Degree Of Relative Density Research Articles

Effect of aspect ratio on the compaction characteristics and micromorphology of copper powders by magnetic pulse compaction

Magnetic pulse compaction (MPC) technology has the advantages of near net shape, high efficiency and density. In this paper, the effect of aspect ratio on the deformation characteristics of copper powders compacted by MPC technology was studied. Specifically, the compaction velocity, volume strain, micromorphology and micro hardness of compacts at various aspect ratios were obtained. Results showed that the compaction velocity and volume strain increased and then decreased with the increase of aspect ratio. The maximum compaction velocity reached 10.28 m/s at aspect ratio of 1.2. At the same compaction moment, the volume strain was decreased as the aspect ratio increased. Then the relationship between compaction pressure and volume strain was revealed. The aspect ratio range of the optimal compaction effect was 0.6–1.0, and the fluctuation degree of relative density was only 1.03%. The aspect ratio had less effect on the micromorphology distribution in the axial direction of the compacts. The micro hardness value of the upper surface was higher than that of the lower surface, and the edge position was greater than the center position.

Incorporating neighbors’ distribution knowledge into support vector machines

The prior knowledge plays an important role in increasing the performance of the support vector machines (SVMs). Traditional SVMs do not consider any prior knowledge of the training set. In this paper, the neighbors’ distribution knowledge is incorporated into SVMs. The neighbors’ distribution can be measured by the sum of the cosine value of the angle, which is between the difference between the sample and its corresponding neighbor, and the difference between the sample and the mean of corresponding neighbors. The neighbors’ distribution knowledge reflects the sample’s importance in the training processing. It can be explained as the relative margin or instance weight. In this paper, the neighbors’ distribution knowledge is regarded as the relative margin and incorporated into the framework of density-induced margin support vector machines whose relative margin is measured by relative density degree. The results of the experiments, performed on both artificial synthetic datasets and real-world benchmark datasets, demonstrate that SVMs performs better after incorporating neighbors’ distribution. Furthermore, experimental results also show that neighbors’ distribution are more suitable than relative density degree to represent the relative margin.

Relative density degree induced boundary detection for one-class SVM

Unlike two-class (multi-class) support vector machines, massive targets and few outliers are available in one-class support vector machine. The strategies to select useful data for two-class (multi-class) support vector machines are not suitable for one-class support vector machine. In this paper, relative density degree is introduced to select useful data for one-class support vector machine. These data would become support vectors after training and locate near the boundary of the data distribution. The relative density degree of the data near the boundary of the training set is smaller than that of the data in the interior of the training set. Thus, the data near the boundary of training set can be preserved and the others can be disposed through relative density degree. Experimental results show that merely preserving about 20 % of the training set, the performance will not decrease and be better than previous related method. But the model is simpler and the training process is faster.

Weighted least squares projection twin support vector machines with local information

Recently proposed least squares projection twin support vector machine (LSPTSVM), as a variant of projection twin support vector machine (PTSVM), attempts to further enhance the performance of PTSVM, whose solution follows from solving two sets of linear equations whereas PTSVM needs to solve two quadratic programming problems along with two sets of linear equations. Unfortunately, LSPTSVM fails to exploit the underlying correlation or similarity information between any pair of data points with the same labels that may be important for classification performance as much as possible. To mitigate the above deficiency, in this paper, we propose a novel binary classifier based on LSPTSVM, called weighted least squares projection support vector machine with local information (LIWLSPTSVM). Compared to LSPTSVM, LIWLSPTSVM mines as much underlying similarity information within samples as possible by computing the relative density degree for each data point according to the weights of the intra-class graph of training set. Because of measuring the importance of samples in the same class by density weighting method, weighted mean, instead of standard mean in LSPTSVM, is used as the class mean. Moreover, LIWLSPTSVM successfully inherits the merit of the LSPTSVM, and it has a special case of LSPTSVM when the relative density degree of each point is degenerated to one. The experimental results on toy as well as publicly available datasets confirm the effectiveness of our method.

Improving fuzzy C‐means clustering algorithm based on a density‐induced distance measure

The authors report an improved fuzzy C-means algorithm in comparison with the conventional one by employing a density-induced distance metric based on a novel calculation method of relative density degree. By using various synthetic and real data sets, the clustering performance of the proposed method is systematically studied and compared with that of the conventional one. The obtained results support the conclusion that this novel method does not only inherit good characteristics of the traditional one, but also possesses improved partitions.

Bi-density twin support vector machines for pattern recognition

In this paper we present a classifier called bi-density twin support vector machines (BDTWSVMs) for data classification. In the training stage, BDTWSVMs first compute the relative density degrees for all training points using the intra-class graph whose weights are determined by a local scaling heuristic strategy, then optimize a pair of nonparallel hyperplanes through two smaller sized support vector machine (SVM)-typed problems. In the prediction stage, BDTWSVMs assign to the class label depending on the kernel density degree-based distances from each test point to the two hyperplanes. BDTWSVMs not only inherit good properties from twin support vector machines (TWSVMs) but also give good description for data points. The experimental results on toy as well as publicly available datasets indicate that BDTWSVMs compare favorably with classical SVMs and TWSVMs in terms of generalization.

Density-induced margin support vector machines

This paper proposes a new classifier called density-induced margin support vector machines (DMSVMs). DMSVMs belong to a family of SVM-like classifiers. Thus, DMSVMs inherit good properties from support vector machines (SVMs), e.g., unique and global solution, and sparse representation for the decision function. For a given data set, DMSVMs require to extract relative density degrees for all training data points. These density degrees can be taken as relative margins of corresponding training data points. Moreover, we propose a method for estimating relative density degrees by using the K nearest neighbor method. We also show the upper bound on the leave-out-one error of DMSVMs for a binary classification problem and prove it. Promising results are obtained on toy as well as real-world data sets.

Density-Induced Support Vector Data Description

The purpose of data description is to give a compact description of the target data that represents most of its characteristics. In a support vector data description (SVDD), the compact description of target data is given in a hyperspherical model, which is determined by a small portion of data called support vectors. Despite the usefulness of the conventional SVDD, however, it may not identify the optimal solution of target description especially when the support vectors do not have the overall characteristics of the target data. To address the issue in SVDD methodology, we propose a new SVDD by introducing new distance measurements based on the notion of a relative density degree for each data point in order to reflect the distribution of a given data set. Moreover, for a real application, we extend the proposed method for the protein localization prediction problem which is a multiclass and multilabel problem. Experiments with various real data sets show promising results.