Class-constrained t-SNE: Combining Data Features and Class Probabilities

TL;DR

This paper tackles the challenge of jointly visualizing data features and class probabilities in a single dimensionality-reduced projection. It introduces class-constrained t-SNE, a dual-objective framework that couples data-feature preservation with a class-probability structure through class landmarks, controlled by a balance parameter $α$ and a distance penalty $λ$. The method optimizes data points $Y$ and class landmarks $V$ via two costs $fc_1=KL(P^d||Q^d)$ and $fc_2=(1/n)\sum_i KL(P^c_i||Q^c_i) + λ D$, with $D=(1/m)\sum_{u=1}^m p^c_{iu} |y_i - v_u|^2$, enabling smooth transitions between perspectives and preserving mental map during exploration. Empirical results on synthetic data, Fashion-MNIST, and document-topic datasets show improved interpretability and practical utility for model evaluation and visual-interactive labeling, while the discussion outlines limitations and avenues for future work, including acceleration and extension to other DR methods.

Abstract

Data features and class probabilities are two main perspectives when, e.g., evaluating model results and identifying problematic items. Class probabilities represent the likelihood that each instance belongs to a particular class, which can be produced by probabilistic classifiers or even human labeling with uncertainty. Since both perspectives are multi-dimensional data, dimensionality reduction (DR) techniques are commonly used to extract informative characteristics from them. However, existing methods either focus solely on the data feature perspective or rely on class probability estimates to guide the DR process. In contrast to previous work where separate views are linked to conduct the analysis, we propose a novel approach, class-constrained t-SNE, that combines data features and class probabilities in the same DR result. Specifically, we combine them by balancing two corresponding components in a cost function to optimize the positions of data points and iconic representation of classes -- class landmarks. Furthermore, an interactive user-adjustable parameter balances these two components so that users can focus on the weighted perspectives of interest and also empowers a smooth visual transition between varying perspectives to preserve the mental map. We illustrate its application potential in model evaluation and visual-interactive labeling. A comparative analysis is performed to evaluate the DR results.

Figures (12)

• Figure 1: A demonstration of DR results based on a single or combined perspective of data feature and class probability where data points are colored by predicted classes. (a) Data feature projection shows data feature characteristics by applying standard distance-based DR to data feature values. (b) Class radial visualization is employed to reveal probability-based model performance. (c) Class-constrained t-SNE enables the combination of data features and class probabilities.
• Figure 2: Illustration of using force to interpret the gradient. Grey points denote data points, and each circle labeled as $v_{i}$ is one class landmark.
• Figure 3: Projection results of a synthetic dataset with various $\alpha$ values using our method (top) and a baseline method (bottom).
• Figure 4: Projection results of a synthetic dataset with various $\lambda$ values ($\alpha=1$).
• Figure 5: Projection results of two datasets with three $\alpha$ values using our method (top) and a baseline method (bottom).