Chun-Guang Li

Xianghan Meng, Zhiyuan Huang, Zhengyu Tong et al.

Human Motion Segmentation (HMS), which aims to partition a video into non-overlapping segments corresponding to different human motions, has recently attracted increasing research attention. Existing HMS approaches are predominantly based on subspace clustering, which are grounded on the assumption that the distribution of high-dimensional temporal features well aligns with a Union-of-Subspaces (UoS). For videos in the real world, however, the raw frame-level features often violate the UoS assumption and yield unsatisfactory segmentation performance. To address this issue, we propose an efficient and effective approach for HMS, named Temporal Deep Self-expressive subspace Clustering (TDSC), which jointly learns temporally consistent structured representations and stabilized affinity for accurate and robust HMS. Specifically, in TDSC, we alternately learn structured representations of the input frame features and self-expressive coefficients via a properly regularized self-expressive model, in which a coding-rate maximization regularizer is incorporated to avoid representation collapse and conform the learned representations to span a desired UoS distribution, and meanwhile, temporal constraints are incorporated to promote temporally adjacent frames to be partitioned into the same groups. Moreover, we develop a temporal momentum averaging mechanism to stabilize affinity evolution and design a reparameterization strategy to enable efficient optimization. We conduct extensive experiments on five benchmark HMS datasets using both conventional (HoG) and up-to-date deep features (i.e., CLIP, DINOv2) to validate the effectiveness of our approach.

Wei He, Shangzhi Zhang, Chun-Guang Li et al.

Spectral clustering, as a popular tool for data clustering, requires an eigen-decomposition step on a given affinity to obtain the spectral embedding. Nevertheless, such a step suffers from the lack of generalizability and scalability. Moreover, the obtained spectral embeddings can hardly provide a good approximation to the ground-truth partition and thus a k-means step is adopted to quantize the embedding. In this paper, we propose a simple yet effective scalable and generalizable approach, called Neural Normalized Cut (NeuNcut), to learn the clustering membership for spectral clustering directly. In NeuNcut, we properly reparameterize the unknown cluster membership via a neural network, and train the neural network via stochastic gradient descent with a properly relaxed normalized cut loss. As a result, our NeuNcut enjoys a desired generalization ability to directly infer clustering membership for out-of-sample unseen data and hence brings us an efficient way to handle clustering task with ultra large-scale data. We conduct extensive experiments on both synthetic data and benchmark datasets and experimental results validate the effectiveness and the superiority of our approach. Our code is available at: https://github.com/hewei98/NeuNcut.

Xianghan Meng, Zhiyuan Huang, Wei He et al.

Subspace clustering is a classical unsupervised learning task, built on a basic assumption that high-dimensional data can be approximated by a union of subspaces (UoS). Nevertheless, the real-world data are often deviating from the UoS assumption. To address this challenge, state-of-the-art deep subspace clustering algorithms attempt to jointly learn UoS representations and self-expressive coefficients. However, the general framework of the existing algorithms suffers from a catastrophic feature collapse and lacks a theoretical guarantee to learn desired UoS representation. In this paper, we present a Principled fRamewOrk for Deep Subspace Clustering (PRO-DSC), which is designed to learn structured representations and self-expressive coefficients in a unified manner. Specifically, in PRO-DSC, we incorporate an effective regularization on the learned representations into the self-expressive model, prove that the regularized self-expressive model is able to prevent feature space collapse, and demonstrate that the learned optimal representations under certain condition lie on a union of orthogonal subspaces. Moreover, we provide a scalable and efficient approach to implement our PRO-DSC and conduct extensive experiments to verify our theoretical findings and demonstrate the superior performance of our proposed deep subspace clustering approach. The code is available at https://github.com/mengxianghan123/PRO-DSC.

Wei He, Xianghan Meng, Zhiyuan Huang et al.

Generalized Category Discovery (GCD) aims to identify both known and unknown categories, with only partial labels given for the known categories, posing a challenging open-set recognition problem. State-of-the-art approaches for GCD task are usually built on multi-modality representation learning, which is heavily dependent upon inter-modality alignment. However, few of them cast a proper intra-modality alignment to generate a desired underlying structure of representation distributions. In this paper, we propose a novel and effective multi-modal representation learning framework for GCD via Semi-Supervised Rate Reduction, called SSR$^2$-GCD, to learn cross-modality representations with desired structural properties based on emphasizing to properly align intra-modality relationships. Moreover, to boost knowledge transfer, we integrate prompt candidates by leveraging the inter-modal alignment offered by Vision Language Models. We conduct extensive experiments on generic and fine-grained benchmark datasets demonstrating superior performance of our approach.

