PFENet++: Boosting Few-Shot Semantic Segmentation With the Noise-Filtered Context-Aware Prior Mask.

In this work, we revisit the prior mask guidance proposed in "Prior Guided Feature Enrichment Network for Few-Shot Segmentation". The prior mask serves as an indicator that highlights the region of interests of unseen categories, and it is effective in achieving better performance on different frameworks of recent studies. However, the current method directly takes the maximum element-to-element correspondence between the query and support features to indicate the probability of belonging to the target class, thus the broader contextual information is seldom exploited during the prior mask generation. To address this issue, first, we propose the Context-aware Prior Mask (CAPM) that leverages additional nearby semantic cues for better locating the objects in query images. Second, since the maximum correlation value is vulnerable to noisy features, we take one step further by incorporating a lightweight Noise Suppression Module (NSM) to screen out the unnecessary responses, yielding high-quality masks for providing the prior knowledge. Both two contributions are experimentally shown to have substantial practical merit, and the new model named PFENet++ significantly outperforms the baseline PFENet as well as all other competitors on three challenging benchmarks PASCAL-5 i, COCO-20 i and FSS-1000. The new state-of-the-art performance is achieved without compromising the efficiency, manifesting the potential for being a new strong baseline in few-shot semantic segmentation.

Double Auto-Weighted Tensor Robust Principal Component Analysis.

Tensor Robust Principal Component Analysis (TRPCA), which aims to recover the low-rank and sparse components from their sum, has drawn intensive interest in recent years. Most existing TRPCA methods adopt the tensor nuclear norm (TNN) and the tensor l1 norm as the regularization terms for the low-rank and sparse components, respectively. However, TNN treats each singular value of the low-rank tensor L equally and the tensor l1 norm shrinks each entry of the sparse tensor S with the same strength. It has been shown that larger singular values generally correspond to prominent information of the data and should be less penalized. The same goes for large entries in S in terms of absolute values. In this paper, we propose a Double Auto-weighted TRPCA (DATRPCA) method. s Instead of using predefined and manually set weights merely for the low-rank tensor as previous works, DATRPCA automatically and adaptively assigns smaller weights and applies lighter penalization to significant singular values of the low-rank tensor and large entries of the sparse tensor simultaneously. We have further developed an efficient algorithm to implement DATRPCA based on the Alternating Direction Method of Multipliers (ADMM) framework. In addition, we have also established the convergence analysis of the proposed algorithm. The results on both synthetic and real-world data demonstrate the effectiveness of DATRPCA for low-rank tensor recovery, color image recovery and background modelling.

Local Orthogonal Moments for Local Features.

By introducing parameters with local information, several types of orthogonal moments have recently been developed for the extraction of local features in an image. But with the existing orthogonal moments, local features cannot be well-controlled with these parameters. The reason lies in that zeros distribution of these moments' basis function cannot be well-adjusted by the introduced parameters. To overcome this obstacle, a new framework, transformed orthogonal moment (TOM), is set up. Most existing continuous orthogonal moments, such as Zernike moments, fractional-order orthogonal moments (FOOMs), etc. are all special cases of TOM. To control the basis function's zeros distribution, a novel local constructor is designed, and local orthogonal moment (LOM) is proposed. Zeros distribution of LOM's basis function can be adjusted with parameters introduced by the designed local constructor. Consequently, locations, where local features extracted from by LOM, are more accurate than those by FOOMs. In comparison with Krawtchouk moments and Hahn moments etc., the range, where local features are extracted from by LOM, is order insensitive. Experimental results demonstrate that LOM can be utilized to extract local features in an image.

Learning Performance of Weighted Distributed Learning With Support Vector Machines.

The divide-and-conquer strategy is a very effective method of dealing with big data. Noisy samples in big data usually have a great impact on algorithmic performance. In this article, we introduce Markov sampling and different weights for distributed learning with the classical support vector machine (cSVM). We first estimate the generalization error of weighted distributed cSVM algorithm with uniformly ergodic Markov chain (u.e.M.c.) samples and obtain its optimal convergence rate. As applications, we obtain the generalization bounds of weighted distributed cSVM with strong mixing observations and independent and identically distributed (i.i.d.) samples, respectively. We also propose a novel weighted distributed cSVM based on Markov sampling (DM-cSVM). The numerical studies of benchmark datasets show that the DM-cSVM algorithm not only has better performance but also has less total time of sampling and training compared to other distributed algorithms.

