Discriminative tensor decomposition with large margin

Tensor decompositions have many application areas in several domains where one key application is revealing relational structure between multiple dimensions simultaneously and thus enabling the compression of relational data. In this paper, we propose the Discriminative Tensor Decomposition with Large Margin (shortly, Large Margin Tensor Decomposition, LMTD), which can be viewed as a tensor-to-tensor projection operation. It is a novel method for calculating the mutual projection matrices that map the tensors into a lower dimensional space such that the nearest neighbor classification accuracy is improved. The LMTD aims finding the mutual discriminative projection matrices which minimize the misclassification rate by minimizing the Frobenius distance between the same class instances (in-class neighbors) and maximizing the distance between different class instances (impostor neighbors). Two versions of LMTD are proposed, where the nearest neighbor classification error is computed in the feature (latent) or input (observations) space. We evaluate the proposed models on real data sets and provide a comparison study with alternative decomposition methods in the literature in terms of their classification accuracy and mean average precision.     

模糊支持张量机图像分类算法及其应用

针对在小样本图像分类应用中,以向量空间作为输入的传统分类算法的不足,提出以张量理论为基础,结合模糊支持向量机思想的基于张量图像样本的模糊支持张量机分类器,利用张量表示图像样本,求解最优张量面。通过手写体数字图像样本实验仿真,验证该算法的性能,随后将其应用到羽绒菱节图像识别中进行对比,该算法较传统算法平均高出6.3%以上的识别率。实验证明该算法更适合应用于图像样本分类识别。     

Tensor scale: An analytic approach with efficient computation and applications

Scale is a widely used notion in computer vision and image understanding that evolved in the form of scale-space theory where the key idea is to represent and analyze an image at various resolutions. Recently, we introduced a notion of local morphometric scale referred to as “tensor scale” using an ellipsoidal model that yields a unified representation of structure size, orientation and anisotropy. In the previous work, tensor scale was described using a 2-D algorithmic approach and a precise analytic definition was missing. Also, the application of tensor scale in 3-D using the previous framework is not practical due to high computational complexity. In this paper, an analytic definition of tensor scale is formulated for n-dimensional (n-D) images that captures local structure size, orientation and anisotropy. Also, an efficient computational solution in 2- and 3-D using several novel differential geometric approaches is presented and the accuracy of results is experimentally examined. Also, a matrix representation of tensor scale is derived facilitating several operations including tensor field smoothing to capture larger contextual knowledge. Finally, the applications of tensor scale in image filtering and n-linear interpolation are presented and the performance of their results is examined in comparison with respective state-of-art methods. Specifically, the performance of tensor scale based image filtering is compared with gradient and Weickert’s structure tensor based diffusive filtering algorithms. Also, the performance of tensor scale based n-linear interpolation is evaluated in comparison with standard n-linear and windowed-sinc interpolation methods.     

基于张量神经网络的音频多语义分类方法

音频特征向量已广泛应用于音频分类的研究,该表示形式虽能有效体现音频的固有特性,但无法表示音频信息多语义特性及各语义间的相关性。提出了基于张量统一内容定位（TUCL）的音频语义表征方式,将音频语义描述表示为三阶张量,并构建多语义张量空间。在此空间中,张量语义离散度（TSD）能有效聚集具有相同语义的音频资源,通过计算各音频资源的TSD来完成对音频资源的分类,并构建了RBF张量神经网络（RBFTNN）来自适应学习分类模型。实验结果表明,在多语义分类的情况下,TSD算法的分类性能明显优于当前典型的高斯混合模型（GMM）算法;通过与支持向量机（SVM）学习模型相比可知,基于TSD的RBFTNN模型分类学习的准确率明显优于基于TSD的SVM模型。     

Classification of complex environments using pixel level fusion of satellite data