Xianghan Meng, Zhengyu Tong, Zhiyuan Huang et al.

Human Motion Segmentation (HMS), which aims to partition videos into non-overlapping human motions, has attracted increasing research attention recently. Existing approaches for HMS are mainly dominated by subspace clustering methods, which are grounded on the assumption that high-dimensional temporal data align with a Union-of-Subspaces (UoS) distribution. However, the frames in video capturing complex human motions with cluttered backgrounds may not align well with the UoS distribution. In this paper, we propose a novel approach for HMS, named Temporal Rate Reduction Clustering ($\text{TR}^2\text{C}$), which jointly learns structured representations and affinity to segment the sequences of frames in video. Specifically, the structured representations learned by $\text{TR}^2\text{C}$ enjoy temporally consistency and are aligned well with a UoS structure, which is favorable for addressing the HMS task. We conduct extensive experiments on five benchmark HMS datasets and achieve state-of-the-art performances with different feature extractors. The code is available at: https://github.com/mengxianghan123/TR2C.

Shangzhi Zhang, Chong You, René Vidal et al.

State-of-the-art subspace clustering methods are based on self-expressive model, which represents each data point as a linear combination of other data points. However, such methods are designed for a finite sample dataset and lack the ability to generalize to out-of-sample data. Moreover, since the number of self-expressive coefficients grows quadratically with the number of data points, their ability to handle large-scale datasets is often limited. In this paper, we propose a novel framework for subspace clustering, termed Self-Expressive Network (SENet), which employs a properly designed neural network to learn a self-expressive representation of the data. We show that our SENet can not only learn the self-expressive coefficients with desired properties on the training data, but also handle out-of-sample data. Besides, we show that SENet can also be leveraged to perform subspace clustering on large-scale datasets. Extensive experiments conducted on synthetic data and real world benchmark data validate the effectiveness of the proposed method. In particular, SENet yields highly competitive performance on MNIST, Fashion MNIST and Extended MNIST and state-of-the-art performance on CIFAR-10. The code is available at https://github.com/zhangsz1998/Self-Expressive-Network.

Yihao Chen, Xin Tang, Xianbiao Qi et al.

Graph Neural Networks (GNNs) have attracted considerable attention and have emerged as a new promising paradigm to process graph-structured data. GNNs are usually stacked to multiple layers and the node representations in each layer are computed through propagating and aggregating the neighboring node features with respect to the graph. By stacking to multiple layers, GNNs are able to capture the long-range dependencies among the data on the graph and thus bring performance improvements. To train a GNN with multiple layers effectively, some normalization techniques (e.g., node-wise normalization, batch-wise normalization) are necessary. However, the normalization techniques for GNNs are highly task-relevant and different application tasks prefer to different normalization techniques, which is hard to know in advance. To tackle this deficiency, in this paper, we propose to learn graph normalization by optimizing a weighted combination of normalization techniques at four different levels, including node-wise normalization, adjacency-wise normalization, graph-wise normalization, and batch-wise normalization, in which the adjacency-wise normalization and the graph-wise normalization are newly proposed in this paper to take into account the local structure and the global structure on the graph, respectively. By learning the optimal weights, we are able to automatically select a single best or a best combination of multiple normalizations for a specific task. We conduct extensive experiments on benchmark datasets for different tasks, including node classification, link prediction, graph classification and graph regression, and confirm that the learned graph normalization leads to competitive results and that the learned weights suggest the appropriate normalization techniques for the specific task. Source code is released here https://github.com/cyh1112/GraphNormalization.

Qishuai Wen, Chun-Guang Li

State-of-the-art methods for Transformer-based semantic segmentation typically adopt Transformer decoders that are used to extract additional embeddings from image embeddings via cross-attention, refine either or both types of embeddings via self-attention, and project image embeddings onto the additional embeddings via dot-product. Despite their remarkable success, these empirical designs still lack theoretical justifications or interpretations, thus hindering potentially principled improvements. In this paper, we argue that there are fundamental connections between semantic segmentation and compression, especially between the Transformer decoders and Principal Component Analysis (PCA). From such a perspective, we derive a white-box, fully attentional DEcoder for PrIncipled semantiC segemenTation (DEPICT), with the interpretations as follows: 1) the self-attention operator refines image embeddings to construct an ideal principal subspace that aligns with the supervision and retains most information; 2) the cross-attention operator seeks to find a low-rank approximation of the refined image embeddings, which is expected to be a set of orthonormal bases of the principal subspace and corresponds to the predefined classes; 3) the dot-product operation yields compact representation for image embeddings as segmentation masks. Experiments conducted on dataset ADE20K find that DEPICT consistently outperforms its black-box counterpart, Segmenter, and it is light weight and more robust.