[Expression and Clinical Significance of MMSA-8 and MMSA-1 in Bone Marrow of Patients with M2 Acute Myeloid Leukemia].

OBJECTIVE: To detect the expression of multiple myeloma-associated antigen (MMSA)-8 and MMSA-1 in bone marrow mononuclear cells of patients with acute myeloid leukemia, and explore their roles in acute myeloid leukemia. METHODS: A total of 83 patients with M2 acute myeloid leukemia in our hospital from January 2019 to January 2020 were selected as research group, during the same period, 15 patients diagnosed iron deficiency anemia were selected as control group. Real-time fluorescence quantitative PCR was used to detect the levels of MMSA-8 and MMSA-1 in bone marrow mononuclear cells. Patients in the research group were divided into remission and non remission according to the clinical curative effect, and were divided into good prognosis, medium prognosis, and poor prognosis according to the prognosis. The relationship between MMSA-8, MMSA-1 and clinical efficacy, prognosis was analyzed. In addition, the general data of patients in the research group were collected, including white blood cell count (WBC), hemoglobin (Hb), platelet count (PLT), and percentage of bone marrow progenitor cells at admission. Pearson method was used to analyze the correlation between MMSA-8, MMSA-1 and clinical data, and MMSA-8 and MMSA-1. RESULTS: The analysis results about mRNA levels of MMSA-8 and MMSA-1 in bone marrow mononuclear cells of patients showed that patients in the research group were significantly higher than those in the control group (P<0.05); In the research group, patients without remission were also significantly higher than those with remission, as well as those with medium and poor prognosis than with good prognosis, while only mRNA level of MMSA-1 in patients with poor prognosis was significantly higher than those with medium prognosis (P<0.05). Pearson analysis showed that MMSA-8, MMSA-1 were positively correlated with WBC (r=0.468, r=0.516), and MMSA-8 was positively correlated with MMSA-1 (r=0.318). CONCLUSION: The levels of MMSA-8 and MMSA-1 in bone marrow mononuclear cells of patients with M2 acute myeloid leukemia are increased, which are closely related to the occurrence and development of the disease, and have certain value for the prognosis.

[Effect of Carvacrol on the Biological Behavior of Leukemia Cells and Its Mechanism].

OBJECTIVE: To explore the effect of carvacrol on the biological behavior of leukemia cells and its regulation to circ-0008717/miR-217 molecular axis. METHODS: Human acute lymphoblastic leukemia cells Molt-4 were cultured in vitro, and different concentrations of carvacrol were added to the cells. si-NC and si-circ-0008717 were transfected into Molt-4 cells (si-NC group, si-circ-0008717 group). pcDNA, pcDNA-circ-0008717, anti-miR-NC, anti-miR-217 were transfected into Molt-4 cells and then added to carvacrol-treated cells (carvacrol+pcDNA group, carvacrol+pcDNA-circ-0008717 group, carvacrol+anti-miR-NC group, carvacrol+anti-miR-217 group). MTT, plate clone formation experiment, and flow cytometry were used to detect the viability of the cell, colony formation number, and apoptosis rate of cells, respectively. The RT-qPCR method was used to detect the expression levels of circ-0008717 and miR-217. The dual luciferase reporter gene experiment was used to detect the targeting relationship between circ-0008717 and miR-217. RESULTS: After carvacrol treatment, the cell viability decreased significantly (r=-0.9405), expression level of circ-0008717 decreased (r=-0.9117), colonies formed number decreased (r=-0.9256), while the cell apoptosis rate increased (r= 0.8464), and the expression level of miR-217 increased (r=0.9468). Compared with the si-NC group, the expression level of miR-217 in si-circ-0008717 group increased (P＜0.001), the cell apoptosis rate increased (P＜0.001), while cell viability decreased (P＜0001), the number of colonies formed decreased (P＜0.001). Compared with the carvacrol+pcDNA group, the cell viability of the carvacrol+pcDNA-circ-0008717 group increased (P＜0.001), the number of colonies formed increased (P＜0.001), while the cell apoptosis rate decreased (P＜0.001). circ-0008717 could target miR-217. The cell viability of the carvacrol+anti-miR-217 group increased (P＜0.001), and the number of colonies formed increased (P＜0.001), while the cell apoptosis rate decreased (P＜0001) as compared with the carvacrol+anti-miR-NC group. CONCLUSION: Carvacrol can promote the expression of miR-217 by down-regulating the expression of circ-0008717, thereby reducing the proliferation and cloning ability of leukemia cells and promoting cell apoptosis.

