arXiv subjects

Zhao Kang

Publications and source records attributed to Zhao Kang.

88 records · Page 5Linked to original sources

arXiv2019

Low-rank Kernel Learning for Graph-based Clustering

Constructing the adjacency graph is fundamental to graph-based clustering. Graph learning in kernel space has shown impressive performance on a number of benchmark data sets. However, its performance is largely determined by the chosen kernel matrix. To address this issue, the previous multiple kernel learning algorithm has been applied to learn an optimal kernel from a group of predefined kernels. This approach might be sensitive to noise and limits the representation ability of the consensus kernel. In contrast to existing methods, we propose to learn a low-rank kernel matrix which exploits the similarity nature of the kernel matrix and seeks an optimal kernel from the neighborhood of candidate kernels. By formulating graph construction and kernel learning in a unified framework, the graph and consensus kernel can be iteratively enhanced by each other. Extensive experimental results validate the efficacy of the proposed method.

cs.LG↗

arXiv2019

Similarity Learning via Kernel Preserving Embedding

Data similarity is a key concept in many data-driven applications. Many algorithms are sensitive to similarity measures. To tackle this fundamental problem, automatically learning of similarity information from data via self-expression has been developed and successfully applied in various models, such as low-rank representation, sparse subspace learning, semi-supervised learning. However, it just tries to reconstruct the original data and some valuable information, e.g., the manifold structure, is largely ignored. In this paper, we argue that it is beneficial to preserve the overall relations when we extract similarity information. Specifically, we propose a novel similarity learning framework by minimizing the reconstruction error of kernel matrices, rather than the reconstruction error of original data adopted by existing work. Taking the clustering task as an example to evaluate our method, we observe considerable improvements compared to other state-of-the-art methods. More importantly, our proposed framework is very general and provides a novel and fundamental building block for many other similarity-based tasks. Besides, our proposed kernel preserving opens up a large number of possibilities to embed high-dimensional data into low-dimensional space.

cs.LG↗

arXiv2018

Robust Graph Learning from Noisy Data

Learning graphs from data automatically has shown encouraging performance on clustering and semisupervised learning tasks. However, real data are often corrupted, which may cause the learned graph to be inexact or unreliable. In this paper, we propose a novel robust graph learning scheme to learn reliable graphs from real-world noisy data by adaptively removing noise and errors in the raw data. We show that our proposed model can also be viewed as a robust version of manifold regularized robust PCA, where the quality of the graph plays a critical role. The proposed model is able to boost the performance of data clustering, semisupervised classification, and data recovery significantly, primarily due to two key factors: 1) enhanced low-rank recovery by exploiting the graph smoothness assumption, 2) improved graph construction by exploiting clean data recovered by robust PCA. Thus, it boosts the clustering, semi-supervised classification, and data recovery performance overall. Extensive experiments on image/document clustering, object recognition, image shadow removal, and video background subtraction reveal that our model outperforms the previous state-of-the-art methods.

cs.CV↗

arXiv2018

Self-weighted Multiple Kernel Learning for Graph-based Clustering and Semi-supervised Classification

Multiple kernel learning (MKL) method is generally believed to perform better than single kernel method. However, some empirical studies show that this is not always true: the combination of multiple kernels may even yield an even worse performance than using a single kernel. There are two possible reasons for the failure: (i) most existing MKL methods assume that the optimal kernel is a linear combination of base kernels, which may not hold true; and (ii) some kernel weights are inappropriately assigned due to noises and carelessly designed algorithms. In this paper, we propose a novel MKL framework by following two intuitive assumptions: (i) each kernel is a perturbation of the consensus kernel; and (ii) the kernel that is close to the consensus kernel should be assigned a large weight. Impressively, the proposed method can automatically assign an appropriate weight to each kernel without introducing additional parameters, as existing methods do. The proposed framework is integrated into a unified framework for graph-based clustering and semi-supervised classification. We have conducted experiments on multiple benchmark datasets and our empirical results verify the superiority of the proposed framework.

stat.ML↗

arXiv2018

Two Birds with One Stone: Transforming and Generating Facial Images with Iterative GAN

Generating high fidelity identity-preserving faces with different facial attributes has a wide range of applications. Although a number of generative models have been developed to tackle this problem, there is still much room for further improvement.In paticular, the current solutions usually ignore the perceptual information of images, which we argue that it benefits the output of a high-quality image while preserving the identity information, especially in facial attributes learning area.To this end, we propose to train GAN iteratively via regularizing the min-max process with an integrated loss, which includes not only the per-pixel loss but also the perceptual loss. In contrast to the existing methods only deal with either image generation or transformation, our proposed iterative architecture can achieve both of them. Experiments on the multi-label facial dataset CelebA demonstrate that the proposed model has excellent performance on recognizing multiple attributes, generating a high-quality image, and transforming image with controllable attributes.