Xianbiao Qi, Yelin He, Jiaquan Ye et al.

Scaling Transformer to a large scale without using some technical tricks such as learning rate warump and using an obviously lower learning rate is an extremely challenging task, and is increasingly gaining more attention. In this paper, we provide a theoretical analysis for the process of training Transformer and reveal the rationale behind the model crash phenomenon in the training process, termed \textit{spectral energy concentration} of ${\bW_q}^{\top} \bW_k$, which is the reason for a malignant entropy collapse, where ${\bW_q}$ and $\bW_k$ are the projection matrices for the query and the key in Transformer, respectively. To remedy this problem, motivated by \textit{Weyl's Inequality}, we present a novel optimization strategy, \ie, making the weight updating in successive steps smooth -- if the ratio $\frac{σ_{1}(\nabla \bW_t)}{σ_{1}(\bW_{t-1})}$ is larger than a threshold, we will automatically bound the learning rate to a weighted multiple of $\frac{σ_{1}(\bW_{t-1})}{σ_{1}(\nabla \bW_t)}$, where $\nabla \bW_t$ is the updating quantity in step $t$. Such an optimization strategy can prevent spectral energy concentration to only a few directions, and thus can avoid malignant entropy collapse which will trigger the model crash. We conduct extensive experiments using ViT, Swin-Transformer and GPT, showing that our optimization strategy can effectively and stably train these Transformers without using learning rate warmup.

Qishuai Wen, Zhiyuan Huang, Xianghan Meng et al.

The attention operator in Transformers can be viewed as a two-layer fast-weight MLP, whose weights are dynamically instantiated from input tokens and whose width equals sequence length $N$. As the context extends, the expressive capacity of such an $N$-width MLP increases, but scaling its fast weights becomes prohibitively expensive for extremely long sequences. Recently, this fast-weight scaling perspective has motivated the Mixture-of-Experts (MoE) attention, which partitions the sequence into fast-weight experts and sparsely routes the tokens to them. In this paper, we elevate this perspective to a unifying framework for a wide range of efficient attention methods by interpreting them as scaling fast weights through routing and/or compression. Then we propose a compress-and-route strategy, which compresses the $N$-width MLP into a narrower one using a small set of landmark queries and constructs deformable experts by gathering top-$k$ activated key-value pairs for each landmark query. We call this strategy a Mixture of Top-$k$ Activations (MiTA), and refer to the resulting efficient mechanism as MiTA attention. Preliminary experiments on vision tasks demonstrate the promise of our MiTA attention and motivate further investigation on its optimization and broader applications in more challenging settings.

Qishuai Wen, Zhiyuan Huang, Chun-Guang Li

Attention mechanisms have achieved significant empirical success in multiple fields, but their underlying optimization objectives remain unclear yet. Moreover, the quadratic complexity of self-attention has become increasingly prohibitive. Although interpretability and efficiency are two mutually reinforcing pursuits, prior work typically investigates them separately. In this paper, we propose a unified optimization objective that derives inherently interpretable and efficient attention mechanisms through algorithm unrolling. Precisely, we construct a gradient step of the proposed objective with a set of forward-pass operations of our \emph{Contract-and-Broadcast Self-Attention} (CBSA), which compresses input tokens towards low-dimensional structures by contracting a few representatives of them. This novel mechanism can not only scale linearly by fixing the number of representatives, but also covers the instantiations of varied attention mechanisms when using different sets of representatives. We conduct extensive experiments to demonstrate comparable performance and superior advantages over black-box attention mechanisms on visual tasks. Our work sheds light on the integration of interpretability and efficiency, as well as the unified formula of attention mechanisms.

Xianbiao Qi, Marco Chen, Wenjie Xiao et al.

