Xiaoning Song

Test cost sensitive multigranulation rough set: Model and minimal cost selection

Abstract Multigranulation rough set is an expansion of the classical rough set by using multiple granular structures. Presently, three important multigranulation rough sets have been proposed, they are optimistic, pessimistic and β-multigranulation approaches. However, such three multigranulation rough sets do not take the test cost into consideration, which is an important issue in both data mining and machine learning. To solve such problem, we propose a test cost sensitive multigranulation rough set model in this paper. We show that test cost sensitive multigranulation rough set is a generalization of optimistic, pessimistic and β-multigranulation rough sets. Furthermore, it is found that the traditional heuristic algorithm is not suitable for granular structure selection with lower test cost, we then propose a backtracking algorithm for granular structure selection with minimal test cost. The algorithms are tested on ten UCI (University of California–Irvine) data sets. Experimental results show the effectiveness of backtracking algorithm by comparing with heuristic algorithm. This study suggests potential application areas and new research trends concerning multigranulation rough set theory.

A parameterized fuzzy adaptive K-SVD approach for the multi-classes study of pursuit algorithms

Sparse representations using over complete dictionaries has concentrated mainly on the study of pursuit algorithms that decompose signals with respect to a given dictionary. Designing dictionaries to better fit the above model can be done by either selecting one from a pre-specified set of linear transforms or adapting the dictionary to a set of training signals. The K-SVD algorithm is an iterative method that alternates between sparse coding of the examples based on the current dictionary and a process of updating the dictionary atoms to better fit the data. However, the existing K-SVD algorithm is employed to dwell on the concept of a binary class assignment, which means that the multi-classes samples are assigned to the given classes definitely. The work proposed in this paper provides a novel parameterized fuzzy adaptive way to adapting dictionaries. In order to achieve the fuzzy sparse signal representations, the update of the dictionary columns is combined with an update of the sparse representations by embedding a new mechanism of fuzzy set, which is called parameterized fuzzy K-SVD. Experimental results conducted on the ORL, Yale and FERET face databases demonstrate the effectiveness of the proposed method.

Hierarchy on multigranulation structures: a knowledge distance approach

Abstract In this paper, a knowledge distance approach is proposed to study the hierarchy under the frame of multigranulation. In our approach, the finest granulation structure is considered as the frame of reference, and then a knowledge distances algebraic lattice is constructed. Through such algebraic lattice, a partial order is derived, which can be used to characterize the finer or coarser relationships among multigranulation structures. It is also shown that the uncertainty measurements are monotonic in terms of the obtained partial order.

Half-Face Dictionary Integration for Representation-Based Classification

This paper presents a half-face dictionary integration (HFDI) algorithm for representation-based classification. The proposed HFDI algorithm measures residuals between an input signal and the reconstructed one, using both the original and the synthesized dual-column (row) half-face training samples. More specifically, we first generate a set of virtual half-face samples for the purpose of training data augmentation. The aim is to obtain high-fidelity collaborative representation of a test sample. In this half-face integrated dictionary, each original training vector is replaced by an integrated dual-column (row) half-face matrix. Second, to reduce the redundancy between the original dictionary and the extended half-face dictionary, we propose an elimination strategy to gain the most robust training atoms. The last contribution of the proposed HFDI method is the use of a competitive fusion method weighting the reconstruction residuals from different dictionaries for robust face classification. Experimental results obtained from the Facial Recognition Technology, Aleix and Robert, Georgia Tech, ORL, and Carnegie Mellon University-pose, illumination and expression data sets demonstrate the effectiveness of the proposed method, especially in the case of the small sample size problem.

Dynamic dictionary optimization for sparse-representation-based face classification using local difference images

Abstract In this study, we present a new sparse-representation-based face-classification algorithm that exploits dynamic dictionary optimization on an extended dictionary using synthesized faces. More specifically, given a dictionary consisting of face examples, we first augment the dictionary with a set of virtual faces generated by calculating the image difference of a pair of faces. This results in an extended dictionary with hybrid training samples, which enhances the capacity of the dictionary to represent new samples. Second, to reduce the redundancy of the extended dictionary and improve the classification accuracy, we use a dictionary-optimization method. We truncate the extended dictionary with a more compact structure by discarding the original samples with small contributions to represent a test sample. Finally, we perform sparse-representation-based face classification using the optimized dictionary. Experimental results obtained using the AR and FERRET face datasets demonstrate the superiority of the proposed method in terms of accuracy, especially for small-sample-size problems.

Using idea of three-step sparse residuals measurement to perform discriminant analysis

Classification of high-dimensional data is usually not amenable to standard pattern recognition techniques owing to lack of necessary, underlying structured information of data. In this paper, we propose a new discriminant analysis based on three-step sparse residuals measurement called DA-TSSR to address this problem. Specifically, in the first stage of the proposed method, the contribution in presenting the test sample of any chosen class is respectively calculated by adding up the total contributions of all the training samples of this class, and then a certain class with the smallest contribution score is eliminated from the set of the training samples. This procedure is iteratively carried out for the set of the training samples of the remaining classes till the predefined termination condition is satisfied. The second stage of DA-TSSR seeks to represent the test sample as a linear combination of all the remaining training samples and exploits the representation ability of each training sample to determine M “nearest neighbors” for the test sample. By this means, it generates unequal number of training samples on each candidate class. The third stage of DA-TSSR again determines a new weighted sum of all unequal numbers of training samples from candidate classes, which is approximately equal to the test sample. We use the new weighted sum to perform the designing of sparse residuals grades, which can be incorporated into the typical discriminant analysis criterion. The proposed method not only has a high accuracy but also can be clearly interpreted. Experimental results conducted on the ORL, XM2VTS, FERET and AR face databases demonstrate the effectiveness of the proposed method.

