Point cloud is often regarded as a discrete sampling of Riemannian manifold and plays a pivotal role in the 3D image interpretation. Particularly, rotation perturbation, an unexpected small change in rotation caused by various factors (like equipment offset, system instability, measurement errors and so on), can easily lead to the inferior results in point cloud learning tasks. However, classical point cloud learning methods are sensitive to rotation perturbation, and the existing networks with rotation robustness also have much room for improvements in terms of performance and noise tolerance. Given these, this paper remodels the point cloud from the perspective of manifold as well as designs a manifold distillation method to achieve the robustness of rotation perturbation without any coordinate transformation. In brief, during the training phase, we introduce a teacher network to learn the rotation robustness information and transfer this information to the student network through online distillation. In the inference phase, the student network directly utilizes the raw 3D coordinate information to achieve the robustness of rotation perturbation. Experiments carried out on four different datasets verify the effectiveness of our method. On average, on the ModelNet40 and ScanObjectNN classification datasets with random rotation perturbations, our method improves classification accuracy by 4.41% and 3.65%, respectively, compared to popular rotation-robust networks. Similarly, on the ShapeNet and S3DIS segmentation datasets, our method achieves improvements in mIoU of 6.96% and 5.12%, respectively. Furthermore, the experimental results also demonstrate that our algorithm exhibits higher computational efficiency and stronger resistance to noise and outliers.

Semantic segmentation is an important branch of image processing and computer vision. With the popularity of deep learning, various convolutional neural networks have been proposed for pixel-level classification and segmentation tasks. In practical scenarios, however, imaging angles are often arbitrary, encompassing instances such as water body images from remote sensing and capillary and polyp images in the medical domain, where prior orientation information is typically unavailable to guide these networks to extract more effective features. In this case, learning features from objects with diverse orientation information poses a significant challenge, as the majority of CNN-based semantic segmentation networks lack rotation equivariance to resist the disturbance from orientation information. To address this challenge, this paper first constructs a universal convolution-group framework aimed at more fully utilizing orientation information and equipping the network with rotation equivariance. Subsequently, we mathematically design a padding-based rotation equivariant convolution mode (PreCM), which is not only applicable to multi-scale images and convolutional kernels but can also serve as a replacement component for various types of convolutions, such as dilated convolutions, transposed convolutions, and asymmetric convolution. To quantitatively assess the impact of image rotation in semantic segmentation tasks, we also propose a new evaluation metric, Rotation Difference (RD). The replacement experiments related to six existing semantic segmentation networks on three datasets (i.e., Satellite Images of Water Bodies, DRIVE, and Floodnet) show that, the average Intersection Over Union (IOU) of their PreCM-based versions respectively improve 6.91%, 10.63%, 4.53%, 5.93%, 7.48%, 8.33% compared to their original versions in terms of random angle rotation. And the average RD values are decreased by 3.58%, 4.56%, 3.47%, 3.66%, 3.47%, 3.43% respectively. The code can be download from https://github.com/XinyuXu414.

Deep neural networks (DNNs) have been widely utilized in synthetic aperture radar (SAR) for automatic target recognition (ATR), demonstrating remarkable performance. Nevertheless, the vulnerability of DNNs to adversarial examples, particularly in SAR ATR tasks with high safety requirements, necessitates a critical examination. Existing adversarial attacks primarily concentrate on scenarios where classifier inputs consist solely of intensity information, leaving a significant research gap for attacks on classifiers that utilize polarimetric SAR (PolSAR) data. To address this gap, we propose a novel attack method aimed at PolSAR classifiers, where we manipulate the scattering matrix rather than its transformed real value images. Moreover, we incorporate a polarimetric feature constraint to enhance the stealth of the adversarial perturbations. This technique enables the generation of subtle yet effective perturbations concentrated on SAR object regions. Our experiments demonstrate high success rates in cheating state-of-the-art PolSAR classifiers and effectively evading advanced adversarial example detection methods.