Transformers have become the de facto backbone of modern deep learning, yet their training typically demands an advanced optimizer with adaptive learning rate like AdamW, rather than a momentum SGDW (mSGDW). Previous works show that it is mainly due to a heavy-tailed distribution of the gradients. In this paper, we introduce a Deeply Normalized Transformer (DNT), which is meticulously engineered to overcome this limitation enabling seamless training with vanilla mSGDW while yielding comparable performance to the Transformers trained via AdamW. To be specific, in DNT, we strategically integrate normalization techniques at proper positions in the Transformers to effectively modulate the Jacobian matrices of each layer, balance the influence of weights, activations, and their interactions, and thus enable the distributions of gradients concentrated. We provide both theoretical justifications of the normalization technique used in our DNT and extensive empirical evaluation on two popular Transformer architectures to validate that: a) DNT outperforms its counterparts (\ie, ViT and GPT), and b) DNT can be effectively trained with vanilla mSGDW.

Mingkun Li, Peng Xu, Chun-Guang Li et al.

In this paper, we address a highly challenging yet critical task: unsupervised long-term person re-identification with clothes change. Existing unsupervised person re-id methods are mainly designed for short-term scenarios and usually rely on RGB cues so that fail to perceive feature patterns that are independent of the clothes. To crack this bottleneck, we propose a silhouette-driven contrastive learning (SiCL) method, which is designed to learn cross-clothes invariance by integrating both the RGB cues and the silhouette information within a contrastive learning framework. To our knowledge, this is the first tailor-made framework for unsupervised long-term clothes change \reid{}, with superior performance on six benchmark datasets. We conduct extensive experiments to evaluate our proposed SiCL compared to the state-of-the-art unsupervised person reid methods across all the representative datasets. Experimental results demonstrate that our proposed SiCL significantly outperforms other unsupervised re-id methods.

Mingkun Li, Shupeng Cheng, Peng Xu et al.

We investigate unsupervised person re-identification (Re-ID) with clothes change, a new challenging problem with more practical usability and scalability to real-world deployment. Most existing re-id methods artificially assume the clothes of every single person to be stationary across space and time. This condition is mostly valid for short-term re-id scenarios since an average person would often change the clothes even within a single day. To alleviate this assumption, several recent works have introduced the clothes change facet to re-id, with a focus on supervised learning person identity discriminative representation with invariance to clothes changes. Taking a step further towards this long-term re-id direction, we further eliminate the requirement of person identity labels, as they are significantly more expensive and more tedious to annotate in comparison to short-term person re-id datasets. Compared to conventional unsupervised short-term re-id, this new problem is drastically more challenging as different people may have similar clothes whilst the same person can wear multiple suites of clothes over different locations and times with very distinct appearance. To overcome such obstacles, we introduce a novel Curriculum Person Clustering (CPC) method that can adaptively regulate the unsupervised clustering criterion according to the clustering confidence. Experiments on three long-term person re-id datasets show that our CPC outperforms SOTA unsupervised re-id methods and even closely matches the supervised re-id models.

He Sun, Mingkun Li, Chun-Guang Li

Unsupervised person re-identification (ReID) aims to match a query image of a pedestrian to the images in gallery set without supervision labels. The most popular approaches to tackle unsupervised person ReID are usually performing a clustering algorithm to yield pseudo labels at first and then exploit the pseudo labels to train a deep neural network. However, the pseudo labels are noisy and sensitive to the hyper-parameter(s) in clustering algorithm. In this paper, we propose a Hybrid Contrastive Learning (HCL) approach for unsupervised person ReID, which is based on a hybrid between instance-level and cluster-level contrastive loss functions. Moreover, we present a Multi-Granularity Clustering Ensemble based Hybrid Contrastive Learning (MGCE-HCL) approach, which adopts a multi-granularity clustering ensemble strategy to mine priority information among the pseudo positive sample pairs and defines a priority-weighted hybrid contrastive loss for better tolerating the noises in the pseudo positive samples. We conduct extensive experiments on two benchmark datasets Market-1501 and DukeMTMC-reID. Experimental results validate the effectiveness of our proposals.

