Representation of Imprecision in Deep Neural Networks for Image Classification.

Quantification and reduction of uncertainty in deep-learning techniques have received much attention but ignored how to characterize the imprecision caused by such uncertainty. In some tasks, we prefer to obtain an imprecise result rather than being willing or unable to bear the cost of an error. For this purpose, we investigate the representation of imprecision in deep-learning (RIDL) techniques based on the theory of belief functions (TBF). First, the labels of some training images are reconstructed using the learning mechanism of neural networks to characterize the imprecision in the training set. In the process, a label assignment rule is proposed to reassign one or more labels to each training image. Once an image is assigned with multiple labels, it indicates that the image may be in an overlapping region of different categories from the feature perspective or the original label is wrong. Second, those images with multiple labels are rechecked. As a result, the imprecision (multiple labels) caused by the original labeling errors will be corrected, while the imprecision caused by insufficient knowledge is retained. Images with multiple labels are called imprecise ones, and they are considered to belong to meta-categories, the union of some specific categories. Third, the deep network model is retrained based on the reconstructed training set, and the test images are then classified. Finally, some test images that specific categories cannot distinguish will be assigned to meta-categories to characterize the imprecision in the results. Experiments based on some remarkable networks have shown that RIDL can improve accuracy (AC) and reasonably represent imprecision both in the training and testing sets.

Orientational Distribution Learning With Hierarchical Spatial Attention for Open Set Recognition.

Open set recognition (OSR) aims to correctly recognize the known classes and reject the unknown classes for increasing the reliability of the recognition system. The distance-based loss is often employed in deep neural networks-based OSR methods to constrain the latent representation of known classes. However, the optimization is usually conducted using the nondirectional euclidean distance in a single feature space without considering the potential impact of spatial distribution. To address this problem, we propose orientational distribution learning (ODL) with hierarchical spatial attention for OSR. In ODL, the spatial distribution of feature representation is optimized orientationally to increase the discriminability of decision boundaries for open set recognition. Then, a hierarchical spatial attention mechanism is proposed to assist ODL to capture the global distribution dependencies in the feature space based on spatial relationships. Moreover, a composite feature space is constructed to integrate the features from different layers and different mapping approaches, and it can well enrich the representation information. Finally, a decision-level fusion method is developed to combine the composite feature space and the naive feature space for producing a more comprehensive classification result. The effectiveness of ODL has been demonstrated on various benchmark datasets, and ODL achieves state-of-the-art performance.

Iteratively distributed instrumental variable-based pseudo-linear information filter for angle-only tracking.

This paper presents a distributed filtering problem for three-dimensional angle-only target tracking (AOTT) in sensor (i.e., observer) networks. An instrumental variable-based pseudo-linear information filter (IVIF) is firstly derived on the basis of the designed bias-compensated pseudo-linear information filtering, with the help of summation forms of information quantities and bias compensation in a centralized fusion manner. Then, the distributed IVIF (DIVIF) is put forward by using finite-time average consensus to obtain the arithmetic means of defined information quantities and compensated bias in observer networks, which ensures that the filtering result of every observer is consistent with the centralized one. Finally, the iteratively DIVIF is proposed via gradually approaching the true values of relative distance and the corresponding angles between the target and every observer to get the filtering parameters more and more accurately, in order to achieve higher filtering precision. In addition, the computational complexity of the proposed method is also analyzed. The advantages of filtering precision of the proposed method over the existing pseudo-linear Kalman filter and its variants are demonstrated by an AOTT example in observer networks in terms of iteration steps, different levels of process noises and observer's accuracy.

Cross-Domain Pattern Classification With Distribution Adaptation Based on Evidence Theory.

