Spectral clustering has gained popularity for clustering non-convex data due to its simplicity and effectiveness. It is essential to construct a similarity graph using a high-quality affinity measure that models the local neighborhood relations among the data samples. However, incomplete data can lead to inaccurate affinity measures, resulting in degraded clustering performance. To address these issues, we propose an imputation-free framework with two novel approaches to improve spectral clustering on incomplete data. Firstly, we introduce a new kernel correction method that enhances the quality of the kernel matrix estimated on incomplete data with a theoretical guarantee, benefiting classical spectral clustering on pre-defined kernels. Secondly, we develop a series of affinity learning methods that equip the selfexpressive framework with ℓp-norm to construct an intrinsic affinity matrix with an adaptive extension. Our methods outperform existing data imputation and distance calibration techniques on benchmark datasets, offering a promising solution to spectral clustering on incomplete data in various real-world applications.

Many approaches in machine learning rely on a weighted graph to encode thesimilarities between samples in a dataset. Entropic affinities (EAs), which are notably used in the popular Dimensionality Reduction (DR) algorithm t-SNE, are particular instances of such graphs. To ensure robustness to heterogeneous sampling densities, EAs assign a kernel bandwidth parameter to every sample in such a way that the entropy of each row in the affinity matrix is kept constant at a specific value, whose exponential is known as perplexity. EAs are inherently asymmetric and row-wise stochastic, but they are used in DR approaches after undergoing heuristic symmetrization methods that violate both the row-wise constant entropy and stochasticity properties. In this work, we uncover a novel characterization of EA as an optimal transport problem, allowing a natural symmetrization that can be computed efficiently using dual ascent. The corresponding novel affinity matrix derives advantages from symmetric doubly stochastic normalization in terms of clustering performance, while also effectively controlling the entropy of each row thus making it particularly robust to varying noise levels. Following, we present a new DR algorithm, SNEkhorn, that leverages this new affinity matrix. We show its clear superiority to state-of-the-art approaches with several indicators on both synthetic and real-world datasets.

In this paper, we propose a spatial propagation networks for learning affinity matrix. We show that by constructing a row/column linear propagation model, the spatially variant transformation matrix constitutes an affinity matrix that models dense, global pairwise similarities of an image. Specifically, we develop a three-way connection for the linear propagation model, which (a) formulates a sparse transformation matrix where all elements can be the output from a deep CNN, but (b) results in a dense affinity matrix that is effective to model any task-specific pairwise similarity.

While there is a significant advancement in human pose estimation, it is still very challenging for a model togeneralize todifferent unknownenvironments andunseen persons. Instead of using a fixed model for every test case, we adapt our pose estimator during test time to exploit person-specific information.

Manifold clustering is an important problem in motion and video segmentation, natural image clustering, and other applications where high-dimensional data lie on multiple, low-dimensional, nonlinear manifolds.

These techniques calibrate an initial non-metric distance matrix estimated on incomplete data to a distance metric.

The network is a differentiable deep architecture consisting of feature extraction and diffusion distance modules for computing diffusion distance on image by end-to-end training. We design low resolution kernel matching loss and high resolution segment matching loss to enforce the network's output to beconsistent withhuman-labeled image segments.

Self-supervised heterogeneous graph learning (SHGL) has shown promising potential in diverse scenarios.