Mingkun Li, Chun-Guang Li, Jun Guo

Unsupervised person re-identification (Re-ID) aims to match pedestrian images from different camera views in unsupervised setting. Existing methods for unsupervised person Re-ID are usually built upon the pseudo labels from clustering. However, the quality of clustering depends heavily on the quality of the learned features, which are overwhelmingly dominated by the colors in images especially in the unsupervised setting. In this paper, we propose a Cluster-guided Asymmetric Contrastive Learning (CACL) approach for unsupervised person Re-ID, in which cluster structure is leveraged to guide the feature learning in a properly designed asymmetric contrastive learning framework. To be specific, we propose a novel cluster-level contrastive loss to help the siamese network effectively mine the invariance in feature learning with respect to the cluster structure within and between different data augmentation views, respectively. Extensive experiments conducted on three benchmark datasets demonstrate superior performance of our proposal.

Chong You, Chun-Guang Li, Daniel P. Robinson et al.

Subspace clustering methods based on expressing each data point as a linear combination of other data points have achieved great success in computer vision applications such as motion segmentation, face and digit clustering. In face clustering, the subspaces are linear and subspace clustering methods can be applied directly. In motion segmentation, the subspaces are affine and an additional affine constraint on the coefficients is often enforced. However, since affine subspaces can always be embedded into linear subspaces of one extra dimension, it is unclear if the affine constraint is really necessary. This paper shows, both theoretically and empirically, that when the dimension of the ambient space is high relative to the sum of the dimensions of the affine subspaces, the affine constraint has a negligible effect on clustering performance. Specifically, our analysis provides conditions that guarantee the correctness of affine subspace clustering methods both with and without the affine constraint, and shows that these conditions are satisfied for high-dimensional data. Underlying our analysis is the notion of affinely independent subspaces, which not only provides geometrically interpretable correctness conditions, but also clarifies the relationships between existing results for affine subspace clustering.

Ying Chen, Chun-Guang Li, Chong You

State-of-the-art subspace clustering methods are based on self-expressive model, which represents each data point as a linear combination of other data points. By enforcing such representation to be sparse, sparse subspace clustering is guaranteed to produce a subspace-preserving data affinity where two points are connected only if they are from the same subspace. On the other hand, however, data points from the same subspace may not be well-connected, leading to the issue of over-segmentation. We introduce dropout to address the issue of over-segmentation, which is based on randomly dropping out data points in self-expressive model. In particular, we show that dropout is equivalent to adding a squared $\ell_2$ norm regularization on the representation coefficients, therefore induces denser solutions. Then, we reformulate the optimization problem as a consensus problem over a set of small-scale subproblems. This leads to a scalable and flexible sparse subspace clustering approach, termed Stochastic Sparse Subspace Clustering, which can effectively handle large scale datasets. Extensive experiments on synthetic data and real world datasets validate the efficiency and effectiveness of our proposal.

Junjian Zhang, Chun-Guang Li, Chong You et al.

Subspace clustering methods based on data self-expression have become very popular for learning from data that lie in a union of low-dimensional linear subspaces. However, the applicability of subspace clustering has been limited because practical visual data in raw form do not necessarily lie in such linear subspaces. On the other hand, while Convolutional Neural Network (ConvNet) has been demonstrated to be a powerful tool for extracting discriminative features from visual data, training such a ConvNet usually requires a large amount of labeled data, which are unavailable in subspace clustering applications. To achieve simultaneous feature learning and subspace clustering, we propose an end-to-end trainable framework, called Self-Supervised Convolutional Subspace Clustering Network (S$^2$ConvSCN), that combines a ConvNet module (for feature learning), a self-expression module (for subspace clustering) and a spectral clustering module (for self-supervision) into a joint optimization framework. Particularly, we introduce a dual self-supervision that exploits the output of spectral clustering to supervise the training of the feature learning module (via a classification loss) and the self-expression module (via a spectral clustering loss). Our experiments on four benchmark datasets show the effectiveness of the dual self-supervision and demonstrate superior performance of our proposed approach.

Chun-Guang Li, Chong You, René Vidal

Sparse subspace clustering (SSC) is a state-of-the-art method for segmenting a set of data points drawn from a union of subspaces into their respective subspaces. It is now well understood that SSC produces subspace-preserving data affinity under broad geometric conditions but suffers from a connectivity issue. In this paper, we develop a novel geometric analysis for a variant of SSC, named affine SSC (ASSC), for the problem of clustering data from a union of affine subspaces. Our contributions include a new concept called affine independence for capturing the arrangement of a collection of affine subspaces. Under the affine independence assumption, we show that ASSC is guaranteed to produce subspace-preserving affinity. Moreover, inspired by the phenomenon that the $\ell_1$ regularization no longer induces sparsity when the solution is nonnegative, we further show that subspace-preserving recovery can be achieved under much weaker conditions for all data points other than the extreme points of samples from each subspace. In addition, we confirm a curious observation that the affinity produced by ASSC may be subspace-dense---which could guarantee the subspace-preserving affinity of ASSC to produce correct clustering under rather weak conditions. We validate the theoretical findings on carefully designed synthetic data and evaluate the performance of ASSC on several real data sets.