The generation of realistic synthetic aperture radar (SAR) images holds notable significance due to their applicability across various crucial domains in remote sensing, such as automatic target recognition and electronic countermeasures. The majority of current SAR image synthesis methods only leverage amplitude, thereby lacking the phase information that also plays an important role in SAR image interpretation. In this letter, we introduce Polarimetric Feature Guided Denoising Diffusion Probabilistic Model (PFG-DDPM), to generate PolSAR images. The proposed method can effectively simulate the distribution of real PolSAR images, encompassing both their amplitude and phase components. Importantly, we introduce an innovative strategy that employs polarimetric features as supervised information to guide the generation process of PolSAR images. This approach allows PFG-DDPM to effectively utilize constraints among distinct polarimetric channels, resulting in generated PolSAR images whose distributions closely approximate real PolSAR data. Experiments underscore the ability of the proposed method to produce realistic PolSAR images valid for human visual perception. More significantly, these images exhibit a remarkable resemblance to real PolSAR images, evidenced by a 44.4% and 5.3% enhancement in alignment with polarimetric and statistical attributes, respectively, compared to the vanilla DDPM.

Polarimetric features, no matter how they are extracted, play a crucial role in synthetic aperture radar (SAR) image interpretation. Since recently developed deep neural network (DNN)-based methods are recognized as very vulnerable to some specifically designed perturbations, it raises an interesting question: are the traditional polarimetric features, calculated according to the scattering mechanism of SAR, still robust to the specially crafted perturbation? In this letter, we investigate the robustness of several traditional polarimetric features, which are widely used in the application of ship target detection, to a particularly designed perturbation, which we call polarimetric interference method (PIM). Specifically, we first calculate the gradients of traditional polarimetric features, respecting each of the polarimetric channels, and then formulate the PIM perturbation as an optimization problem, and finally, we give the PIM algorithm to perturb polarimetric features. Experiments are carried out on two polarimetric SAR (PolSAR) datasets to demonstrate the following: 1) traditional polarimetric features are vulnerable to the PIM perturbation, even if it is imperceptible in the SAR images; 2) the PIM perturbation can remarkably degrade the performance of the traditional polarimetric features in the task of ship detection, leading to more than 50% decrease in detection rate; and 3) the proposed perturbation is transferable, which means that the PIM interference regarding one type of the traditional polarimetric features also works in most cases for other types of polarimetric features.

Abstract Self‐supervised learning‐based depth completion is a cost‐effective way for 3D environment perception. However, it is also a challenging task because sparse depth may deactivate neural networks. In this paper, a novel Sparse‐Dense Depth Consistency Loss (SDDCL) is proposed to penalize not only the estimated depth map with sparse input points but also consecutive completed dense depth maps. Combined with the pose consistency loss, a new self‐supervised learning scheme is developed, using multi‐view geometric constraints, to achieve more accurate depth completion results. Moreover, to tackle the sparsity issue of input depth, a Quasi Dense Representations (QDR) module with triplet branches for spatial pyramid pooling is proposed to produce more dense feature maps. Extensive experimental results on VOID, NYUv2, and KITTI datasets show that the method outperforms state‐of‐the‐art self‐supervised depth completion methods.

Deep neural networks are vulnerable to adversarial perturbation. Recent researches indicate that misclassification may result from the distribution mismatch between adversarial examples and clean images. Inspired by a common consensus that the human neural representation is sparse and redundant, we propose an input-transformation-based defense method based on sparse representation to bridge the distribution mismatch. In our method, we first learn a global overcomplete dictionary from a set of image patches extracted from training images, and then, purify input images before feeding them into the neural networks, using the sparse representation technique with the learned dictionary. Compared with other attack-agnostic defenses, our method obtains comparable results on CIFAR-10 and ImageNet in various attack settings.

Polarimetric synthetic aperture radar (PolSAR) designed to obtain the polarimetric information of scenes is a crucial tool for microwave remote sensing. Recently, a complete polarimetric covariance difference matrix [CP] was built to detect ships of PolSAR image. Along this work, this paper extends its application to the spectrum domain. Briefly speaking, four sub-aperture images are first separated from the original PolSAR data. Then, four different power values corresponding to the [CP] matrices of these sub-aperture images are respectively calculated. At last, via multiplying these values together, a PolSAR ship detector named MPS (Multiplicative Polarimetric SPAN) is proposed. The experiment carried out on one real PolSAR image demonstrates that, compared to traditional power detectors SPAN and$SPAN_{CP,}$MPS holds a better ability to detect small ships.