cs.CV↗

arXiv2017

Unified Spectral Clustering with Optimal Graph

Spectral clustering has found extensive use in many areas. Most traditional spectral clustering algorithms work in three separate steps: similarity graph construction; continuous labels learning; discretizing the learned labels by k-means clustering. Such common practice has two potential flaws, which may lead to severe information loss and performance degradation. First, predefined similarity graph might not be optimal for subsequent clustering. It is well-accepted that similarity graph highly affects the clustering results. To this end, we propose to automatically learn similarity information from data and simultaneously consider the constraint that the similarity matrix has exact c connected components if there are c clusters. Second, the discrete solution may deviate from the spectral solution since k-means method is well-known as sensitive to the initialization of cluster centers. In this work, we transform the candidate solution into a new one that better approximates the discrete one. Finally, those three subtasks are integrated into a unified framework, with each subtask iteratively boosted by using the results of the others towards an overall optimal solution. It is known that the performance of a kernel method is largely determined by the choice of kernels. To tackle this practical problem of how to select the most suitable kernel for a particular data set, we further extend our model to incorporate multiple kernel learning ability. Extensive experiments demonstrate the superiority of our proposed method as compared to existing clustering approaches.

cs.LG↗

arXiv2017

Twin Learning for Similarity and Clustering: A Unified Kernel Approach

Many similarity-based clustering methods work in two separate steps including similarity matrix computation and subsequent spectral clustering. However, similarity measurement is challenging because it is usually impacted by many factors, e.g., the choice of similarity metric, neighborhood size, scale of data, noise and outliers. Thus the learned similarity matrix is often not suitable, let alone optimal, for the subsequent clustering. In addition, nonlinear similarity often exists in many real world data which, however, has not been effectively considered by most existing methods. To tackle these two challenges, we propose a model to simultaneously learn cluster indicator matrix and similarity information in kernel spaces in a principled way. We show theoretical relationships to kernel k-means, k-means, and spectral clustering methods. Then, to address the practical issue of how to select the most suitable kernel for a particular clustering task, we further extend our model with a multiple kernel learning ability. With this joint model, we can automatically accomplish three subtasks of finding the best cluster indicator matrix, the most accurate similarity relations and the optimal combination of multiple kernels. By leveraging the interactions between these three subtasks in a joint framework, each subtask can be iteratively boosted by using the results of the others towards an overall optimal solution. Extensive experiments are performed to demonstrate the effectiveness of our method.

cs.LG↗

arXiv2016

A Fast Factorization-based Approach to Robust PCA

Robust principal component analysis (RPCA) has been widely used for recovering low-rank matrices in many data mining and machine learning problems. It separates a data matrix into a low-rank part and a sparse part. The convex approach has been well studied in the literature. However, state-of-the-art algorithms for the convex approach usually have relatively high complexity due to the need of solving (partial) singular value decompositions of large matrices. A non-convex approach, AltProj, has also been proposed with lighter complexity and better scalability. Given the true rank $r$ of the underlying low rank matrix, AltProj has a complexity of $O(r^2dn)$, where $d\times n$ is the size of data matrix. In this paper, we propose a novel factorization-based model of RPCA, which has a complexity of $O(kdn)$, where $k$ is an upper bound of the true rank. Our method does not need the precise value of the true rank. From extensive experiments, we observe that AltProj can work only when $r$ is precisely known in advance; however, when the needed rank parameter $r$ is specified to a value different from the true rank, AltProj cannot fully separate the two parts while our method succeeds. Even when both work, our method is about 4 times faster than AltProj. Our method can be used as a light-weight, scalable tool for RPCA in the absence of the precise value of the true rank.

cs.CV↗

arXiv2016

Top-N Recommendation on Graphs

Recommender systems play an increasingly important role in online applications to help users find what they need or prefer. Collaborative filtering algorithms that generate predictions by analyzing the user-item rating matrix perform poorly when the matrix is sparse. To alleviate this problem, this paper proposes a simple recommendation algorithm that fully exploits the similarity information among users and items and intrinsic structural information of the user-item matrix. The proposed method constructs a new representation which preserves affinity and structure information in the user-item rating matrix and then performs recommendation task. To capture proximity information about users and items, two graphs are constructed. Manifold learning idea is used to constrain the new representation to be smooth on these graphs, so as to enforce users and item proximities. Our model is formulated as a convex optimization problem, for which we need to solve the well-known Sylvester equation only. We carry out extensive empirical evaluations on six benchmark datasets to show the effectiveness of this approach.

cs.IR↗

arXiv2016

Top-N Recommendation with Novel Rank Approximation

The importance of accurate recommender systems has been widely recognized by academia and industry. However, the recommendation quality is still rather low. Recently, a linear sparse and low-rank representation of the user-item matrix has been applied to produce Top-N recommendations. This approach uses the nuclear norm as a convex relaxation for the rank function and has achieved better recommendation accuracy than the state-of-the-art methods. In the past several years, solving rank minimization problems by leveraging nonconvex relaxations has received increasing attention. Some empirical results demonstrate that it can provide a better approximation to original problems than convex relaxation. In this paper, we propose a novel rank approximation to enhance the performance of Top-N recommendation systems, where the approximation error is controllable. Experimental results on real data show that the proposed rank approximation improves the Top-$N$ recommendation accuracy substantially.