Chun-Guang Li, Junjian Zhang, Jun Guo

Subspace clustering refers to the problem of segmenting high dimensional data drawn from a union of subspaces into the respective subspaces. In some applications, partial side-information to indicate "must-link" or "cannot-link" in clustering is available. This leads to the task of subspace clustering with side-information. However, in prior work the supervision value of the side-information for subspace clustering has not been fully exploited. To this end, in this paper, we present an enhanced approach for constrained subspace clustering with side-information, termed Constrained Sparse Subspace Clustering plus (CSSC+), in which the side-information is used not only in the stage of learning an affinity matrix but also in the stage of spectral clustering. Moreover, we propose to estimate clustering accuracy based on the partial side-information and theoretically justify the connection to the ground-truth clustering accuracy in terms of the Rand index. We conduct experiments on three cancer gene expression datasets to validate the effectiveness of our proposals.

Ruo-Pei Guo, Chun-Guang Li, Yonghua Li et al.

Person reidentification (ReID) refers to the task of verifying the identity of a pedestrian observed from nonoverlapping views in a surveillance camera network. It has recently been validated that reranking can achieve remarkable performance improvements in person ReID systems. However, current reranking approaches either require feedback from users or suffer from burdensome computational costs. In this paper, we propose to exploit a density-adaptive smooth kernel technique to achieve efficient and effective reranking. Specifically, we adopt a smooth kernel function to formulate the neighbor relationships among data samples with a density-adaptive parameter. Based on this new formulation, we present two simple yet effective reranking methods, termed \emph{inverse} density-adaptive kernel based reranking (inv-DAKR) and \emph{bidirectional} density-adaptive kernel based reranking (bi-DAKR), in which the local density information in the vicinity of each gallery sample is elegantly exploited. Moreover, we extend the proposed inv-DAKR and bi-DAKR methods to incorporate the available extra probe samples and demonstrate that when and why these extra probe samples are able to improve the local neighborhood and thus further refine the ranking results. Extensive experiments are conducted on six benchmark datasets, including: PRID450s, VIPeR, CUHK03, GRID, Market-1501 and Mars. The experimental results demonstrate that our proposals are effective and efficient.

Jianlou Si, Honggang Zhang, Chun-Guang Li et al.

Typical person re-identification (ReID) methods usually describe each pedestrian with a single feature vector and match them in a task-specific metric space. However, the methods based on a single feature vector are not sufficient enough to overcome visual ambiguity, which frequently occurs in real scenario. In this paper, we propose a novel end-to-end trainable framework, called Dual ATtention Matching network (DuATM), to learn context-aware feature sequences and perform attentive sequence comparison simultaneously. The core component of our DuATM framework is a dual attention mechanism, in which both intra-sequence and inter-sequence attention strategies are used for feature refinement and feature-pair alignment, respectively. Thus, detailed visual cues contained in the intermediate feature sequences can be automatically exploited and properly compared. We train the proposed DuATM network as a siamese network via a triplet loss assisted with a de-correlation loss and a cross-entropy loss. We conduct extensive experiments on both image and video based ReID benchmark datasets. Experimental results demonstrate the significant advantages of our approach compared to the state-of-the-art methods.

Chun-Guang Li, Chong You, René Vidal

Subspace clustering refers to the problem of segmenting data drawn from a union of subspaces. State-of-the-art approaches for solving this problem follow a two-stage approach. In the first step, an affinity matrix is learned from the data using sparse or low-rank minimization techniques. In the second step, the segmentation is found by applying spectral clustering to this affinity. While this approach has led to state-of-the-art results in many applications, it is sub-optimal because it does not exploit the fact that the affinity and the segmentation depend on each other. In this paper, we propose a joint optimization framework --- Structured Sparse Subspace Clustering (S$^3$C) --- for learning both the affinity and the segmentation. The proposed S$^3$C framework is based on expressing each data point as a structured sparse linear combination of all other data points, where the structure is induced by a norm that depends on the unknown segmentation. Moreover, we extend the proposed S$^3$C framework into Constrained Structured Sparse Subspace Clustering (CS$^3$C) in which available partial side-information is incorporated into the stage of learning the affinity. We show that both the structured sparse representation and the segmentation can be found via a combination of an alternating direction method of multipliers with spectral clustering. Experiments on a synthetic data set, the Extended Yale B data set, the Hopkins 155 motion segmentation database, and three cancer data sets demonstrate the effectiveness of our approach.

