In the field of 3D digitization of real objects using modern scanning devices, dense point clouds can be obtained. This data point can have redundancy. To solve this problem, we present a new simplification method based on clustering and Shannon's entropy. This approach optimizes the number of 3D point clouds by keeping the original point cloud characteristics. To show the robustness of the technique, we have applied it on different point cloud and making comparisons with other methods. It can be said, according to the obtained results, that our method is effective.
KEYWORDS: Principal component analysis, Nonlinear dynamics, Statistical modeling, Performance modeling, Dimension reduction, Data processing, Process modeling, Feature selection, Estimation theory
In this paper, we introduce a new technique for nonlinear monitoring process relying on kernel entropy principal component analysis (KEPCA). KEPCA can transform input data into high-dimensional feature space using the nonlinear kernel function and determine the number of principal components (PCs) based on the computation of the entropy. The retained PCs are the ones that explain the maximum entropy of data in the feature space. Then, we introduce a new approach to calculate the upper control limits (UCLs) for the squared prediction error (SPE) and the T2 Hotelling in the feature space based on the density estimation via the k-nearest neighbors (kNN) estimator. The abovementioned approaches were applied to fault detection for the benchmark Tennessee Eastman process (TE). Results were robust and supply better performance than KPCA.
In this paper, we propose a kernel version of the credal classification rule (CCR) to perform the classification in a feature space of high dimension. Kernels based approaches have become popular for several years to solve supervised or unsupervised learning problems. In this paper, our method is extended to the CCR. It is realized by replacing the inner product with an appropriate positive definite function, and the corresponding algorithms are called kernel Credal Classification Rule (KCCR). The approach is applied to the classification of the generated and real data to evaluate and compare the performance of the KCCR method with other classification methods.
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