conditionally positive definite
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2021 ◽  
Vol 13 (15) ◽  
pp. 8321
Author(s):  
Dinh Hoa Nguyen

The occupancy of residential energy consumers is an important subject to be studied to account for the changes on the load curve shape caused by paradigm shifts to consumer-centric energy markets or by significant energy demand variations due to pandemics, such as COVID-19. For non-intrusive occupancy analysis, multiple types of sensors can be installed to collect data based on which the consumer occupancy can be learned. However, the overall system cost will be increased as a result. Therefore, this research proposes a cheap and lightweight machine learning approach to predict the energy consumer occupancy based solely on their electricity consumption data. The proposed approach employs a support vector machine (SVM), in which different kernels are used and compared, including positive semi-definite and conditionally positive definite kernels. Efficiency of the proposed approach is depicted by different performance indexes calculated on simulation results with a realistic, publicly available dataset. Among SVM models with different kernels, those with Gaussian (rbf) and sigmoid kernels have the highest performance indexes, hence they may be most suitable to be used for residential energy consumer occupancy prediction.


Author(s):  
Geewook Kim ◽  
Akifumi Okuno ◽  
Kazuki Fukui ◽  
Hidetoshi Shimodaira

We propose weighted inner product similarity (WIPS) for neural network-based graph embedding. In addition to the parameters of neural networks, we optimize the weights of the inner product by allowing positive and negative values. Despite its simplicity, WIPS can approximate arbitrary general similarities including positive definite, conditionally positive definite, and indefinite kernels. WIPS is free from similarity model selection, since it can learn any similarity models such as cosine similarity, negative Poincaré distance and negative Wasserstein distance. Our experiments show that the proposed method can learn high-quality distributed representations of nodes from real datasets, leading to an accurate approximation of similarities as well as high performance in inductive tasks.


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