Clustering is one of the most fundamental problems in machine learning and data mining, and many algorithms have been proposed in the past decades. Among them, subspace clustering and spectral clustering are the most famous approaches. In this paper, we provide an explanation for subspace clustering and spectral clustering from the perspective of optimal transport. Optimal transport studies how to move samples from one distribution to another distribution with minimal transport cost, and has shown a powerful ability to extract geometric information. By considering a self optimal transport model with only one group of samples, we observe that both subspace clustering and spectral clustering can be explained in the framework of optimal transport, and the optimal transport matrix bridges the spaces of features and spectral embeddings. Inspired by this connection, we propose a spectral optimal transport barycenter model, which learns spectral embeddings by solving a barycenter problem equipped with an optimal transport discrepancy and guidance of data. Based on our proposed model, we take advantage of optimal transport to exploit both feature and metric information involved in data for learning coupled spectral embeddings and affinity matrix in a unified model. We develop an alternating optimization algorithm to solve the resultant problems, and conduct experiments in different settings to evaluate the performance of our proposed methods.
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Relational inference aims to identify interactions between parts of a dynamical system from the observed dynamics. Current state-of-the-art methods fit the dynamics with a graph neural network (GNN) on a learnable graph. They use one-step message-passing GNNs---intuitively the right choice since non-locality of multi-step or spectral GNNs may confuse direct and indirect interactions. But the effective interaction graph depends on the sampling rate and it is rarely localized to direct neighbors, leading to poor local optima for the one-step model. In this work, we propose a graph dynamics prior (GDP) for relational inference. GDP constructively uses error amplification in non-local polynomial filters to steer the solution to the ground-truth graph. To deal with non-uniqueness, GDP simultaneously fits a ``shallow'' one-step model and a polynomial multi-step model with shared graph topology. Experiments show that GDP reconstructs graphs far more accurately than earlier methods, with remarkable robustness to under-sampling. Since appropriate sampling rates for unknown dynamical systems are not known a priori, this robustness makes GDP suitable for real applications in scientific machine learning. Reproducible code is available at https://github.com/DaDaCheng/GDP.
In recent years, spectral graph neural networks, characterized by polynomial filters, have garnered increasing attention and have achieved remarkable performance in tasks such as node classification. These models typically assume that eigenvalues for the normalized Laplacian matrix are distinct from each other, thus expecting a polynomial filter to have a high fitting ability. However, this paper empirically observes that normalized Laplacian matrices frequently possess repeated eigenvalues. Moreover, we theoretically establish that the number of distinguishable eigenvalues plays a pivotal role in determining the expressive power of spectral graph neural networks. In light of this observation, we propose an eigenvalue correction strategy that can free polynomial filters from the constraints of repeated eigenvalue inputs. Concretely, the proposed eigenvalue correction strategy enhances the uniform distribution of eigenvalues, thus mitigating repeated eigenvalues, and improving the fitting capacity and expressive power of polynomial filters. Extensive experimental results on both synthetic and real-world datasets demonstrate the superiority of our method.
Graph Comparative Learning (GCL) is a self-supervised method that combines the advantages of Graph Convolutional Networks (GCNs) and comparative learning, making it promising for learning node representations. However, the GCN encoders used in these methods rely on the Fourier transform to learn fixed graph representations, which is inherently limited by the uncertainty principle involving spatial and spectral localization trade-offs. To overcome the inflexibility of existing methods and the computationally expensive eigen-decomposition and dense matrix multiplication, this paper proposes an Adaptive Spectral Wavelet Transform-based Self-Supervised Graph Neural Network (ASWT-SGNN). The proposed method employs spectral adaptive polynomials to approximate the filter function and optimize the wavelet using contrast loss. This design enables the creation of local filters in both spectral and spatial domains, allowing flexible aggregation of neighborhood information at various scales and facilitating controlled transformation between local and global information. Compared to existing methods, the proposed approach reduces computational complexity and addresses the limitation of graph convolutional neural networks, which are constrained by graph size and lack flexible control over the neighborhood aspect. Extensive experiments on eight benchmark datasets demonstrate that ASWT-SGNN accurately approximates the filter function in high-density spectral regions, avoiding costly eigen-decomposition. Furthermore, ASWT-SGNN achieves comparable performance to state-of-the-art models in node classification tasks.