Converted-face identification: using synthesized images to replace original images for recognition

The changes in appearance of faces, usually caused by pose, expression and illumination variations, increase data uncertainty in the task of face recognition. Insufficient training samples cannot provide abundant multi-view observations of a face. To address this issue, many pioneering works focus on generating virtual training images for better recognition performance. However, the issue also exists in a test set where a test image only conveys a split-second representation of a face and cannot cover more comprehensive features. In this paper, we propose a new face synthesis method for face recognition. In the proposed pipeline, we synthesize a virtual image using both the original image and its corresponding mirror one. Note that, we apply this technique both to the training and test sets. Then we use the newly generated training and test images to replace the original ones for face recognition. The aim is to increase the similarity between a test image and its corresponding intra-class training images. This proposed method is effective and computationally efficient. In order to verify this, we tested our system using multiple face recognition methods in terms of the recognition accuracy, based on either the synthesized images or original images. The methods used in the paper include statistical subspace learning algorithms and representation-based classification approaches. Experimental results obtained on FERET, ORL, GT, PIE and LFW show that the proposed approach improves the face recognition accuracy, especially on faces with left-right pose variations.

Towards multi-scale fuzzy sparse discriminant analysis using local third-order tensor model of face images

Traditional discriminant analysis (DA) methods are usually not amenable to being studied only with a few or even single facial image per subject. The?fundamental?reason?lies in the fact that the traditional DA approaches cannot fully reflect the variations of a query sample with illumination, occlusion and pose variations, especially in the case of small sample size. In this paper, we develop a multi-scale fuzzy sparse discriminant analysis using a local third-order tensor model to perform robust face classification. More specifically, we firstly introduced a local third-order tensor model of face images to exploit a set of multi-scale characteristics of the Ridgelet transform. Secondly, a set of Ridgelet transformed coefficients with respect to each block from a face image are respectively generated. We then merge all these coefficients to form a new representative vector for the image. Lastly, we evaluate the sparse similarity grade between each training sample and class by constructing a sparse similarity metric, and redesign the traditional discriminant criterion that contains considerable fuzzy sparse similarity grades to perform robust classification. Experimental results conducted on a set of well-known face databases demonstrate the merits of the proposed method, especially in the case of insufficient training samples. Exploit a set of multi-scale characteristics using Ridgelet transform.Solve Ridgelet transformed coefficients with respect to each image block.Synthesize a new coefficient vector for each training image.Evaluate the sparse similarity grade between each training sample and class.Redesign a new discriminant criterion to perform robust classification.

Progressive sparse representation-based classification using local discrete cosine transform evaluation for image recognition

Abstract. This paper proposes a progressive sparse representation-based classification algorithm using local discrete cosine transform (DCT) evaluation to perform face recognition. Specifically, the sum of the contributions of all training samples of each subject is first taken as the contribution of this subject, then the redundant subject with the smallest contribution to the test sample is iteratively eliminated. Second, the progressive method aims at representing the test sample as a linear combination of all the remaining training samples, by which the representation capability of each training sample is exploited to determine the optimal “nearest neighbors” for the test sample. Third, the transformed DCT evaluation is constructed to measure the similarity between the test sample and each local training sample using cosine distance metrics in the DCT domain. The final goal of the proposed method is to determine an optimal weighted sum of nearest neighbors that are obtained under the local correlative degree evaluation, which is approximately equal to the test sample, and we can use this weighted linear combination to perform robust classification. Experimental results conducted on the ORL database of faces (created by the Olivetti Research Laboratory in Cambridge), the FERET face database (managed by the Defense Advanced Research Projects Agency and the National Institute of Standards and Technology), AR face database (created by Aleix Martinez and Robert Benavente in the Computer Vision Center at U.A.B), and USPS handwritten digit database (gathered at the Center of Excellence in Document Analysis and Recognition at SUNY Buffalo) demonstrate the effectiveness of the proposed method.

Sparse representation-based classification using generalized weighted extended dictionary

Sparse representation-based classification (SRC) has been a breakthrough of face recognition and signal reconstruction recently. However, few face images from the same subject provide insufficient observations. Meanwhile, owing to uncertainty of training images with variations in the appearance of facial illumination, pose and facial expression, it is difficult to successfully address the issues of image recognition and signal reconstruction. Thus, how to construct an optimized comprehensive dictionary is still a non-trivial task. In this paper, we develop a generalized virtual extended dictionary of SRC (V-SRC) to deal with data uncertainty problem, establishing a weighted mechanism which assigns different coefficients between arbitrary two within-class samples to obtain the virtual samples. More specifically, we firstly construct a set of synthesized training samples by means of weighted combination of existing training samples. Secondly, we combine the original and synthesized training samples as an initial extended dictionary. Thirdly, in order to decrease the constructed error in sparse representation, we exploit an elimination scheme to gain the robust training samples with respect to the initial extended training dictionary. The final goal of the proposed method is to utilize the linear combination of competitive training samples to perform face classification. Experimental results conducted on the AR, FERET and Georgia Tech databases demonstrate the effectiveness of the proposed method especially in the case of small sample size problem.