et al., 10 Nov 2024).

A plausible implication is that when categorical input levels exhibit similar responses with respect to the outcome variable, clustering based on target encodings not only provides appropriate grouping for improved statistical modeling but also offers a data-driven alternative to domain-driven grouping in the absence of explicit structure.

7. Summary

Clustering-based strategies using target encodings fundamentally reshape the handling of categorical variables by embedding each level according to its statistical relation to the target, enabling principled clustering. The derived group structure can then be used to define more expressive covariance kernels, robust error-correcting codes, or adaptive models in both offline and online settings. This approach is validated as computationally efficient, accurate, and adaptable—outperforming naive baselines and competitive alternatives—particularly on real-world datasets lacking prior categorical group knowledge (Perez et al., 2 Oct 2025). The generality of this paradigm suggests continued applicability across supervised, unsupervised, and semi-supervised settings in contemporary machine learning research.