Self-supervised monocular depth estimation from video sequences is promising for 3D environments perception. However, most existing methods use complicated depth networks to realize monocular depth estimation, which are often difficultly applied to resource-constrained devices. To solve this problem, in this letter, we propose a novel encoder-decoder-based lightweight depth network (LD-Net). Briefly speaking, the encoder is composed of six efficient downsampling units and the Atrous Spatial Pyramid Pooling (ASPP) module. The decoder consists of some novel upsampling units that adopt the sub-pixel convolutional layer (SP). Experiments tested on the KITTI dataset show that the proposed LD-Net can reach nearly 150 frames per second (FPS) on GPU, and remarkably decreases the model parameters while maintaining competitive accuracy compared with other state-of-the-art self-supervised monocular depth estimation methods.

As a fundamental and essential task in the field of remote sensing and photogrammetry, feature matching endeavors to establish reliable correspondences between two sets of feature points extracted from an image pair of the same scene. In this article, we propose an efficient and general algorithm, which is called local affine preservation (LAP) matching, for robust feature matching of remote sensing images. We start by constructing the putative point correspondences according to the similarity of well-designed feature descriptors and then focus on removing false matches from the putative set. The key idea of LAP is to search motion-consistent neighborhoods and maintain the local neighborhood topological structures of the true putative matches. To this end, we present a local geometric constraint, which exploits the property of affine invariance to measure the preservation degree of neighborhood topology, since the property is still held under both rigid and complex nonrigid transformations for a minimum topological unit. Moreover, in order to avoid the random distribution of outliers to destroy the neighborhood structure preservation of inliers, a neighbor mining strategy is introduced to search motion-consistent neighbors for each correspondence. We formulate the problem into an optimization model and derive a closed-form solution with linearithmic time complexity. Extensive experimental results on remote sensing images demonstrate that our LAP is able to achieve better performance over the current state-of-the-art approaches.

In the above article[1], the average TCR values inTable IIwere incorrectly presented. The corrected table is given here:

To more effectively detect small ships, in this article, a novel region-based polarimetric covariance difference matrix [RP] is put forward, which mainly consists of two stages. Briefly speaking, in the first stage, a new pixel representation way is proposed to depict the spatial characteristics of pixel, through which the difference information related to pixel’s local region is calculated as well. In the second stage, the global region difference information of pixel is computed. Finally, we construct [RP] via fusing these two different kinds of information together with a balance factor$c$. Meanwhile, considering that the backscattering energy of ships is useful for ship detection, a new intensity-driven polarimetric notch filter (ID-PNFRP) is also derived from [RP]. Three different datasets are adopted to evaluate the effectiveness of [RP] and ID-PNFRP. Experimental results show that: 1) compared with the polarimetric covariance matrix [$C$] and the polarimetric covariance difference matrix [$P$], [RP] is more suitable for ship detection and 2) compared with the original geometrical perturbation-polarimetric notch filter (GP-PNF) and the total power detector SPAN, the proposed method ID-PNFRPcan better detect small ships with greater figure of merit (FoM) and target-to-clutter ratio (TCR) values.

The self-supervised learning-based depth and visual odometry (VO) estimators trained on monocular videos without ground truth have drawn significant attention recently. Prior works use photometric consistency as supervision, which is fragile under complex realistic environments due to illumination variations. More importantly, it suffers from scale inconsistency in the depth and pose estimation results. In this paper, robust geometric losses are proposed to deal with this problem. Specifically, we first align the scales of two reconstructed depth maps estimated from the adjacent image frames, and then enforce forward-backward relative pose consistency to formulate scale-consistent geometric constraints. Finally, a novel training framework is constructed to implement the proposed losses. Extensive evaluations on KITTI and Make3D datasets demonstrate that, i) by incorporating the proposed constraints as supervision, the depth estimation model can achieve state-of-the-art (SOTA) performance among the self-supervised methods, and ii) it is effective to use the proposed training framework to obtain a uniform global scale VO model.

Remote sensing (RS) image scene classification is a challenging task due to its intraclass variety and the interclass similarity. Recently, many convolutional neural network (CNN)-based methods explore the network to handle this task. However, RS images usually have confusing background in addition to the relevant objects, and features only derived from the whole RS images cannot achieve satisfying results. To solve the problem, this letter proposed a method of utilizing the attention network to localize multiscale discriminative regions of the RS scene images and combining features learned from the localized regions by a classification network. Specifically, the classification network is composed of three subnetworks, which are trained by certain scaled regions separately. To learn more discriminative feature representations, feature fusion module is introduced to fuse the features of the three subnetworks in a more effective way. Experiments conducted on the AID and NWPU-RESISC45 data sets evaluate the effectiveness of the proposed method.