In pattern classification, there may not exist labeled patterns in the target domain to train a classifier. Domain adaptation (DA) techniques can transfer the knowledge from the source domain with massive labeled patterns to the target domain for learning a classification model. In practice, some objects in the target domain are easily classified by this classification model, and these objects usually can provide more or less useful information for classifying the other objects in the target domain. So a new method called distribution adaptation based on evidence theory (DAET) is proposed to improve the classification accuracy by combining the complementary information derived from both the source and target domains. In DAET, the objects that are easy to classify are first selected as easy-target objects, and the other objects are regarded as hard-target objects. For each hard-target object, we can obtain one classification result with the assistance of massive labeled patterns in the source domain, and another classification result can be acquired based on the easy-target objects with confidently predicted (pseudo) labels. However, the weights of these classification results may vary because the reliabilities of the used information sources are different. The weights are estimated by mean difference reflecting the information source quality. Then, we discount the classification results with the corresponding weights under the framework of the evidence theory, which is expert at dealing with uncertain information. These discounted classification results are combined by an evidential combination rule for making the final class decision. The effectiveness of DAET for cross-domain pattern classification is evaluated with respect to some advanced DA methods, and the experiment results show DAET can significantly improve the classification accuracy.

A New Progressive Multisource Domain Adaptation Network With Weighted Decision Fusion.

Multisource unsupervised domain adaptation (MUDA) is an important and challenging topic for target classification with the assistance of labeled data in source domains. When we have several labeled source domains, it is difficult to map all source domains and target domain into a common feature space for classifying the targets well. In this article, a new progressive multisource domain adaptation network (PMSDAN) is proposed to further improve the classification performance. PMSDAN mainly consists of two steps for distribution alignment. First, the multiple source domains are integrated as one auxiliary domain to match the distribution with the target domain. By doing this, we can generally reduce the distribution discrepancy between each source and target domains, as well as the discrepancy between different source domains. It can efficiently explore useful knowledge from the integrated source domain. Second, to mine assistance knowledge from each source domain as much as possible, the distribution of the target domain is separately aligned with that of each source domain. A weighted fusion method is employed to combine the multiple classification results for making the final decision. In the optimization of domain adaption, weighted hybrid maximum mean discrepancy (WHMMD) is proposed, and it considers both the interclass and intraclass discrepancies. The effectiveness of the proposed PMSDAN is demonstrated in the experiments comparing with some state-of-the-art methods.

A New Belief-Based Bidirectional Transfer Classification Method.

In pattern classification, we may have a few labeled data points in the target domain, but a number of labeled samples are available in another related domain (called the source domain). Transfer learning can solve such classification problems via the knowledge transfer from source to target domains. The source and target domains can be represented by heterogeneous features. There may exist uncertainty in domain transformation, and such uncertainty is not good for classification. The effective management of uncertainty is important for improving classification accuracy. So, a new belief-based bidirectional transfer classification (BDTC) method is proposed. In BDTC, the intraclass transformation matrix is estimated at first for mapping the patterns from source to target domains, and this matrix can be learned using the labeled patterns of the same class represented by heterogeneous domains (features). The labeled patterns in the source domain are transferred to the target domain by the corresponding transformation matrix. Then, we learn a classifier using all the labeled patterns in the target domain to classify the objects. In order to take full advantage of the complementary knowledge of different domains, we transfer the query patterns from target to source domains using the K-NN technique and do the classification task in the source domain. Thus, two pieces of classification results can be obtained for each query pattern in the source and target domains, but the classification results may have different reliabilities/weights. A weighted combination rule is developed to combine the two classification results based on the belief functions theory, which is an expert at dealing with uncertain information. We can efficiently reduce the uncertainty of transfer classification via the combination strategy. Experiments on some domain adaptation benchmarks show that our method can effectively improve classification accuracy compared with other related methods.

An Automatic and Optimal MPA Design Method.