The present study reports classification and analysis of composite land features using fusion images obtained by fusing two original hyperspectral and multispectral datasets. The high spatial-spectral resolution, multi-instrument and multi-period satellite images were used for fusion. Three pixel level fusion based techniques, Color Normalized Spectral Sharpening (CNSS), Principal Component Spectral Sharpening Transform (PCSST) and Gram-Schmidt Transform (GST), were implemented on the datasets. Performance evaluations of three fusion algorithms were done using classification results. The Support Vector Machine (SVM) and Gaussian Maximum Likelihood Classification (MLC) were used for classification using five types of images, viz. hyperspectral, multispectral and three fused images. Number of classes considered was eight. Sufficient number of ground field data for each class has also been acquired which was needed for supervise based classification. The accuracy was improved from 74.44 to 97.65% when the fused images were considered with SVM classifier. Similarly, the results were improved from 69.25 to 94.61% with original and fused data using MLC classifier. The fusion image technique was found to be superior to the single original image and the SVM is better than the MLC method.

     

Thinning algorithms based on quadtree and octree representations

Thinning is a critical pre-processing step to obtain skeletons for pattern analysis. Quadtree and octree are hierarchical data representations in image processing and computer graphics. In this paper, we present new 2-D area-based and 3-D surface-based thinning algorithms for directly converting quadtree and octree representations to skeletons. The computational complexity of our thinning algorithm for a 2-D or a 3-D image with each length N is respectively O(N²) or O(N³), which is more efficient than the existing algorithms of O(N³) or O(N⁴). Furthermore, our thinning algorithms can lessen boundary noise spurs and are suited for parallel implementation.     

总间隔v-模糊支持向量机研究

为获得更好的分类性能,对传统模糊支持向量机(FSVM)进行扩展,提出一种总间隔v-模糊支持向量机(TM-v-FSVM)。通过使用差异成本及引入总间隔和模糊隶属度,同时解决不平衡训练样本问题和传统软间隔分类机的过拟合问题,从而提升学习机的泛化能力。采用UCI实际数据集进行模式分类实验,结果表明TM-v-FSVM具有稳定的分类性能。     

Constrained ALS-based tensor blind receivers for multi-user MIMO systems

Tensor factorizations has shown to be an efficient approach for symbols and/or channel estimation in multi-input multi-output (MIMO) systems, where the factor matrices of tensor that correspond to symbols, channel, code/diversity of signals, are often estimated by using alternating least squares (ALS) algorithm. Although the performance of tensor approaches strongly depend on the initializations of the factor matrices. However, due to the absence of a priori on channels, these initializations are done randomly in traditional ALS algorithm. This generally implies a slow convergence. Further, ALS does not take into account the potential orthogonal structure in the factor matrices, which can be exploited to improve the accuracy of factor matrices recovery. To address these insures, this paper proposes constrained ALS tensor blind receivers for multi-user MIMO systems. We show that the multi-user MIMO signals can be expressed as a third-order tensor model, where the matrices of users symbols, direction-of-arrival (DOA) and delay can be viewed as three factor matrices of the tensor model. Two constrained ALS blind algorithms that take into account the potential orthogonal and Vandermonde structures in the factor matrices, are proposed to learn the tensor model, where the users symbols, DOA and delay are joint estimated as three factor matrices. Besides provide the estimations for the factor matrices, the orthogonal and Vandermonde structures also give a better uniqueness results for the use of tensor model. Interestingly, these structures are the nature properties of the factor matrices in our system. This results in an efficient blind approach that has better performance and lower complexity compare with the traditional ALS.     

一种融合小波变化和张量PCA的人耳识别的算法*

小波变换具有良好的时频分析特性,而且具有较快的算法特点,同时还能起到降维的作用。张量主成分分析方法用于人耳识别能获得比PCA方法更高的识别率。综合利用这两个算法的优点,提出了一种新的人耳识别方法,对人耳图像先采用小波变换做预处理得到4个子带图像,然后对每个子带图像用张量PCA进行特征提取,最后利用最近邻的方法实现人耳图像识别。实验结果表明,利用此方法与只用主成分分析识别相比,提高了识别率。