Interpretable Dimensionality Reduction by Feature-preserving Manifold Approximation and Projection

Yang Yang, Hongjian Sun, Jialei Gong, Di Yu

Keywords: Interpretable, Gradient, Tangent space, Manifold learning

TL;DR: Using manifold gradients to interpret the embedding of nonlinear dimensionality reduction.

Abstract: Nonlinear dimensionality reduction often lacks interpretability due to the absence of source features in low-dimensional embedding space. We propose FeatureMAP, an interpretable method that preserves source features by tangent space embedding. The core of FeatureMAP is to use local principal component analysis (PCA) to approximate tangent spaces. By leveraging these tangent spaces, FeatureMAP computes gradients to locally reveal feature directions and importance. Additionally, FeatureMAP embeds the tangent spaces into low-dimensional space while preserving alignment between them, providing local gauges for projecting the high-dimensional data points. Unlike UMAP, FeatureMAP employs anisotropic projection to preserve both the manifold structure and the original data density. We apply FeatureMAP to interpreting digit classification, object detection and MNIST adversarial examples, where it effectively distinguishes digits and objects using feature importance and provides explanations for misclassifications in adversarial attacks. We also compare FeatureMAP with other state-of-the-art methods using both local and global metrics.

Primary Area: unsupervised, self-supervised, semi-supervised, and supervised representation learning

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Submission Number: 4334