Generalized and Discriminative Collaborative Representation for Multiclass Classification.

This article presents a generalized collaborative representation-based classification (GCRC) framework, which includes many existing representation-based classification (RC) methods, such as collaborative RC (CRC) and sparse RC (SRC) as special cases. This article also advances the GCRC theory by exploring theoretical conditions on the general regularization matrix. A key drawback of CRC and SRC is that they fail to use the label information of training data and are essentially unsupervised in computing the representation vector. This largely compromises the discriminative ability of the learned representation vector and impedes the classification performance. Guided by the GCRC theory, we propose a novel RC method referred to as discriminative RC (DRC). The proposed DRC method has the following three desirable properties: 1) discriminability: DRC can leverage the label information of training data and is supervised in both representation and classification, thus improving the discriminative ability of the representation vector; 2) efficiency: it has a closed-form solution and is efficient in computing the representation vector and performing classification; and 3) theory: it also has theoretical guarantees for classification. Experimental results on benchmark databases demonstrate both the efficacy and efficiency of DRC for multiclass classification.

Weighted Error Entropy-Based Information Theoretic Learning for Robust Subspace Representation.

In most of the existing representation learning frameworks, the noise contaminating the data points is often assumed to be independent and identically distributed (i.i.d.), where the Gaussian distribution is often imposed. This assumption, though greatly simplifies the resulting representation problems, may not hold in many practical scenarios. For example, the noise in face representation is usually attributable to local variation, random occlusion, and unconstrained illumination, which is essentially structural, and hence, does not satisfy the i.i.d. property or the Gaussianity. In this article, we devise a generic noise model, referred to as independent and piecewise identically distributed (i.p.i.d.) model for robust presentation learning, where the statistical behavior of the underlying noise is characterized using a union of distributions. We demonstrate that our proposed i.p.i.d. model can better describe the complex noise encountered in practical scenarios and accommodate the traditional i.i.d. one as a special case. Assisted by the proposed noise model, we then develop a new information-theoretic learning framework for robust subspace representation through a novel minimum weighted error entropy criterion. Thanks to the superior modeling capability of the i.p.i.d. model, our proposed learning method achieves superior robustness against various types of noise. When applying our scheme to the subspace clustering and image recognition problems, we observe significant performance gains over the existing approaches.

hsa­miR­429 targets CBX8 to promote cell apoptosis in diffuse large B­cell lymphoma.

Diffuse large B­cell lymphoma (DLBCL) is the most common type of non­Hodgkin lymphoma worldwide. Several studies have indicated that Homo sapiens (hsa)­microRNA (miR)­429 exerts a tumor­suppressive effect on a variety of malignant tumors. To the best of our knowledge, the molecular function and mechanism of action of hsa­miR­429 in DLBCL have not been evaluated to date. The present study demonstrated that the expression of hsa­miR­429 in DLBCL cells was significantly reduced. hsa­miR­429 inhibited the proliferation of the DLBCL cell lines, SUDHL­4 and DB, and promoted apoptosis. A dual luciferase reporter assay was used to demonstrate that chromobox 8 (CBX8) was the target gene of hsa­miR­429. Overexpression of CBX8 promoted the proliferation of SUDHL­4 and DB cells and inhibited apoptosis, thereby playing a cancer­promoting role. Transfection of hsa­miR­429 mimic into DB cells overexpressing CBX8 antagonized the effect of CBX8 on the proliferation of DB cells. Moreover, the apoptotic rate was increased in DB cells overexpressing CBX8 and transfected with hsa­miR­429 mimic, while the proportion of cells in the G2/M phase was significantly reduced. These results demonstrated the antagonistic effect of hsa­miR­429 on the oncogenic function of CBX8. Therefore, in DLBCL, the tumor suppressor effect of hsa­miR­429 may be achieved by targeted downregulation of CBX8, suggesting that hsa­miR­429 may be used as a diagnostic marker and a potential nucleic acid drug for DLBCL. CBX8 may also represent an effective therapeutic target for DLBCL.

Robust Sparse Representation in Quaternion Space.