Aircraft detection from high resolution remote sensing image is a challenging task due to the lack of annotation information, large-scale image size, and sparse distribution of aircraft. Recently, some convolutional neural network(CNN) based methods explore the attention based weakly supervised way to localize the aircraft without manual annotation information. However, the detection results are not satisfied with high false detection ratio. In this paper, a method of utilizing weakly supervised attention model to localize the multi-scale aircrafts is presented, in which the attention model is carried out in a weakly supervised way. Compared with other CNN based method, the proposed attention model can obtain more accurate attention map and localize the aircrafts more precisely. The experimental results on two challenging datasets demonstrate that the proposed method achieves higher detection accuracy and lower false detection ratio than other methods.

Sea surface and ship have different backscattering mechanisms, in which surface scattering is predominant for sea surface in the low sea state case. Based on this fact, many ship detectors have been developed by suppressing the surface scattering resulted from sea surface. Actually, small ship may also have strong surface scattering sometimes. In such a case, the methods of avoiding using surface scattering features may easily miss the detection of small ships. To verify this point, in this paper, we first analyze the shortcomings of An's method which is based on surface scattering similarity and the power maximization synthesis detector (PMS), and then improve it for detecting small ships more effectively. In order to demonstrate the performance of the proposed method, AIRSAR L-Band Polarimetric SAR dataset is exploited. Comparing to other methods, the new method shows a better ship detection performance.

Full-polarimetric synthetic aperture radar (SAR) images have the ability to provide physical patterns of the earth observation, no more than geometric information. In order to learn physical patterns from non-full-polarimetric SAR images, a complex-valued CNN is leveraged to learn a model containing physical parameters. The parameters are learned from the original complex scattering matrix of full-polarimetric SAR images and they can be adopted to extract physical patterns from non-full-polarimetric SAR images. Cloude and Pottier's H-α division, as the annotation principle, is computed by way of coherence matrix. We perform experiments on (German Aerospace Center) DLR's full-polarimetric, airborne F-SAR data, demonstrating that extracting physical patterns from non-full-polarimetric images is feasible. The comparative results illustrate that: 1) The best physical categoric patterns can be extracted from HV and VH polarimetric images in general, while performance from HH and VV polarimetric images are limited; 2) Cross-polarimetric SAR images have greater ability for surface and volume scattering, while co-polarimetric ones are better for multiple scattering extraction.

In this paper, we proposed a complete polarimetric covariance difference matrix [CP]-based algorithm for ship detection in polarimetric synthetic aperture radar (PolSAR) imagery. To calculate [C P], we first developed a scheme to reflect the polarimetric scattering differences between ship pixel (SP) and its neighboring pixels (ISPs) and, then, dividedly accumulated the amplitude and phase differences between SP and ISPs. Compared to the polarimetric covariance difference matrix [P] developed in our earlier work, [C P] effectively overcomes the drawback of the lack of the phase information in [P]. To demonstrate the effectiveness of the proposed algorithm, we applied the [CP]-based ship detection algorithm to four PolSAR data sets, including one UAVSAR L-band data set with 21 ships, two AIRSAR L-band data sets with 11 and 22 ships, respectively, and one Radarsat-2 C-band data set with 8 ships. Experimental results show that: (1) the proposed algorithm can effectively detect ships with high target-to-clutter ratio (TCR) values and (2) [C P] has a better performance than the traditional polarimetric covariance matrix [C] and [P] on ship detection. To be more specific, the average TCR value of the proposed algorithm (23.86 dB) is 6.07 and 7.47 dB higher than PNFC(i.e., the geometrical perturbation-polarimetric notch filter) and RSC(i.e., the reflection symmetry method), respectively.