Chong You, Chun-Guang Li, Daniel P. Robinson et al.

State-of-the-art subspace clustering methods are based on expressing each data point as a linear combination of other data points while regularizing the matrix of coefficients with $\ell_1$, $\ell_2$ or nuclear norms. $\ell_1$ regularization is guaranteed to give a subspace-preserving affinity (i.e., there are no connections between points from different subspaces) under broad theoretical conditions, but the clusters may not be connected. $\ell_2$ and nuclear norm regularization often improve connectivity, but give a subspace-preserving affinity only for independent subspaces. Mixed $\ell_1$, $\ell_2$ and nuclear norm regularizations offer a balance between the subspace-preserving and connectedness properties, but this comes at the cost of increased computational complexity. This paper studies the geometry of the elastic net regularizer (a mixture of the $\ell_1$ and $\ell_2$ norms) and uses it to derive a provably correct and scalable active set method for finding the optimal coefficients. Our geometric analysis also provides a theoretical justification and a geometric interpretation for the balance between the connectedness (due to $\ell_2$ regularization) and subspace-preserving (due to $\ell_1$ regularization) properties for elastic net subspace clustering. Our experiments show that the proposed active set method not only achieves state-of-the-art clustering performance, but also efficiently handles large-scale datasets.

Xianbiao Qi, Guoying Zhao, Chun-Guang Li et al.

Indirect Immunofluorescence (IIF) HEp-2 cell image is an effective evidence for diagnosis of autoimmune diseases. Recently computer-aided diagnosis of autoimmune diseases by IIF HEp-2 cell classification has attracted great attention. However the HEp-2 cell classification task is quite challenging due to large intra-class variation and small between-class variation. In this paper we propose an effective and efficient approach for the automatic classification of IIF HEp-2 cell image by fusing multi-resolution texture information and richer shape information. To be specific, we propose to: a) capture the multi-resolution texture information by a novel Pairwise Rotation Invariant Co-occurrence of Local Gabor Binary Pattern (PRICoLGBP) descriptor, b) depict the richer shape information by using an Improved Fisher Vector (IFV) model with RootSIFT features which are sampled from large image patches in multiple scales, and c) combine them properly. We evaluate systematically the proposed approach on the IEEE International Conference on Pattern Recognition (ICPR) 2012, IEEE International Conference on Image Processing (ICIP) 2013 and ICPR 2014 contest data sets. The experimental results for the proposed methods significantly outperform the winners of ICPR 2012 and ICIP 2013 contest, and achieve comparable performance with the winner of the newly released ICPR 2014 contest.

Xianbiao Qi, Chun-Guang Li, Guoying Zhao et al.

Dynamic texture and scene classification are two fundamental problems in understanding natural video content. Extracting robust and effective features is a crucial step towards solving these problems. However the existing approaches suffer from the sensitivity to either varying illumination, or viewpoint changing, or even camera motion, and/or the lack of spatial information. Inspired by the success of deep structures in image classification, we attempt to leverage a deep structure to extract feature for dynamic texture and scene classification. To tackle with the challenges in training a deep structure, we propose to transfer some prior knowledge from image domain to video domain. To be specific, we propose to apply a well-trained Convolutional Neural Network (ConvNet) as a mid-level feature extractor to extract features from each frame, and then form a representation of a video by concatenating the first and the second order statistics over the mid-level features. We term this two-level feature extraction scheme as a Transferred ConvNet Feature (TCoF). Moreover we explore two different implementations of the TCoF scheme, i.e., the \textit{spatial} TCoF and the \textit{temporal} TCoF, in which the mean-removed frames and the difference between two adjacent frames are used as the inputs of the ConvNet, respectively. We evaluate systematically the proposed spatial TCoF and the temporal TCoF schemes on three benchmark data sets, including DynTex, YUPENN, and Maryland, and demonstrate that the proposed approach yields superior performance.