Sparse representation has achieved great success across various fields including signal processing, machine learning and computer vision. However, most existing sparse representation methods are confined to the real valued data. This largely limit their applicability to the quaternion valued data, which has been widely used in numerous applications such as color image processing. Another critical issue is that their performance may be severely hampered due to the data noise or outliers in practice. To tackle the problems above, in this work we propose a robust quaternion valued sparse representation (RQVSR) method in a fully quaternion valued setting. To handle the quaternion noises, we first define a new robust estimator referred as quaternion Welsch estimator to measure the quaternion residual error. Compared to the conventional quaternion mean square error, it can largely suppress the impact of large data corruption and outliers. To implement RQVSR, we have overcome the difficulties raised by the noncommutativity of quaternion multiplication and developed an effective algorithm by leveraging the half-quadratic theory and the alternating direction method of multipliers framework. The experimental results show the effectiveness and robustness of the proposed method for quaternion sparse signal recovery and color image reconstruction.

Self-Adaptive Multiprototype-Based Competitive Learning Approach: A k-Means-Type Algorithm for Imbalanced Data Clustering.

Class imbalance problem has been extensively studied in the recent years, but imbalanced data clustering in unsupervised environment, that is, the number of samples among clusters is imbalanced, has yet to be well studied. This paper, therefore, studies the imbalanced data clustering problem within the framework of k -means-type competitive learning. We introduce a new method called self-adaptive multiprototype-based competitive learning (SMCL) for imbalanced clusters. It uses multiple subclusters to represent each cluster with an automatic adjustment of the number of subclusters. Then, the subclusters are merged into the final clusters based on a novel separation measure. We also propose a new internal clustering validation measure to determine the number of final clusters during the merging process for imbalanced clusters. The advantages of SMCL are threefold: 1) it inherits the advantages of competitive learning and meanwhile is applicable to the imbalanced data clustering; 2) the self-adaptive multiprototype mechanism uses a proper number of subclusters to represent each cluster with any arbitrary shape; and 3) it automatically determines the number of clusters for imbalanced clusters. SMCL is compared with the existing counterparts for imbalanced clustering on the synthetic and real datasets. The experimental results show the efficacy of SMCL for imbalanced clusters.

Low-Rank Matrix Recovery from Noise via an MDL Framework-Based Atomic Norm.

The recovery of the underlying low-rank structure of clean data corrupted with sparse noise/outliers is attracting increasing interest. However, in many low-level vision problems, the exact target rank of the underlying structure and the particular locations and values of the sparse outliers are not known. Thus, the conventional methods cannot separate the low-rank and sparse components completely, especially in the case of gross outliers or deficient observations. Therefore, in this study, we employ the minimum description length (MDL) principle and atomic norm for low-rank matrix recovery to overcome these limitations. First, we employ the atomic norm to find all the candidate atoms of low-rank and sparse terms, and then we minimize the description length of the model in order to select the appropriate atoms of low-rank and the sparse matrices, respectively. Our experimental analyses show that the proposed approach can obtain a higher success rate than the state-of-the-art methods, even when the number of observations is limited or the corruption ratio is high. Experimental results utilizing synthetic data and real sensing applications (high dynamic range imaging, background modeling, removing noise and shadows) demonstrate the effectiveness, robustness and efficiency of the proposed method.

SVM-Boosting based on Markov resampling: Theory and algorithm.

In this article we introduce the idea of Markov resampling for Boosting methods. We first prove that Boosting algorithm with general convex loss function based on uniformly ergodic Markov chain (u.e.M.c.) examples is consistent and establish its fast convergence rate. We apply Boosting algorithm based on Markov resampling to Support Vector Machine (SVM), and introduce two new resampling-based Boosting algorithms: SVM-Boosting based on Markov resampling (SVM-BM) and improved SVM-Boosting based on Markov resampling (ISVM-BM). In contrast with SVM-BM, ISVM-BM uses the support vectors to calculate the weights of base classifiers. The numerical studies based on benchmark datasets show that the proposed two resampling-based SVM Boosting algorithms for linear base classifiers have smaller misclassification rates, less total time of sampling and training compared to three classical AdaBoost algorithms: Gentle AdaBoost, Real AdaBoost, Modest AdaBoost. In addition, we compare the proposed SVM-BM algorithm with the widely used and efficient gradient Boosting algorithm-XGBoost (eXtreme Gradient Boosting), SVM-AdaBoost and present some useful discussions on the technical parameters.

Clinical characteristics of patients with 2019 coronavirus disease in a non-Wuhan area of Hubei Province, China: a retrospective study.