Single- and dual-polarimetric synthetic aperture radar (SAR) images provide very limited capabilities to interpret physical radar signatures. For generality and simplicity, we call single-polarimetric, dual-polarimetric, and fully polarimetric SAR (PolSAR) images flexible PolSAR images. In order to sufficiently extract physical scattering signatures from this kind of data and explore the potentials of different polarization modes on this task, this paper proposes a contrastive-regulated convolutional neural network (CNN) in the complex domain, attempting to learn a physically interpretable deep learning model directly from the original backscattered data. To achieve a better deep model containing physically interpretable parameters, the objective cost is compared to and selected from several commonly used loss functions in the complex form. The required ground-truth labels are generated automatically according to Cloude and Pottier's H-alpha division plane, which significantly reduces intensive labor cost and transfers this method to an unsupervised learning mechanism. The boundaries between different scattering signatures, however, sometimes show an erroneous separation. With the aim of aggregating intra-class instances and alienating inter-class instances, meanwhile, a complex-valued contrastive regularization term is computed mathematically and is added to the objective cost by a tradeoff factor. Moreover, data augmentation is applied to relieve the side effects caused by data imbalance. Finally, we performed experiments on German Aerospace Center's (DLR)'s L-band, high-resolution (HR), and airborne F-SAR data. Our results demonstrate the possibility of extracting physical scattering signatures from flexible PolSAR images. Physically interpretable potentials of SAR images with different polarization modes are analyzed, and we conclude with physical signature identification.

The goal of fine-grained image recognition is to recognize hundreds of sub-categories affiliating to the same basic-level category (e.g., bird species). It is a highly challenging task due to the large intra-class variance and small inter-class variance. Existing approaches deal with the subtle difference among object classes via learning and localizing discriminative parts. However, most of the part localization methods follow a step-to-step manner that first localizes larger parts and then generates smaller parts from the larger ones, which is not efficient. In this paper, we present a Multi-part Convolutional Attention Network (M-CAN), which simultaneously focuses on the discriminative image parts at multiple scales. In specific, a convolutional attention based part localization network is presented to localize multi-scale parts from different layers of the deep Convolutional Neural Networks (CNN). Importantly, our part localization network requires no part annotations but only the image labels, which avoids the heavy labor of complex part labeling. We conduct comprehensive experiments and the experimental results show that, our method outperforms the state-of-the-art approaches on three challenging fine-grained datasets, including CUB-Birds, Stanford-Dogs and Stanford-Cars.

Polarimetric Synthetic Aperture Radar data has been widely used for ship detection. In our earlier study, based on the differences between ship pixels and their surrounding background pixels, we designed a polarimetric covariance difference matrix (PCDM) to detect ships. Inadequately, the phase information of scattering differences is not included in PCD-M. Aiming at this deficiency, here, we present an improved PCDM matrix (IPCDM). Then an IPCDM-based ship detector is further proposed. To demonstrate the effectiveness of the method, two full polarimetric datasets are adopted. In comparing with other methods, we find that the result of our method is better.

In paper, we present a novel multi-part compact bilinear convolutional neural network (CNN) model, which consists of a bilinear CNN and two part-networks aiming to learn the global features and the finer local features simultaneously. The bilinear operation is simplified with recently proposed compact bilinear pooling method, and bilinear vectors are averagely pooled to keep more local spatial information. The proposed model is trained by using a histogram loss function in order to reduce the distribution overlap of positive pairs and negative pairs. Experiments show that, the combination of compact bilinear CNN and histogram loss can significantly improve the original models, and performs favorably compared to the state of the art.

Matching a specific person across non-overlapping cameras, known as person re-identification, is an important yet challenging task owing to the intra-class variations of the images from the same person in pose, illumination, and occlusion. Most existing body-parts based deep methods simply concatenate the features or scores obtained from spatial parts and ignore the complex spatial correlation between them. In this paper, we present a bi-directional Long Short-Term Memory (Bi-LSTM) architecture that can process the spatial parts sequentially, and enable the messages of different parts to go through in a bi-directional manner. Therefore, the spatial and contextual visual information can be modeled efficiently by the bi-directional connections and the internal gating function in LSTM. Furthermore, we propose a modified triplet loss to learn more discriminative features to distinguish positive pairs from negative pairs. Experiments on CUHK01 and CUHK03 datasets are carried out to demonstrate the effectiveness of the proposed method.

