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In order to handle semi-supervised clustering scenarios where only part of the pairwise constraint information is available in the target dataset, on the basis of nonnegative matrix factorization (NMF) architecture, this paper proposes a nonnegative matrix factorization-based clustering algorithm using joint regularization of manifold learning and pairwise constraints (NMF-JRMLPC) by learning given pairwise constraint knowledge and using manifold regularization theory. On the one hand, graph Laplacian is introduced to depict the manifold structure information contained in a large number of unlabeled samples, and on the other hand, the must-link or cannot-link pair-constraint rules among known samples are integrated into the target optimization design, which greatly improves the clustering performance of the algorithm. In addition, the [l2,1] norm based loss function design also helps to optimize the robustness of NMF-JRMLPC. Experimental results on eight real datasets confirm the validity of the proposed method.

Historically,there have been many restorations and explorations of the structure of the Houfeng seismograph,but there are unreasonable points. This has caused the public and some scholars to question its authenticity,so a reasonable principle model needs to be proposed. We found a stable inverted pendulum structure that does not require the use of springs. It have a low natural frequency while ensuring the size and manufacturing process in line with historical facts,and can be used to develop the Houfeng seismograph that meets the requirements of the later Han. And we simulated the structure in matlab. The result proves that the structure can respond to the seismic wave and issue a warning. It is a reasonable model of the Houfeng seismograph.