We revisit the consistency and specificity of LRP and LLP, and design a new unified structural fusion strategy to integrate both linear and locally linear
structures from a global perspective. We reveal that the proposed structural fusion strategy is a generalization of LLP under a newly defined η-norm.
We rethink existing paradigms and find that a common design is to construct the bipartite graph directly from the input data,
i.e. only consider the unidirectional "encoding" process. Inspired by the popular "encoding-decoding" design in deep learning,
we transfer it into graph machine learning and propose a novel model.
One crucial finding is that the existence of noisy features will incur "anchor shift",
which deviates from the potential centroids.
We propose a novel noisy feature filter mechanism to remedy the anchor shift,
and we theoretically analyze the bounds of the bipartite graph's sparsity.
We investigate an important issue that how to localize the kernel matrix in multi-kernel clustering. Compared to the traditional KNN manner that neglects the ranking relationship of neighbors, this paper proposes a novel localized MKC algorithm coupled flexible graph learning, termd LSWMKC, which achieves fully exploring the latent local manifold.
We mathematically disassemble the noise within kernel partition into dual noise,
namely, Null space noise (N-noise) and Column space noise (C-noise),
and propose an elegant method to minimize them. We observe that dual noise will pollute the block diagonal structures. An interesting finding is that C-noise exhibits stronger destruction than N-noise.
We explore deep-in reasons of representation collapse in deep graph clustering and improve the dual correlation reduction network with the affinity recovery strategy.
We propose to replace the complicated and consuming graph data augmentations by designing the parameter un-shared siamese encoders and perurbing the node embeddings.
We propose Hard Sample Aware Network (HSAN) to mine both the hard positive samples and hard negative samples with a comprehensive similarity measure criterion and a general dynamic sample weighing strategy.