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Infrared moving target tracking plays a fundamental role in many burgeoning research areas of Smart City. Challenges in developing a suitable tracker for infrared images are particularly caused by pose variation, occlusion, and noise. In order to overcome these adverse interferences, a total variation regularization term-based low-rank and sparse matrix representation (TV-LRSMR) model is designed in order to exploit a robust infrared moving target tracker in this paper. First of all, the observation matrix that is derived from the infrared sequence is decomposed into a low-rank target matrix and a sparse occlusion matrix. For the purpose of preventing the noise pixel from being separated into the occlusion term, a total variation regularization term is proposed to further constrain the occlusion matrix. Then an alternating algorithm combing principal component analysis and accelerated proximal gradient methods is employed to separately optimize the two matrices. For long-term tracking, the presented algorithm is implemented using a Bayesien state inference under the particle filtering framework along with a dynamic model update mechanism. Both qualitative and quantitative experiments that were examined on real infrared video sequences verify that our algorithm outperforms other state-of-the-art methods in terms of precision rate and success rate.

Background There are two significant problems associated with predicting protein-protein interactions using the sequences of amino acids. The first problem is representing each sequence as a feature vector, and the second is designing a model that can identify the protein interactions. Thus, effective feature extraction methods can lead to improved model performance. In this study, we used two types of feature extraction methods—global encoding and pseudo-substitution matrix representation (PseudoSMR)—to represent the sequences of amino acids in human proteins and Human Immunodeficiency Virus type 1 (HIV-1) to address the classification problem of predicting protein-protein interactions. We also compared principal component analysis (PCA) with independent principal component analysis (IPCA) as methods for transforming Rotation Forest. Results The results show that using global encoding and PseudoSMR as a feature extraction method successfully represents the amino acid sequence for the Rotation Forest classifier with PCA or with IPCA. This can be seen from the comparison of the results of evaluation metrics, which were >73 % across the six different parameters. The accuracy of both methods was >74 % . The results for the other model performance criteria, such as sensitivity, specificity, precision, and F1-score, were all >73 % . The data used in this study can be accessed using the following link: https://www.dsc.ui.ac.id/research/amino-acid-pred/ . Conclusions Both global encoding and PseudoSMR can successfully represent the sequences of amino acids. Rotation Forest (PCA) performed better than Rotation Forest (IPCA) in terms of predicting protein-protein interactions between HIV-1 and human proteins. Both the Rotation Forest (PCA) classifier and the Rotation Forest IPCA classifier performed better than other classifiers, such as Gradient Boosting, K-Nearest Neighbor, Logistic Regression, Random Forest, and Support Vector Machine (SVM). Rotation Forest (PCA) and Rotation Forest (IPCA) have accuracy, sensitivity, specificity, precision, and F1-score values >70 % while the other classifiers have values <70 % .

We compute the generic realization of the Lie algebra (3) over both the real and complex fields simultaneously, and present explicit realizations of rank two and rank three. The generic realization is emphasized because other realizations of (3) can be obtained as its projections. Realizations in spaces of two and three variables are constructed and proposed for use in subsequent investigations aimed at identifying invariant Newton-type systems. Finally, we construct the realization that corresponds to the lowest-dimensional matrix representation of (3).

In Text Classification, modern neural networks have achieved great performance, but simultaneously, it is sensitive to adversarial examples. Existing studies usually use synonym replacement or token insertion strategies to generate adversarial examples. These strategies focus on obtaining semantically similar adversarial examples, but they ignore the richness of generating adversarial examples. To expand the richness of adversarial samples. Here, we propose a simple Rule-based Adversarial sample Generator (RAG) to generate adversarial samples by controlling the size of the perturbation added to the sentence matrix representation. Concretely, we introduce two methods to control the size of the added perturbation, i) Control the number of word replacements in sentences (RAG(R)); ii) Control the size of the offset value added to the sentence matrix representation (RAG(A)). Based on RAG, we will obtain numerous adversarial samples to make the model more robust to adversarial noise, and thereby improving the model’s generalization ability. Compared with the BERT and BiLSTM model baseline, experiments show that our method reduces the error rate by an average of 18% on four standard training datasets. Especially in low-training data scenarios, the overall average accuracy is increased by 12%. Extensive experimental results demonstrate that our method not only achieves excellent classification performance on the standard training datasets, but it still gets prominent performance on few-shot text classification.