BACKGROUND: Since December 2019, the 2019 coronavirus disease (COVID-19) has expanded to cause a worldwide outbreak that more than 600,000 people infected and tens of thousands died. To date, the clinical characteristics of COVID-19 patients in the non-Wuhan areas of Hubei Province in China have not been described. METHODS: We retrospectively analyzed the clinical characteristics and treatment progress of 91 patients diagnosed with COVID-19 in Jingzhou Central Hospital. RESULTS: Of the 91 patients diagnosed with COVID-19, 30 cases (33.0%) were severe and two patients (2.2%) died. The severe disease group tended to be older (50.5 vs. 42.0 years; p = 0.049) and have more chronic disease (40% vs. 14.8%; p = 0.009) relative to mild disease group. Only 73.6% of the patients were quantitative polymerase chain reaction (qPCR)-positive on their first tests, while typical chest computed tomography images were obtained for each patient. The most common complaints were cough (n = 75; 82.4%), fever (n = 59; 64.8%), fatigue (n = 35; 38.5%), and diarrhea (n = 14; 15.4%). Non-respiratory injury was identified by elevated levels of aspartate aminotransferase (n = 18; 19.8%), creatinine (n = 5; 5.5%), and creatine kinase (n = 14; 15.4%) in laboratory tests. Twenty-eight cases (30.8%) suffered non-respiratory injury, including 50% of the critically ill patients and 21.3% of the mild patients. CONCLUSIONS: Overall, the mortality rate of patients in Jingzhou was lower than that of Wuhan. Importantly, we found liver, kidney, digestive tract, and heart injuries in COVID-19 cases besides respiratory problems. Combining chest computed tomography images with the qPCR analysis of throat swab samples can improve the accuracy of COVID-19 diagnosis.

Quasi Fourier-Mellin Transform for Affine Invariant Features.

Fourier-Mellin transform (FMT) has been widely used for the extraction of rotation- and scale-invariant features. However, affine transform is a more reasonable approximation model for real viewpoint change. Due to shearing, the integral along the angular direction in the calculation of FMT cannot be used to extract the inherent features of an image undergoing affine transform. To eliminate the effect of shearing, whitening transform should be conducted on the integral along the radial direction. FMT can hardly be modified by conventional whitening-based methods with low computational cost due to additional processes. In this paper, two factors are constructed and embedded into FMT. Quasi Fourier-Mellin transform (QFMT) is proposed. The embedding of these factors is equivalent to whitening transform and can eliminate the effect of shearing in the affine transform. In particular, QFMT can also be calculated by integrating along the radial direction followed by integrating along the angular direction, as in FMT. Based on QFMT, the quasi Fourier-Mellin descriptor (QFMD) is constructed for the extraction of affine invariant features. Some experiments have also been conducted to test the performance of the proposed method.

Sparse Supervised Representation-Based Classifier for Uncontrolled and Imbalanced Classification.

The sparse representation-based classification (SRC) has been utilized in many applications and is an effective algorithm in machine learning. However, the performance of SRC highly depends on the data distribution. Some existing works proved that SRC could not obtain satisfactory results on uncontrolled data sets. Except the uncontrolled data sets, SRC cannot deal with imbalanced classification either. In this paper, we proposed a model named sparse supervised representation classifier (SSRC) to solve the above-mentioned issues. The SSRC involves the class label information during the test sample representation phase to deal with the uncontrolled data sets. In SSRC, each class has the opportunity to linearly represent the test sample in its subspace, which can decrease the influences of the uncontrolled data distribution. In order to classify imbalanced data sets, a class weight learning model is proposed and added to SSRC. Each class weight is learned from its corresponding training samples. The experimental results based on the AR face database (uncontrolled) and 15 KEEL data sets (imbalanced) with an imbalanced rate ranging from 1.48 to 61.18 prove SSRC can effectively classify uncontrolled and imbalanced data sets.

Bayes Imbalance Impact Index: A Measure of Class Imbalanced Data Set for Classification Problem.