cs.IR↗

arXiv2016

Top-N Recommender System via Matrix Completion

Top-N recommender systems have been investigated widely both in industry and academia. However, the recommendation quality is far from satisfactory. In this paper, we propose a simple yet promising algorithm. We fill the user-item matrix based on a low-rank assumption and simultaneously keep the original information. To do that, a nonconvex rank relaxation rather than the nuclear norm is adopted to provide a better rank approximation and an efficient optimization strategy is designed. A comprehensive set of experiments on real datasets demonstrates that our method pushes the accuracy of Top-N recommendation to a new level.

cs.IR↗

arXiv2015

Robust PCA via Nonconvex Rank Approximation

Numerous applications in data mining and machine learning require recovering a matrix of minimal rank. Robust principal component analysis (RPCA) is a general framework for handling this kind of problems. Nuclear norm based convex surrogate of the rank function in RPCA is widely investigated. Under certain assumptions, it can recover the underlying true low rank matrix with high probability. However, those assumptions may not hold in real-world applications. Since the nuclear norm approximates the rank by adding all singular values together, which is essentially a $\ell_1$-norm of the singular values, the resulting approximation error is not trivial and thus the resulting matrix estimator can be significantly biased. To seek a closer approximation and to alleviate the above-mentioned limitations of the nuclear norm, we propose a nonconvex rank approximation. This approximation to the matrix rank is tighter than the nuclear norm. To solve the associated nonconvex minimization problem, we develop an efficient augmented Lagrange multiplier based optimization algorithm. Experimental results demonstrate that our method outperforms current state-of-the-art algorithms in both accuracy and efficiency.

cs.CV↗

arXiv2015

Robust Subspace Clustering via Tighter Rank Approximation

Matrix rank minimization problem is in general NP-hard. The nuclear norm is used to substitute the rank function in many recent studies. Nevertheless, the nuclear norm approximation adds all singular values together and the approximation error may depend heavily on the magnitudes of singular values. This might restrict its capability in dealing with many practical problems. In this paper, an arctangent function is used as a tighter approximation to the rank function. We use it on the challenging subspace clustering problem. For this nonconvex minimization problem, we develop an effective optimization procedure based on a type of augmented Lagrange multipliers (ALM) method. Extensive experiments on face clustering and motion segmentation show that the proposed method is effective for rank approximation.

cs.CV↗

arXiv2015

Robust Subspace Clustering via Smoothed Rank Approximation

Matrix rank minimizing subject to affine constraints arises in many application areas, ranging from signal processing to machine learning. Nuclear norm is a convex relaxation for this problem which can recover the rank exactly under some restricted and theoretically interesting conditions. However, for many real-world applications, nuclear norm approximation to the rank function can only produce a result far from the optimum. To seek a solution of higher accuracy than the nuclear norm, in this paper, we propose a rank approximation based on Logarithm-Determinant. We consider using this rank approximation for subspace clustering application. Our framework can model different kinds of errors and noise. Effective optimization strategy is developed with theoretical guarantee to converge to a stationary point. The proposed method gives promising results on face clustering and motion segmentation tasks compared to the state-of-the-art subspace clustering algorithms.

cs.CV↗

arXiv2015

LogDet Rank Minimization with Application to Subspace Clustering

Low-rank matrix is desired in many machine learning and computer vision problems. Most of the recent studies use the nuclear norm as a convex surrogate of the rank operator. However, all singular values are simply added together by the nuclear norm, and thus the rank may not be well approximated in practical problems. In this paper, we propose to use a log-determinant (LogDet) function as a smooth and closer, though non-convex, approximation to rank for obtaining a low-rank representation in subspace clustering. Augmented Lagrange multipliers strategy is applied to iteratively optimize the LogDet-based non-convex objective function on potentially large-scale data. By making use of the angular information of principal directions of the resultant low-rank representation, an affinity graph matrix is constructed for spectral clustering. Experimental results on motion segmentation and face clustering data demonstrate that the proposed method often outperforms state-of-the-art subspace clustering algorithms.

cs.CV↗

arXiv2013

High-resolution gamma-ray spectroscopy with a microwave-multiplexed transition-edge sensor array

We demonstrate very high resolution photon spectroscopy with a microwave-multiplexed two-pixel transition-edge sensor (TES) array. We measured a $^{153}$Gd photon source and achieved an energy resolution of 63 eV full-width-at-half-maximum at 97 keV and an equivalent readout system noise of 86 pA/$\sqrt{\text{Hz}}$ at the TES. The readout circuit consists of superconducting microwave resonators coupled to radio-frequency superconducting-quantum-interference-devices (SQUID) and transduces changes in input current to changes in phase of a microwave signal. We use flux-ramp modulation to linearize the response and evade low-frequency noise. This demonstration establishes one path for the readout of cryogenic X-ray and gamma-ray sensor arrays with more than $10^3$ elements and spectral resolving powers $R=λ/Δλ> 10^3$.

physics.ins-det↗