To date, parallel simulation algorithms for spiking neural P (SNP) systems are based on a matrix representation. This way, the simulation is implemented with linear algebra operations, which can be easily parallelized on high performance computing platforms such as GPUs. Although it has been convenient for the first generation of GPU-based simulators, such as CuSNP, there are some bottlenecks to sort out. For example, the proposed matrix representations of SNP systems lead to very sparse matrices, where the majority of values are zero. It is known that sparse matrices can compromise the performance of algorithms since they involve a waste of memory and time. This problem has been extensively studied in the literature of parallel computing. In this paper, we analyze some of these ideas and apply them to represent some variants of SNP systems. We also provide a new simulation algorithm based on a novel compressed representation for sparse matrices. We also conclude which SNP system variant better suits our new compressed matrix representation.

Supertree methods merge a set of overlapping phylogenetic trees into a supertree containing all taxa of the input trees. The challenge in supertree reconstruction is the way of dealing with conflicting information in the input trees. Many different algorithms for different objective functions have been suggested to resolve these conflicts. In particular, there exist methods based on encoding the source trees in a matrix, where the supertree is constructed applying a local search heuristic to optimize the respective objective function. We present a novel heuristic supertree algorithm called Bad Clade Deletion (BCD) supertrees. It uses minimum cuts to delete a locally minimal number of columns from such a matrix representation so that it is compatible. This is the complement problem to Matrix Representation with Compatibility (Maximum Split Fit). Our algorithm has guaranteed polynomial worst-case running time and performs swiftly in practice. Different from local search heuristics, it guarantees to return the directed perfect phylogeny for the input matrix, corresponding to the parent tree of the input trees, if one exists. Comparing supertrees to model trees for simulated data, BCD shows a better accuracy (F1 score) than the state-of-the-art algorithms SuperFine (up to 3%) and Matrix Representation with Parsimony (up to 7%); at the same time, BCD is up to 7 times faster than SuperFine, and up to 600 times faster than Matrix Representation with Parsimony. Finally, using the BCD supertree as a starting tree for a combined Maximum Likelihood analysis using RAxML, we reach significantly improved accuracy (1% higher F1 score) and running time (1.7-fold speedup).

In this article, a recursive formula is obtained by using the simplified substitution of the 3-parameter generalized quaternion left matrix representation. Based on it, the direct formula of nth power calculation including real quaternions, split quaternions, split semi-quaternions, and 1/4-quaternions, is derived, which is more universal to solve the problem of inconvenient calculation with the De Moivres formula when the power n is large. Finally, the correctness of the obtained results is verified by two examples.

We study the Wasserstein metric to measure distances between molecules represented by the atom index dependent adjacency 'Coulomb' matrix, used in kernel ridge regression based supervised learning. Resulting machine learning models of quantum properties, a.k.a. quantum machine learning models exhibit improved training efficiency and result in smoother predictions of energies related to molecular distortions. We first illustrate smoothness for the continuous extraction of an atom from some organic molecule. Learning curves, quantifying the decay of the atomization energy's prediction error as a function of training set size, have been obtained for tens of thousands of organic molecules drawn from the QM9 data set. In comparison to conventionally used metrics (L1 and L2 norm), our numerical results indicate systematic improvement in terms of learning curve off-set for random as well as sorted (by norms of row) atom indexing in Coulomb matrices. Our findings suggest that this metric corresponds to a favorable similarity measure which introduces index-invariance in any kernel based model relying on adjacency matrix representations.

Non-isomorphic direct decompositions of torsion-free Abelian groups are reflected in their endomorphism ring decompositions which admit matrix representations. The set of possible direct decompositions of a special kind matrix rings into direct sums of one-sided indecomposable ideals is described. This leads to the combinatorial constructions of isomorphisms between non-commutative differently decomposable ring structures.

With the development of remote sensing image applications, remote sensing imagery is an important technology to make a dynamic detection for changes of lands or coastal zones. Though high resolution remote sensing imagery provides very good performance and large information for the spatial structure variation, the limitation of its spatial structure makes change detection difficult. In this paper, we propose two change detection methods for multi-temporal remote sensing images which are based on low-rank sparse decomposition and based on low-rank matrix representation. An observation matrix is constructed by ordering each band of remote sensing images into a vector. We utilize bilateral random projection method to make low rank decomposition to get a sparse matrix. We then obtain the change map by using nearest neighbor to cluster the change parts from the sparse matrix. On the other hand, by dividing the difference set of multi-temporal remote sensing images into non-overlapping squares with equal size and tiling these squares, an observation matrix is built up. We make up a feature space matrix by low rank matrix representation to build a sparse representation model, and combine nearest neighbor method to make change detection for multi-temporal remote sensing dataset. This change detection method is addressed by iterating between kernel norm minimization and sparsity minimization. The experimental results show that our proposed methods perform better in detecting changes than the other change detection methods.