Raw polarimetric images are captured by a focal plane polarimeter which is covered by a micro-polarizer array (MPA). The design of the MPA plays a crucial role in polarimetric imaging. MPAs are predominantly designed according to expert engineering experience and rules of thumb. Typically, only one optimization criterion, maximizing bandwidth, is used to design the MPA. To select a design, an exhaustive search is usually performed on a very limited set of available polarizing patterns, which must be constrained in order to make the search tractable. In contrast, this paper proposes a fully automated and optimal MPA design method (AO-MPA) which generates significantly improved MPAs. Instead of the single criterion of bandwidth, we propose six design principles, and show how they can be utilized to mutually optimize the MPA design by formulating a tri-objective optimization problem with multiple constraints. A much larger set of possible MPA patterns is rapidly and automatically searched by applying advanced multi-objective optimization techniques. We have tested AO-MPA using two groups of experiments, in which AO-MPA is compared against several other leading MPA design methods, and the patterns generated by AO-MPA are compared against state-of-the-art patterns from the literature. The results, obtained using a public benchmark dataset, show that the AO-MPA method is very computationally efficient, and can find all optimal MPA patterns for all array sizes. Moreover, for each size, AO-MPA obtains all optimal layouts simultaneously. AO-MPA generates designs which require fewer polarization orientations, while also yielding better performance in estimating intensity measurements, Stokes vector and the degree of linear polarization. This results in MPAs which are easier to manufacture while also being more robust to noise.

Rotation Awareness Based Self-Supervised Learning for SAR Target Recognition With Limited Training Samples.

The scattering signatures of a synthetic aperture radar (SAR) target image will be highly sensitive to different azimuth angles/poses, which aggravates the demand for training samples in learning-based SAR image automatic target recognition (ATR) algorithms, and makes SAR ATR a more challenging task. This paper develops a novel rotation awareness-based learning framework termed RotANet for SAR ATR under the condition of limited training samples. First, we propose an encoding scheme to characterize the rotational pattern of pose variations among intra-class targets. These targets will constitute several ordered sequences with different rotational patterns via permutations. By further exploiting the intrinsic relation constraints among these sequences as the supervision, we develop a novel self-supervised task which makes RotANet learn to predict the rotational pattern of a baseline sequence and then autonomously generalize this ability to the others without external supervision. Therefore, this task essentially contains a learning and self-validation process to achieve human-like rotation awareness, and it serves as a task-induced prior to regularize the learned feature domain of RotANet in conjunction with an individual target recognition task to improve the generalization ability of the features. Extensive experiments on moving and stationary target acquisition and recognition benchmark database demonstrate the effectiveness of our proposed framework. Compared with other state-of-the-art SAR ATR algorithms, RotANet will remarkably improve the recognition accuracy especially in the case of very limited training samples without performing any other data augmentation strategy.

Combination of Transferable Classification With Multisource Domain Adaptation Based on Evidential Reasoning.

In applications of domain adaptation, there may exist multiple source domains, which can provide more or less complementary knowledge for pattern classification in the target domain. In order to improve the classification accuracy, a decision-level combination method is proposed for the multisource domain adaptation based on evidential reasoning. The classification results obtained from different source domains usually have different reliabilities/weights, which are calculated according to domain consistency. Therefore, the multiple classification results are discounted by the corresponding weights under belief functions framework, and then, Dempster's rule is employed to combine these discounted results. In order to reduce errors, a neighborhood-based cautious decision-making rule is developed to make the class decision depending on the combination result. The object is assigned to a singleton class if its neighborhoods can be (almost) correctly classified. Otherwise, it is cautiously committed to the disjunction of several possible classes. By doing this, we can well characterize the partial imprecision of classification and reduce the error risk as well. A unified utility value is defined here to reflect the benefit of such classification. This cautious decision-making rule can achieve the maximum unified utility value because partial imprecision is considered better than an error. Several real data sets are used to test the performance of the proposed method, and the experimental results show that our new method can efficiently improve the classification accuracy with respect to other related combination methods.

Change Detection in Heterogenous Remote Sensing Images via Homogeneous Pixel Transformation.