In the existing spectral GNNs, polynomial-based methods occupy the mainstream in designing a filter through the Laplacian matrix. However, polynomial combinations factored by the Laplacian matrix naturally have limitations in message passing (e.g., over-smoothing). Furthermore, most existing spectral GNNs are based on polynomial bases, which struggle to capture the high-frequency parts of the graph spectral signal. Additionally, we also find that even increasing the polynomial order does not change this situation, which means polynomial-based models have a natural deficiency when facing high-frequency signals. To tackle these problems, we propose WaveNet, which aims to effectively capture the high-frequency part of the graph spectral signal from the perspective of wavelet bases through reconstructing the message propagation matrix. We utilize Multi-Resolution Analysis (MRA) to model this question, and our proposed method can reconstruct arbitrary filters theoretically. We also conduct node classification experiments on real-world graph benchmarks and achieve superior performance on most datasets. Our code is available at https://github.com/Bufordyang/WaveNet
Graph contrastive learning (GCL), learning the node representation by contrasting two augmented graphs in a self-supervised way, has attracted considerable attention. GCL is usually believed to learn the invariant representation. However, does this understanding always hold in practice? In this paper, we first study GCL from the perspective of causality. By analyzing GCL with the structural causal model (SCM), we discover that traditional GCL may not well learn the invariant representations due to the non-causal information contained in the graph. How can we fix it and encourage the current GCL to learn better invariant representations? The SCM offers two requirements and motives us to propose a novel GCL method. Particularly, we introduce the spectral graph augmentation to simulate the intervention upon non-causal factors. Then we design the invariance objective and independence objective to better capture the causal factors. Specifically, (i) the invariance objective encourages the encoder to capture the invariant information contained in causal variables, and (ii) the independence objective aims to reduce the influence of confounders on the causal variables. Experimental results demonstrate the effectiveness of our approach on node classification tasks.
High-dimensional images, known for their rich semantic information, are widely applied in remote sensing and other fields. The spatial information in these images reflects the object's texture features, while the spectral information reveals the potential spectral representations across different bands. Currently, the understanding of high-dimensional images remains limited to a single-domain perspective with performance degradation. Motivated by the masking texture effect observed in the human visual system, we present a multi-domain diffusion-driven feature learning network (MDFL) , a scheme to redefine the effective information domain that the model really focuses on. This method employs diffusion-based posterior sampling to explicitly consider joint information interactions between the high-dimensional manifold structures in the spectral, spatial, and frequency domains, thereby eliminating the influence of masking texture effects in visual models. Additionally, we introduce a feature reuse mechanism to gather deep and raw features of high-dimensional data. We demonstrate that MDFL significantly improves the feature extraction performance of high-dimensional data, thereby providing a powerful aid for revealing the intrinsic patterns and structures of such data. The experimental results on three multi-modal remote sensing datasets show that MDFL reaches an average overall accuracy of 98.25%, outperforming various state-of-the-art baseline schemes. Code available at https://github.com/LDXDU/MDFL-AAAI-24.
Hyperspectral Image Reconstruction via Combinatorial Embedding of Cross-Channel Spatio-Spectral Clues
PDF ↗Existing learning-based hyperspectral reconstruction methods show limitations in fully exploiting the information among the hyperspectral bands. As such, we propose to investigate the chromatic inter-dependencies in their respective hyperspectral embedding space. These embedded features can be fully exploited by querying the inter-channel correlations in a combinatorial manner, with the unique and complementary information efficiently fused into the final prediction. We found such independent modeling and combinatorial excavation mechanisms are extremely beneficial to uncover marginal spectral features, especially in the long wavelength bands. In addition, we have proposed a spatio-spectral attention block and a spectrum-fusion attention module, which greatly facilitates the excavation and fusion of information at both semantically long-range levels and fine-grained pixel levels across all dimensions. Extensive quantitative and qualitative experiments show that our method (dubbed CESST) achieves SOTA performance. Code for this project is at: https://github.com/AlexYangxx/CESST.
Recently, CLIP has found practical utility in the domain of pixel-level zero-shot segmentation tasks. The present landscape features two-stage methodologies beset by issues such as intricate pipelines and elevated computational costs. While current one-stage approaches alleviate these concerns and incorporate Visual Prompt Training (VPT) to uphold CLIP's generalization capacity, they still fall short in fully harnessing CLIP's potential for pixel-level unseen class demarcation and precise pixel predictions. To further stimulate CLIP's zero-shot dense prediction capability, we propose SPT-SEG, a one-stage approach that improves CLIP's adaptability from image to pixel. Specifically, we initially introduce Spectral Prompt Tuning (SPT), incorporating spectral prompts into the CLIP visual encoder's shallow layers to capture structural intricacies of images, thereby enhancing comprehension of unseen classes. Subsequently, we introduce the Spectral Guided Decoder (SGD), utilizing both high and low-frequency information to steer the network's spatial focus towards more prominent classification features, enabling precise pixel-level prediction outcomes. Through extensive experiments on two public datasets, we demonstrate the superiority of our method over state-of-the-art approaches, performing well across all classes and particularly excelling in handling unseen classes.
