SAMN: A Sample Attention Memory Network Combining SVM and NN in One Architecture

Support vector machine (SVM) and neural networks (NN) have strong complementarity. SVM focuses on the inner operation among samples while NN focuses on the operation among the features within samples. Thus, it is promising and attractive to combine SVM and NN, as it may provide a more powerful function than SVM or NN alone. However, current work on combining them lacks true integration. To address this, we propose a sample attention memory network (SAMN) that effectively combines SVM and NN by incorporating sample attention module, class prototypes, and memory block to NN. SVM can be viewed as a sample attention machine. It allows us to add a sample attention module to NN to implement the main function of SVM. Class prototypes are representatives of all classes, which can be viewed as alternatives to support vectors. The memory block is used for the storage and update of class prototypes. Class prototypes and memory block effectively reduce the computational cost of sample attention and make SAMN suitable for multi-classification tasks. Extensive experiments show that SAMN achieves better classification performance than single SVM or single NN with similar parameter sizes, as well as the previous best model for combining SVM and NN. The sample attention mechanism is a flexible module that can be easily deepened and incorporated into neural networks that require it.

MaxMin-L2-SVC-NCH: A Novel Approach for Support Vector Classifier Training and Parameter Selection

The selection of Gaussian kernel parameters plays an important role in the applications of support vector classification (SVC). A commonly used method is the k-fold cross validation with grid search (CV), which is extremely time-consuming because it needs to train a large number of SVC models. In this paper, a new approach is proposed to train SVC and optimize the selection of Gaussian kernel parameters. We first formulate the training and parameter selection of SVC as a minimax optimization problem named as MaxMin-L2-SVC-NCH, in which the minimization problem is an optimization problem of finding the closest points between two normal convex hulls (L2-SVC-NCH) while the maximization problem is an optimization problem of finding the optimal Gaussian kernel parameters. A lower time complexity can be expected in MaxMin-L2-SVC-NCH because CV is not needed. We then propose a projected gradient algorithm (PGA) for training L2-SVC-NCH. The famous sequential minimal optimization (SMO) algorithm is a special case of the PGA. Thus, the PGA can provide more flexibility than the SMO. Furthermore, the solution of the maximization problem is done by a gradient ascent algorithm with dynamic learning rate. The comparative experiments between MaxMin-L2-SVC-NCH and the previous best approaches on public datasets show that MaxMin-L2-SVC-NCH greatly reduces the number of models to be trained while maintaining competitive test accuracy. These findings indicate that MaxMin-L2-SVC-NCH is a better choice for SVC tasks.

MaxMin-L2-SVC-NCH: A New Method to Train Support Vector Classifier with the Selection of Model's Parameters

The selection of model's parameters plays an important role in the application of support vector classification (SVC). The commonly used method of selecting model's parameters is the k-fold cross validation with grid search (CV). It is extremely time-consuming because it needs to train a large number of SVC models. In this paper, a new method is proposed to train SVC with the selection of model's parameters. Firstly, training SVC with the selection of model's parameters is modeled as a minimax optimization problem (MaxMin-L2-SVC-NCH), in which the minimization problem is an optimization problem of finding the closest points between two normal convex hulls (L2-SVC-NCH) while the maximization problem is an optimization problem of finding the optimal model's parameters. A lower time complexity can be expected in MaxMin-L2-SVC-NCH because CV is abandoned. A gradient-based algorithm is then proposed to solve MaxMin-L2-SVC-NCH, in which L2-SVC-NCH is solved by a projected gradient algorithm (PGA) while the maximization problem is solved by a gradient ascent algorithm with dynamic learning rate. To demonstrate the advantages of the PGA in solving L2-SVC-NCH, we carry out a comparison of the PGA and the famous sequential minimal optimization (SMO) algorithm after a SMO algorithm and some KKT conditions for L2-SVC-NCH are provided. It is revealed that the SMO algorithm is a special case of the PGA. Thus, the PGA can provide more flexibility. The comparative experiments between MaxMin-L2-SVC-NCH and the classical parameter selection models on public datasets show that MaxMin-L2-SVC-NCH greatly reduces the number of models to be trained and the test accuracy is not lost to the classical models. It indicates that MaxMin-L2-SVC-NCH performs better than the other models. We strongly recommend MaxMin-L2-SVC-NCH as a preferred model for SVC task.