In this paper, a new algorithm for ship detection with Synthetic Aperture Radar (SAR) images is presented. We develop the proposed method by combing Principal Component Analysis (PCA) and the Geometrical Perturbation-Polarimetric Notch Filter (GP-PNF) method. In the first step, we replace the feature vector composed by the elements of the covariance matrix with more polarimetric features. Then, PCA is used to reduce the feature space. The new reduced feature vector is then used to detect ships by using the framework of the GP-PNF. In order to demonstrate the effectiveness of the proposed method, we exploited Sentinel-1 datasets. In this abstract, a dataset obtained in Gibraltar is considered. A comparison with other methods showed improvements in detection capability.

In this paper, a new algorithm for detecting ship and removing azimuth ambiguities is presented. The proposed method is developed by combing the third eigenvalue and the Geometrical Perturbation-Polarimetric Notch Filter (GP-PNF) methods. We firstly improve the GP-PNF feature vector with the third eigenvalue calculated by the eigenvalues-eigenvector decomposition method. Then, the new feature vector is used to remove azimuth ambiguities in the framework of the GP-PNF method. To demonstrate the effectiveness of the proposed method, we exploited one AIRSAR C-band dataset here. In comparing with the traditional GP-PNF method, we find our method has a better capability in removing azimuth ambiguities and detect real ships.

In this paper, we present a multiclass data classifier, denoted by optimal conformal transformation kernel (OCTK), based on learning a specific kernel model, the CTK, and utilize it in two types of image recognition tasks, namely, face recognition and object categorization. We show that the learned CTK can lead to a desirable spatial geometry change in mapping data from the input space to the feature space, so that the local spatial geometry of the heterogeneous regions is magnified to favor a more refined distinguishing, while that of the homogeneous regions is compressed to neglect or suppress the intraclass variations. This nature of the learned CTK is of great benefit in image recognition, since in image recognition we always have to face a challenge that the images to be classified are with a large intraclass diversity and interclass similarity. Experiments on face recognition and object categorization show that the proposed OCTK classifier achieves the best or second best recognition result compared with that of the state-of-the-art classifiers, no matter what kind of feature or feature representation is used. In computational efficiency, the OCTK classifier can perform significantly faster than the linear support vector machine classifier (linear LIBSVM) can.

Ship target detection using PolSAR data has been an active research area and many algorithms have been developed in recent years. In this paper, we present a new method based on the difference between the ship pixels and background pixels, using a model similar to LBP (Local Binary Pattern). After that, the polarimetric signature method, namely, the SPAN (total power) detector, is used to detect ships. We adopt one Radarsat-2 data set with four-look processing for experiment, which was obtained in the Strait of Gibraltar ocean area. In comparing with other methods, we find that the result of our method is better than other detectors.

In this paper, we present a novel locally active learning method for synthetic aperture radar (SAR) image classification. This method aims at reducing the labeling acquisition cost but at the same time retaining the classification accuracy. Based on active learning framework, the most informative samples are selected so that the required number of samples can be reduced greatly. At each iteration, we use local area as the candidates for choosing the training samples so that the ground survey is easy to take and thus the time and cost for labeling could be further reduced. The experiments on TerraSAR-X SAR images show that the proposed method obtains a promising performance for SAR image classification.

The Gaussian process (GP) approaches to classification synthesize Bayesian methods and kernel techniques, which are developed for the purpose of small sample analysis. Here we propose a GP model and investigate it for the facial expression recognition in the Japanese female facial expression dataset. By the strategy of leave-one-out cross validation, the accuracy of the GP classifiers reaches 93.43% without any feature selection/extraction. Even when tested on all expressions of any particular expressor, the GP classifier trained by the other samples outperforms some frequently used classifiers significantly. In order to survey the robustness of this novel method, the random trial of 10-fold cross validations is repeated many times to provide an overview of recognition rates. The experimental results demonstrate a promising performance of this application.

With microarray data being dramatically accumulated, integrating data from related studies represents a natural way to increase sample size so that more reliable statistical analysis may be performed. However, inherent variation among different microarray platforms makes the data integration not a trivial task. In this paper, we present a simple and effective integration scheme, called normalized linear transform (NLT), to combine data from different microarray platforms. The NLT scheme is compared with three other integration schemes for two tasks: classification analysis and gene marker selection. Our experiments demonstrate that the NLT scheme performs best in terms of classification accuracy under various classification settings, and leads to more biologically significant marker genes.

