We present a study of a kernel-based two-sample test statistic related to the Maximum Mean Discrepancy (MMD) in the manifold data setting, assuming that high-dimensional observations are close to a low-dimensional manifold. We characterize the test level and power in relation to the kernel ...
To run these tests extract the testing package in the same folder as your embree installation. e.g.: tar -xzf embree-4.3.2-testing.zip -C /path/to/installed/embree The tests are extracted into a new folder inside you embree installation and can be run with: cd /path/to/installed/...
Although it requires simple computations, provides good performance on linear classification tasks and offers a suitable environment for active learning st
Synthetic Data. To verify the proposed method and analyze its performance, we generate two sets of syn- thetic data, one linearly separable and the other one not separable linearly (hence we believe it would be best classified nonlinearly). For both cases, the data comprise two classes of...
Two kernel based methods named diffusion maps and the kernel two-sample test are utilized. Diffusion maps generates a low-dimensional representation of the data, in which important characteristic factors are identified. The kernel two-sample test is a statistical test for comparing whether high-...
In contrast, the discriminator is trained to identify the data manifold, also known as an explicit energy-based model. To demonstrate the effectiveness of our approach, we undertook experiments on two-dimensional toy datasets. Our results highlight that our generator adeptly captures the accurate ...
In contrast, the discriminator is trained to identify the data manifold, also known as an explicit energy-based model. To demonstrate the effectiveness of our approach, we undertook experiments on two-dimensional toy datasets. Our results highlight that our generator adeptly captures th...
The purpose of this section is to provide an introduction to KNPE and Standard_SBC, which will be utilized in Section 4 for the diagnosis of rotating machinery faults. 2.1. Neighborhood Preserving Embedding In order to maintain the local manifold structure of the given data, neighborhood preservin...
The two final steps of the methodology, i.e., the training and the test of the KPCA monitoring model, tend to be similar and it is therefore useful to comment on them together. The expression “training” refers to the part in which the model is trained using data extrapolated from the...