In this paper, we address the nonrigid shape matching with outliers by a novel and effective pointwise map refinement method, termed Locality Preserving Refinement. For accurate pointwise conversion from a given functional map, our method formulates a two-step procedure. Firstly, starting with noisy point-to-point correspondences, we identify inliers by leveraging the neighborhood support, which yields a closed-form solution with linear time complexity. After obtained the reliable correspondences of inliers, we refine the pointwise correspondences for outliers using local linear embedding, which operates in an adaptive spectral similarity space to further eliminate the ambiguities that are difficult to handle in the functional space. By refining pointwise correspondences with local consistency thus embedding geometric constraints into functional spaces, our method achieves considerable improvement in accuracy with linearithmic time and space cost. Extensive experiments on public benchmarks demonstrate the superiority of our method over the state-of-the-art methods. Our code is publicly available at https://github.com/XiaYifan1999/LOPR.
Enhancing Hyperspectral Images via Diffusion Model and Group-Autoencoder Super-resolution Network
PDF ↗Existing hyperspectral image (HSI) super-resolution (SR) methods struggle to effectively capture the complex spectral-spatial relationships and low-level details, while diffusion models represent a promising generative model known for their exceptional performance in modeling complex relations and learning high and low-level visual features. The direct application of diffusion models to HSI SR is hampered by challenges such as difficulties in model convergence and protracted inference time. In this work, we introduce a novel Group-Autoencoder (GAE) framework that synergistically combines with the diffusion model to construct a highly effective HSI SR model (DMGASR). Our proposed GAE framework encodes high-dimensional HSI data into low-dimensional latent space where the diffusion model works, thereby alleviating the difficulty of training the diffusion model while maintaining band correlation and considerably reducing inference time. Experimental results on both natural and remote sensing hyperspectral datasets demonstrate that the proposed method is superior to other state-of-the-art methods both visually and metrically.
Multi-spectral object Re-identification (ReID) aims to retrieve specific objects by leveraging complementary information from different image spectra. It delivers great advantages over traditional single-spectral ReID in complex visual environment. However, the significant distribution gap among different image spectra poses great challenges for effective multi-spectral feature representations. In addition, most of current Transformer-based ReID methods only utilize the global feature of class tokens to achieve the holistic retrieval, ignoring the local discriminative ones. To address the above issues, we step further to utilize all the tokens of Transformers and propose a cyclic token permutation framework for multi-spectral object ReID, dubbled TOP-ReID. More specifically, we first deploy a multi-stream deep network based on vision Transformers to preserve distinct information from different image spectra. Then, we propose a Token Permutation Module (TPM) for cyclic multi-spectral feature aggregation. It not only facilitates the spatial feature alignment across different image spectra, but also allows the class token of each spectrum to perceive the local details of other spectra. Meanwhile, we propose a Complementary Reconstruction Module (CRM), which introduces dense token-level reconstruction constraints to reduce the distribution gap across different image spectra. With the above modules, our proposed framework can generate more discriminative multi-spectral features for robust object ReID. Extensive experiments on three ReID benchmarks (i.e., RGBNT201, RGBNT100 and MSVR310) verify the effectiveness of our methods. The code is available at https://github.com/924973292/TOP-ReID.
Existing deep pan-sharpening methods lack the learning of complementary information between PAN and MS modalities in the intermediate layers, and exhibit low interpretability due to their black-box designs. To this end, an interpretable deep unfolded network with intrinsic supervision for pan-sharpening is proposed. Building upon the observation degradation process, it formulates the pan-sharpening task as a variational model minimization with spatial consistency prior and spectral projection prior. The former prior requires a joint component decomposition of PAN and MS images to extract intrinsic features. By being supervised in the intermediate layers, it can selectively provide high-frequency information for spatial enhancement. The latter prior constrains the intensity correlation between MS and PAN images derived from physical observations, so as to improve spectral fidelity. To further enhance the transparency of network design, we develop an iterative solution algorithm following the half-quadratic splitting to unfold the deep model. It rigorously adheres to the variational model, significantly enhancing the interpretability behind network design and efficiently alternating the optimization of the network. Extensive experiments demonstrate the advantages of our method compared to state-of-the-arts, showcasing its remarkable generalization capability to real-world scenes. Our code is publicly available at https://github.com/Baixuzx7/DISPNet.