One important application of gene expression analysis is to classify tissue samples according to their gene expression levels. Gene expression data are typically characterized by high dimensionality and small sample size, which makes the classification task quite challenging. In this paper, we present a data-dependent kernel for microarray data classification. This kernel function is engineered so that the class separability of the training data is maximized. A bootstrapping-based resampling scheme is introduced to reduce the possible training bias. The effectiveness of this adaptive kernel for microarray data classification is illustrated with a k-Nearest Neighbor (KNN) classifier. Our experimental study shows that the data-dependent kernel leads to a significant improvement in the accuracy of KNN classifiers. Furthermore, this kernel-based KNN scheme has been demonstrated to be competitive to, if not better than, more sophisticated classifiers such as Support Vector Machines (SVMs) and the Uncorrelated Linear Discriminant Analysis (ULDA) for classifying gene expression data.

BACKGROUND: The most fundamental task using gene expression data in clinical oncology is to classify tissue samples according to their gene expression levels. Compared with traditional pattern classifications, gene expression-based data classification is typically characterized by high dimensionality and small sample size, which make the task quite challenging. RESULTS: In this paper, we present a modified K-nearest-neighbor (KNN) scheme, which is based on learning an adaptive distance metric in the data space, for cancer classification using microarray data. The distance metric, derived from the procedure of a data-dependent kernel optimization, can substantially increase the class separability of the data and, consequently, lead to a significant improvement in the performance of the KNN classifier. Intensive experiments show that the performance of the proposed kernel-based KNN scheme is competitive to those of some sophisticated classifiers such as support vector machines (SVMs) and the uncorrelated linear discriminant analysis (ULDA) in classifying the gene expression data. CONCLUSION: A novel distance metric is developed and incorporated into the KNN scheme for cancer classification. This metric can substantially increase the class separability of the data in the feature space and, hence, lead to a significant improvement in the performance of the KNN classifier.

In this paper, we present a method of kernel optimization by maximizing a measure of class separability in the empirical feature space, an Euclidean space in which the training data are embedded in such a way that the geometrical structure of the data in the feature space is preserved. Employing a data-dependent kernel, we derive an effective kernel optimization algorithm that maximizes the class separability of the data in the empirical feature space. It is shown that there exists a close relationship between the class separability measure introduced here and the alignment measure defined recently by Cristianini. Extensive simulations are carried out which show that the optimized kernel is more adaptive to the input data, and leads to a substantial, sometimes significant, improvement in the performance of various data classification algorithms.

Codebook initialization usually has a significant effect on the performance of vector quantization algorithms. This letter presents a new scheme of codebook initialization in which the competitive learning and code vector splitting are incorporated together to produce a good initial codebook. Based mainly on the geometrical measurements of the learning tracks of the code vectors, the competitive splitting mechanism shows an ability to appropriately allocate code vectors according to the spatial distribution of the input data and, therefore, tends to give a better initial codebook. Comparisons with other initialization techniques demonstrate the effectiveness of the new scheme.

This paper presents a new self-creating model of a neural network in which a branching mechanism is incorporated with competitive learning. Unlike other self-creating models, the proposed scheme, called branching competitive learning (BCL), adopts a special node-splitting criterion, which is based mainly on the geometrical measurements of the movement of the synaptic vectors in the weight space. Compared with other self-creating and nonself-creating competitive learning models, the BCL network is more efficient to capture the spatial distribution of the input data and, therefore, tends to give better clustering or quantization results. We demonstrate the ability of the BCL model to appropriately estimate the cluster number in a data distribution, show its adaptability to nonstationary data inputs and, moreover, present a scheme leading to a multiresolution data clustering. Extensive experiments on vector quantization of image compression are given to illustrate the effectiveness of the BCL algorithm.

This paper presents a new approach to deal with the translation- and scale-invariant problem of the discrete wavelet transform (DWT). Using a signal-dependent filter, whose impulse response is calculated by the first two moments of the original signal and a scale function of an orthonormal wavelet, we adaptively renormalized a signal. The renormalized signal is then decomposed by using the algorithm of the conventional DWT. The final wavelet transform coefficients, called adaptive wavelet invariant moments (AWIM), are proved to be both translation- and scale-invariant. Furthermore, as an application, we define a new textural feature in the framework of our adaptive wavelet decomposition, show its stability to shift and scaling, and demonstrate its efficiency for the task of scale-invariant texture identification.