Knowledge graph completion (KGC) methods aim to predict missing links by learning from existing facts in a knowledge graph. Different from KGC, Temporal Knowledge Graph Completion (TKGC) further incorporates the time validity of facts (tagged timestamps) during the learning and inference to improve the completion accuracy. Many TKGC methods achieve this by projecting the static entity representations (time-invariant) of KGC embedding methods to time-dependent representations, which vary across timestamps. However, when measuring a fact, these TKGC methods only consider its subject/object entity representations corresponding to the tagged timestamp, but ignore their historical contexts that normally carry essential supportive information. With this observation, we propose a novel context aggregation (ContxE) method to include historical contexts of subject/object entities for TKGC. To achieve that, we propose a linear-rotary time embedding to obtain time-dependent entity representations that can preserve temporal relationships, and a relation-based attention to aggregate historical context for the score measurement. Comprehensive experiments on three temporal knowledge graph datasets show that the proposed ContxE achieves improved knowledge graph completion results compared to strong counterpart methods.

The success of advanced Background Subtraction (BGS) algorithms for dynamic backgrounds is mostly in land scenes such as those in CDNet benchmarks; few handle underwater scenes, since existing underwater video datasets are either in low resolution or with only static backgrounds. Consequently, the lack of reliable BGS support makes supervised Moving-Objects Segmentation (MOS) algorithms much harder to adapt to unknown underwater scenes because of the diversities of the aquatic environments. For example, those trained by the latest underwater image dataset, SUIM, are ineffective in the underwater videos of our experiments.The underwater waving objects (e.g., plants) often render existing BGS algorithms inaccurate due to three types of errors: (a) incompletely identified MOs (Moving Objects), (b) missing MOs, and (c) falsely identified MOs. In this paper, we propose a novel Clustering-Based Multi-State Background Representation (CBMSBR) model to learn and represent the repeatable patterns of waving movements in k background states (i.e., color ranges) per pixel, and thus accurately subtract the background waving objects to reduce these errors. In addition, we further develop a CBMSBR+ model to remove the more challenging background objects in unusually large magnitudes of wavings. Both models come from a basic observation: the video pixels in the waving zones repeatedly switch among multiple background states; e.g., a pixel switches among water state, plant 1 state, and plant 2 state. To test our proposed models, we create experiments using three types of challenging scenarios that each often covers at least two error types, i.e., the scattered MOs scenario covering (b) and (c), the crowded MOs scenario covering (a) - (c), and the slow MOs scenario covering (a) and (c). Experiments on these scenarios demonstrate the accuracy, effectiveness, and efficiency of our models and their applications in MOS improvements.

Eigenvalue decomposition is widely used in dimensionality reduction for knowledge engineering, in particular principal component analysis and other similar spectral methods. Traditional eigenvalue decomposition algorithms for decomposing a matrix of size n ×nn×n are usually of complexity O(n3)O(n3), due to a bottleneck in using Householder/Givens transforms to convert a general matrix to a tri-diagonal one. It is proposed in this article a new algorithm that takes only O(n2.584963log 1/ε) computational complexity to achieve accuracy ε of eigenvalue decomposition for any ε > 0ε>0. The basic idea of our algorithm is to convert a matrix into a diagonal form in multi-scale divide and conquer scheme, and the conversion is to iteratively and recursively apply two phases of operations called diagonal attractions and diagonal absorptions respectively. In a diagonal attraction, it attracts the off-diagonal entries to make the entries nearer to the diagonal larger in magnitude than those farther away from the diagonal. In a diagonal absorption, it absorbs the near-to-diagonal nonzero entries into the diagonal. In such a scheme, no Householder or Givens transforms are involved. Moreover, diagonal attractions and diagonal absorptions can be implemented with fast matrix multiplications. The scheme's divide and conquer pattern also allows our algorithm to be easily mapped to modern computer hardware. Our algorithm also complements well the family of randomized eigenvalue/SVD algorithms using sampling techinques, which are of complexity O(nαpolylog(1/ε)) with small α but very large overheads in the polylog. Their strength in the small exponent αα of nn in complexity was easily cancelled by the exploding overheads in the polylog. Now, with their low-accuracy estimate refined by our algorithm for high accuracy, their strength can be boosted significantly.