Khang Le

Khang Le, Joaquín Torres-Sospedra, Philipp Müller

Fixed Radius Near Neighbor (FRNN) search is an alternative to the widely used k Nearest Neighbors (kNN) search. Unlike kNN, FRNN determines a label or an estimate for a test sample based on all training samples within a predefined distance. While this approach is beneficial in certain scenarios, assuming a fixed maximum distance for all training samples can decrease the accuracy of the FRNN. Therefore, in this paper we propose the Adaptive Radius Near Neighbor (ARNN) and the Weighted ARNN (WARNN), which employ adaptive distances and in latter case weights. All three methods are compared to kNN and twelve of its variants for a regression problem, namely WiFi fingerprinting indoor positioning, using 22 different datasets to provide a comprehensive analysis. While the performances of the tested FRNN and ARNN versions were amongst the worse, three of the four best methods in the test were WARNN versions, indicating that using weights together with adaptive distances achieves performance comparable or even better than kNN variants.

Khang Le, Ha Thach, Anh M. Vu et al.

Weakly supervised semantic segmentation (WSSS) in histopathology relies heavily on classification backbones, yet these models often localize only the most discriminative regions and struggle to capture the full spatial extent of tissue structures. Vision-language models such as CONCH offer rich semantic alignment and morphology-aware representations, while modern segmentation backbones like SegFormer preserve fine-grained spatial cues. However, combining these complementary strengths remains challenging, especially under weak supervision and without dense annotations. We propose a prototype learning framework for WSSS in histopathological images that integrates morphology-aware representations from CONCH, multi-scale structural cues from SegFormer, and text-guided semantic alignment to produce prototypes that are simultaneously semantically discriminative and spatially coherent. To effectively leverage these heterogeneous sources, we introduce text-guided prototype initialization that incorporates pathology descriptions to generate more complete and semantically accurate pseudo-masks. A structural distillation mechanism transfers spatial knowledge from SegFormer to preserve fine-grained morphological patterns and local tissue boundaries during prototype learning. Our approach produces high-quality pseudo masks without pixel-level annotations, improves localization completeness, and enhances semantic consistency across tissue types. Experiments on BCSS-WSSS datasets demonstrate that our prototype learning framework outperforms existing WSSS methods while remaining computationally efficient through frozen foundation model backbones and lightweight trainable adapters.

Khang Le, Anh Mai Vu, Thi Kim Trang Vo et al.

Weakly supervised semantic segmentation (WSSS) in histopathology reduces pixel-level labeling by learning from image-level labels, but it is hindered by inter-class homogeneity, intra-class heterogeneity, and CAM-induced region shrinkage (global pooling-based class activation maps whose activations highlight only the most distinctive areas and miss nearby class regions). Recent works address these challenges by constructing a clustering prototype bank and then refining masks in a separate stage; however, such two-stage pipelines are costly, sensitive to hyperparameters, and decouple prototype discovery from segmentation learning, limiting their effectiveness and efficiency. We propose a cluster-free, one-stage learnable-prototype framework with diversity regularization to enhance morphological intra-class heterogeneity coverage. Our approach achieves state-of-the-art (SOTA) performance on BCSS-WSSS, outperforming prior methods in mIoU and mDice. Qualitative segmentation maps show sharper boundaries and fewer mislabels, and activation heatmaps further reveal that, compared with clustering-based prototypes, our learnable prototypes cover more diverse and complementary regions within each class, providing consistent qualitative evidence for their effectiveness.

Khang Le, Dung Le, Huy Nguyen et al.

We study the entropic Gromov-Wasserstein and its unbalanced version between (unbalanced) Gaussian distributions with different dimensions. When the metric is the inner product, which we refer to as inner product Gromov-Wasserstein (IGW), we demonstrate that the optimal transportation plans of entropic IGW and its unbalanced variant are (unbalanced) Gaussian distributions. Via an application of von Neumann's trace inequality, we obtain closed-form expressions for the entropic IGW between these Gaussian distributions. Finally, we consider an entropic inner product Gromov-Wasserstein barycenter of multiple Gaussian distributions. We prove that the barycenter is a Gaussian distribution when the entropic regularization parameter is small. We further derive a closed-form expression for the covariance matrix of the barycenter.

Khang Le, Huy Nguyen, Tung Pham et al.

We study the multi-marginal partial optimal transport (POT) problem between $m$ discrete (unbalanced) measures with at most $n$ supports. We first prove that we can obtain two equivalence forms of the multimarginal POT problem in terms of the multimarginal optimal transport problem via novel extensions of cost tensor. The first equivalence form is derived under the assumptions that the total masses of each measure are sufficiently close while the second equivalence form does not require any conditions on these masses but at the price of more sophisticated extended cost tensor. Our proof techniques for obtaining these equivalence forms rely on novel procedures of moving mass in graph theory to push transportation plan into appropriate regions. Finally, based on the equivalence forms, we develop optimization algorithm, named ApproxMPOT algorithm, that builds upon the Sinkhorn algorithm for solving the entropic regularized multimarginal optimal transport. We demonstrate that the ApproxMPOT algorithm can approximate the optimal value of multimarginal POT problem with a computational complexity upper bound of the order $\tilde{\mathcal{O}}(m^3(n+1)^{m}/ \varepsilon^2)$ where $\varepsilon > 0$ stands for the desired tolerance.

Khang Le, Huy Nguyen, Quang Nguyen et al.

We consider robust variants of the standard optimal transport, named robust optimal transport, where marginal constraints are relaxed via Kullback-Leibler divergence. We show that Sinkhorn-based algorithms can approximate the optimal cost of robust optimal transport in $\widetilde{\mathcal{O}}(\frac{n^2}{\varepsilon})$ time, in which $n$ is the number of supports of the probability distributions and $\varepsilon$ is the desired error. Furthermore, we investigate a fixed-support robust barycenter problem between $m$ discrete probability distributions with at most $n$ number of supports and develop an approximating algorithm based on iterative Bregman projections (IBP). For the specific case $m = 2$, we show that this algorithm can approximate the optimal barycenter value in $\widetilde{\mathcal{O}}(\frac{mn^2}{\varepsilon})$ time, thus being better than the previous complexity $\widetilde{\mathcal{O}}(\frac{mn^2}{\varepsilon^2})$ of the IBP algorithm for approximating the Wasserstein barycenter.

Khiem Pham, Khang Le, Nhat Ho et al.

We provide a computational complexity analysis for the Sinkhorn algorithm that solves the entropic regularized Unbalanced Optimal Transport (UOT) problem between two measures of possibly different masses with at most $n$ components. We show that the complexity of the Sinkhorn algorithm for finding an $\varepsilon$-approximate solution to the UOT problem is of order $\widetilde{\mathcal{O}}(n^2/ \varepsilon)$, which is near-linear time. To the best of our knowledge, this complexity is better than the complexity of the Sinkhorn algorithm for solving the Optimal Transport (OT) problem, which is of order $\widetilde{\mathcal{O}}(n^2/\varepsilon^2)$. Our proof technique is based on the geometric convergence of the Sinkhorn updates to the optimal dual solution of the entropic regularized UOT problem and some properties of the primal solution. It is also different from the proof for the complexity of the Sinkhorn algorithm for approximating the OT problem since the UOT solution does not have to meet the marginal constraints.