S2CycleDiff: Spatial-Spectral-Bilateral Cycle-Diffusion Framework for Hyperspectral Image Super-resolution
PDF ↗Hyperspectral image super-resolution (HISR) is a technique that can break through the limitation of imaging mechanism to obtain the hyperspectral image (HSI) with high spatial resolution. Although some progress has been achieved by existing methods, most of them directly learn the spatial-spectral joint mapping between the observed images and the target high-resolution HSI (HrHSI), failing to fully reserve the spectral distribution of low-resolution HSI (LrHSI) and the spatial distribution of high-resolution multispectral imagery (HrMSI). To this end, we propose a spatial-spectral-bilateral cycle-diffusion framework (S2CycleDiff) for HISR, which can step-wise generate the HrHSI with high spatial-spectral fidelity by learning the conditional distribution of spatial and spectral super-resolution processes bilaterally. Specifically, a customized conditional cycle-diffusion framework is designed as the backbone to achieve the spatial-spectral-bilateral super-resolution by repeated refinement, wherein the spatial/spectral guided pyramid denoising (SGPD) module seperately takes HrMSI and LrHSI as the guiding factors to achieve the spatial details injection and spectral correction. The outputs of the conditional cycle-diffusion framework are fed into a complementary fusion block to integrate the spatial and spectral details to generate the desired HrHSI. Experiments have been conducted on three widely used datasets to demonstrate the superiority of the proposed method over state-of-the-art HISR methods. The code is available at https://github.com/Jiahuiqu/S2CycleDiff.
Progressive High-Frequency Reconstruction for Pan-Sharpening with Implicit Neural Representation
PDF ↗Pan-sharpening aims to leverage the high-frequency signal of the panchromatic (PAN) image to enhance the resolution of its corresponding multi-spectral (MS) image. However, deep neural networks (DNNs) tend to prioritize learning the low-frequency components during the training process, which limits the restoration of high-frequency edge details in MS images. To overcome this limitation, we treat pan-sharpening as a coarse-to-fine high-frequency restoration problem and propose a novel method for achieving high-quality restoration of edge information in MS images. Specifically, to effectively obtain fine-grained multi-scale contextual features, we design a Band-limited Multi-scale High-frequency Generator (BMHG) that generates high-frequency signals from the PAN image within different bandwidths. During training, higher-frequency signals are progressively injected into the MS image, and corresponding residual blocks are introduced into the network simultaneously. This design enables gradients to flow from later to earlier blocks smoothly, encouraging intermediate blocks to concentrate on missing details. Furthermore, to address the issue of pixel position misalignment arising from multi-scale features fusion, we propose a Spatial-spectral Implicit Image Function (SIIF) that employs implicit neural representation to effectively represent and fuse spatial and spectral features in the continuous domain. Extensive experiments on different datasets demonstrate that our method outperforms existing approaches in terms of quantitative and visual measurements for high-frequency detail recovery.
Coded aperture snapshot spectral imaging (CASSI) system is an effective manner for hyperspectral snapshot compressive imaging. The core issue of CASSI is to solve the inverse problem for the reconstruction of hyperspectral image (HSI). In recent years, Transformer-based methods achieve promising performance in HSI reconstruction. However, capturing both long-range dependencies and local information while ensuring reasonable computational costs remains a challenging problem. In this paper, we propose a Transformer-based HSI reconstruction method called dual-window multiscale Transformer (DWMT), which is a coarse-to-fine process, reconstructing the global properties of HSI with the long-range dependencies. In our method, we propose a novel U-Net architecture using a dual-branch encoder to refine pixel information and full-scale skip connections to fuse different features, enhancing the extraction of fine-grained features. Meanwhile, we design a novel self-attention mechanism called dual-window multiscale multi-head self-attention (DWM-MSA), which utilizes two different-sized windows to compute self-attention, which can capture the long-range dependencies in a local region at different scales to improve the reconstruction performance. We also propose a novel position embedding method for Transformer, named con-abs position embedding (CAPE), which effectively enhances positional information of the HSIs. Extensive experiments on both the simulated and the real data are conducted to demonstrate the superior performance, stability, and generalization ability of our DWMT. Code of this project is at https://github.com/chenx2000/DWMT.