Recent studies of imbalanced data classification have shown that the imbalance ratio (IR) is not the only cause of performance loss in a classifier, as other data factors, such as small disjuncts, noise, and overlapping, can also make the problem difficult. The relationship between the IR and other data factors has been demonstrated, but to the best of our knowledge, there is no measurement of the extent to which class imbalance influences the classification performance of imbalanced data. In addition, it is also unknown which data factor serves as the main barrier for classification in a data set. In this article, we focus on the Bayes optimal classifier and examine the influence of class imbalance from a theoretical perspective. We propose an instance measure called the Individual Bayes Imbalance Impact Index (IBI3) and a data measure called the Bayes Imbalance Impact Index (BI3). IBI3 and BI3 reflect the extent of influence using only the imbalance factor, in terms of each minority class sample and the whole data set, respectively. Therefore, IBI3 can be used as an instance complexity measure of imbalance and BI3 as a criterion to demonstrate the degree to which imbalance deteriorates the classification of a data set. We can, therefore, use BI3 to access whether it is worth using imbalance recovery methods, such as sampling or cost-sensitive methods, to recover the performance loss of a classifier. The experiments show that IBI3 is highly consistent with the increase of the prediction score obtained by the imbalance recovery methods and that BI3 is highly consistent with the improvement in the F1 score obtained by the imbalance recovery methods on both synthetic and real benchmark data sets.

Modal Regression-Based Atomic Representation for Robust Face Recognition and Reconstruction.

Representation-based classification (RC) methods, such as sparse RC, have shown great potential in face recognition (FR) in recent years. Most previous RC methods are based on the conventional regression models, such as lasso regression, ridge regression, or group lasso regression. These regression models essentially impose a predefined assumption on the distribution of the noise variable in the query sample, such as the Gaussian or Laplacian distribution. However, the complicated noises in practice may violate the assumptions and impede the performance of these RC methods. In this paper, we propose a modal regression (MR)-based atomic representation and classification (MRARC) framework to alleviate such limitations. MR is a robust regression framework which aims to reveal the relationship between the input and response variables by regressing toward the conditional mode function. Atomic representation is a general atomic norm regularized linear representation framework which includes many popular representation methods, such as sparse representation, collaborative representation, and low-rank representation as special cases. Unlike previous RC methods, the MRARC framework does not require the noise variable to follow any specific predefined distributions. This gives rise to the capability of MRARC in handling various complex noises in reality. Using MRARC as a general platform, we also develop four novel RC methods for unimodal and multimodal FR, respectively. In addition, we devise a general optimization algorithm for the unified MRARC framework based on the alternating direction method of multipliers and half-quadratic theory. The experiments on real-world data validate the efficacy of MRARC for robust FR and reconstruction.

Content-Adaptive Noise Estimation for Color Images with Cross-Channel Noise Modeling.

Noise estimation is crucial in many image processing tasks such as denoising. Most of the existing noise estimation methods are specially developed for grayscale images. For color images, these methods simply handle each color channel independently, without considering the correlation across channels. Moreover, these methods often assume a globally fixed noise model throughout the entire image, neglecting the adaptation to the local structures. In this work, we propose a contentadaptive multivariate Gaussian approach to model the noise in color images, in which we explicitly consider both the contentdependence and the inter-dependence among color channels. We design an effective method for estimating the noise covariance matrices within the proposed model. Specifically, a patch selection scheme is first introduced to select weakly textured patches via thresholding the texture strength indicators. Noticing that the patch selection actually depends on the unknown noise covariance, we present an iterative noise covariance estimation algorithm, where the patch selection and the covariance estimation are conducted alternately. For the remaining textured regions, we estimate a distinct covariance matrix associated with each pixel using a linear shrinkage estimator, which adaptively fuses the estimate coming from the weakly textured region and the sample covariance estimated from the local region. Experimental results show that our method can effectively estimate the noise covariance. The usefulness of our method is demonstrated with several image processing applications such as color image denoising and noise-robust superpixel.

Atomic Representation-Based Classification: Theory, Algorithm, and Applications.

Representation-based classification (RC) methods such as sparse RC (SRC) have attracted great interest in pattern recognition recently. Despite their empirical success, few theoretical results are reported to justify their effectiveness. In this paper, we establish the theoretical guarantees for a general unified framework termed as atomic representation-based classification (ARC), which includes most RC methods as special cases. We introduce a new condition called atomic classification condition (ACC), which reveals important geometric insights for the theory of ARC. We show that under such condition ARC is provably effective in correctly recognizing any new test sample, even corrupted with noise. Our theoretical analysis significantly broadens the range of conditions under which RC methods succeed for classification in the following two aspects: (1) prior theoretical advances of RC are mainly concerned with the single SRC method while our theory can apply to the general unified ARC framework, including SRC and many other RC methods; and (2) previous works are confined to the analysis of noiseless test data while we provide theoretical guarantees for ARC using both noiseless and noisy test data. Numerical results are provided to validate and complement our theoretical analysis of ARC and its important special cases for both noiseless and noisy test data.