The change detection in heterogeneous remote sensing images remains an important and open problem for damage assessment. We propose a new change detection method for heterogeneous images (i.e., SAR and optical images) based on homogeneous pixel transformation (HPT). HPT transfers one image from its original feature space (e.g., gray space) to another space (e.g., spectral space) in pixel-level to make the pre-event and post-event images represented in a common space for the convenience of change detection. HPT consists of two operations, i.e., the forward transformation and the backward transformation. In forward transformation, for each pixel of pre-event image in the first feature space, we will estimate its mapping pixel in the second space corresponding to post-event image based on the known unchanged pixels. A multi-value estimation method with noise tolerance is introduced to determine the mapping pixel using -nearest neighbors technique. Once the mapping pixels of pre-event image are available, the difference values between the mapping image and the post-event image can be directly calculated. After that, we will similarly do the backward transformation to associate the post-event image with the first space, and one more difference value for each pixel will be obtained. Then, the two difference values are combined to improve the robustness of detection with respect to the noise and heterogeneousness (modality difference) of images. Fuzzy-c means clustering algorithm is employed to divide the integrated difference values into two clusters: changed pixels and unchanged pixels. This detection results may contain some noisy regions (i.e., small error detections), and we develop a spatial-neighbor-based noise filter to further reduce the false alarms and missing detections using belief functions theory. The experiments for change detection with real images (e.g., SPOT, ERS, and NDVI) during a flood in U.K. are given to validate the effectiveness of the proposed method.

Classifier Fusion With Contextual Reliability Evaluation.

Classifier fusion is an efficient strategy to improve the classification performance for the complex pattern recognition problem. In practice, the multiple classifiers to combine can have different reliabilities and the proper reliability evaluation plays an important role in the fusion process for getting the best classification performance. We propose a new method for classifier fusion with contextual reliability evaluation (CF-CRE) based on inner reliability and relative reliability concepts. The inner reliability, represented by a matrix, characterizes the probability of the object belonging to one class when it is classified to another class. The elements of this matrix are estimated from the -nearest neighbors of the object. A cautious discounting rule is developed under belief functions framework to revise the classification result according to the inner reliability. The relative reliability is evaluated based on a new incompatibility measure which allows to reduce the level of conflict between the classifiers by applying the classical evidence discounting rule to each classifier before their combination. The inner reliability and relative reliability capture different aspects of the classification reliability. The discounted classification results are combined with Dempster-Shafer's rule for the final class decision making support. The performance of CF-CRE have been evaluated and compared with those of main classical fusion methods using real data sets. The experimental results show that CF-CRE can produce substantially higher accuracy than other fusion methods in general. Moreover, CF-CRE is robust to the changes of the number of nearest neighbors chosen for estimating the reliability matrix, which is appealing for the applications.

A new incomplete pattern classification method based on evidential reasoning.

The classification of incomplete patterns is a very challenging task because the object (incomplete pattern) with different possible estimations of missing values may yield distinct classification results. The uncertainty (ambiguity) of classification is mainly caused by the lack of information of the missing data. A new prototype-based credal classification (PCC) method is proposed to deal with incomplete patterns thanks to the belief function framework used classically in evidential reasoning approach. The class prototypes obtained by training samples are respectively used to estimate the missing values. Typically, in a c -class problem, one has to deal with c prototypes, which yield c estimations of the missing values. The different edited patterns based on each possible estimation are then classified by a standard classifier and we can get at most c distinct classification results for an incomplete pattern. Because all these distinct classification results are potentially admissible, we propose to combine them all together to obtain the final classification of the incomplete pattern. A new credal combination method is introduced for solving the classification problem, and it is able to characterize the inherent uncertainty due to the possible conflicting results delivered by different estimations of the missing values. The incomplete patterns that are very difficult to classify in a specific class will be reasonably and automatically committed to some proper meta-classes by PCC method in order to reduce errors. The effectiveness of PCC method has been tested through four experiments with artificial and real data sets.