Deep learning models for point clouds have shown to be vulnerable to adversarial attacks, which have received increasing attention in various safety-critical applications such as autonomous driving, robotics, and surveillance. Existing 3D attack methods generally employ global distance losses to implicitly constrain the point-wise perturbations for optimization. However, these simple losses are quite difficult to accurately measure and restrict the proper 3D geometry as point clouds are highly structured. Although few recent works try to exploit additional shape-aware surface knowledge to globally constrain the point position, they still fail to preserve the detailed point-to-point geometric dependency in different local regions. To this end, in this paper, we propose a novel Multi-grained Geometry-aware Attack (MGA), which explicitly captures the local topology characteristics in different 3D regions for adversarial constraint. Specifically, we first develop multi-scale spectral local filter banks adapting to different 3D object shapes to explore potential geometric structures in local regions. Considering that objects may contain complex geometries, we then extend each filter bank into multi-layer ones to gradually capture the topology contexts of the same region in a coarse-to-fine manner. Hence, the focused local geometric structures will be highlighted in the coefficients calculated by the filtering process. At last, by restricting these coefficients between benign and adversarial samples, our MGA is able to properly measure and preserve the detailed geometry contexts in the whole 3D object with trivial perturbations. Extensive experiments demonstrate that our attack can achieve superior performance on various 3D classification models, with satisfying adversarial imperceptibility and strong resistance to different defense methods.
Pan-sharpening is a task that aims to super-resolve the low-resolution multispectral (LRMS) image with the guidance of a corresponding high-resolution panchromatic (PAN) image. The key challenge in pan-sharpening is to accurately modeling the relationship between the MS and PAN images. While supervised deep learning methods are commonly employed to address this task, the unavailability of ground-truth severely limits their effectiveness. In this paper, we propose a mutually guided detail restoration method for unsupervised pan-sharpening. Specifically, we treat pan-sharpening as a blind image deblurring task, in which the blur kernel can be estimated by a CNN. Constrained by the blur kernel, the pan-sharpened image retains spectral information consistent with the LRMS image. Once the pan-sharpened image is obtained, the PAN image is blurred using a pre-defined blur operator. The pan-sharpened image, in turn, is used to guide the detail restoration of the blurred PAN image. By leveraging the mutual guidance between MS and PAN images, the pan-sharpening network can implicitly learn the spatial relationship between the two modalities. Extensive experiments show that the proposed method significantly outperforms existing unsupervised pan-sharpening methods.
In this paper, we propose SpectralNeRF, an end-to-end Neural Radiance Field (NeRF)-based architecture for high-quality physically based rendering from a novel spectral perspective. We modify the classical spectral rendering into two main steps, 1) the generation of a series of spectrum maps spanning different wavelengths, 2) the combination of these spectrum maps for the RGB output. Our SpectralNeRF follows these two steps through the proposed multi-layer perceptron (MLP)-based architecture (SpectralMLP) and Spectrum Attention UNet (SAUNet). Given the ray origin and the ray direction, the SpectralMLP constructs the spectral radiance field to obtain spectrum maps of novel views, which are then sent to the SAUNet to produce RGB images of white-light illumination. Applying NeRF to build up the spectral rendering is a more physically-based way from the perspective of ray-tracing. Further, the spectral radiance fields decompose difficult scenes and improve the performance of NeRF-based methods. Comprehensive experimental results demonstrate the proposed SpectralNeRF is superior to recent NeRF-based methods when synthesizing new views on synthetic and real datasets. The codes and datasets are available at https://github.com/liru0126/SpectralNeRF.
Pan-sharpening involves reconstructing missing high-frequency information in multi-spectral images with low spatial resolution, using a higher-resolution panchromatic image as guidance. Although the inborn connection with frequency domain, existing pan-sharpening research has not almost investigated the potential solution upon frequency domain. To this end, we propose a novel Frequency Adaptive Mixture of Experts (FAME) learning framework for pan-sharpening, which consists of three key components: the Adaptive Frequency Separation Prediction Module, the Sub-Frequency Learning Expert Module, and the Expert Mixture Module. In detail, the first leverages the discrete cosine transform to perform frequency separation by predicting the frequency mask. On the basis of generated mask, the second with low-frequency MOE and high-frequency MOE takes account for enabling the effective low-frequency and high-frequency information reconstruction. Followed by, the final fusion module dynamically weights high frequency and low-frequency MOE knowledge to adapt to remote sensing images with significant content variations. Quantitative and qualitative experiments over multiple datasets demonstrate that our method performs the best against other state-of-the-art ones and comprises a strong generalization ability for real-world scenes. Code will be made publicly at https://github.com/alexhe101/FAME-Net.