In statistical relational learning, knowledge graph completion deals with automatically understanding the structure of large knowledge graphs---labeled directed graphs---and predicting missing relationships---labeled edges. State-of-the-art embedding models propose different trade-offs between modeling expressiveness, and time and space complexity. We reconcile both expressiveness and complexity through the use of complex-valued embeddings and explore the link between such complex-valued embeddings and unitary diagonalization. We corroborate our approach theoretically and show that all real square matrices---thus all possible relation adjacency matrices---are the real part of some unitarily diagonalizable matrix. This results opens the door to a lot of other applications of square matrices factorization. Our approach based on complex embeddings is arguably simple, as it only involves a Hermitian dot product, the complex counterpart of the standard dot product between real vectors, whereas other methods resort to more and more complicated composition functions to increase their expressiveness. The proposed complex embeddings are scalable to large data sets as it remains linear in both space and time, while consistently outperforming alternative approaches on standard link prediction benchmarks.
Some works on recommender systems use complex numbers as an encoding facility, to merge two real-valued relations, similarity and liking, into one single complex-valued matrix which is then decomposed with complex embeddings @cite_53 @cite_6 . Still, unlike our work, it is not real data that is decomposed in the complex domain.
@cite_53 @cite_6
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For statistical learning, categorical variables in a table are usually considered as discrete entities and encoded separately to feature vectors, e.g., with one-hot encoding. “Dirty” non-curated data give rise to categorical variables with a very high cardinality but redundancy: several categories reflect the same entity. In databases, this issue is typically solved with a deduplication step. We show that a simple approach that exposes the redundancy to the learning algorithm brings significant gains. We study a generalization of one-hot encoding, similarity encoding, that builds feature vectors from similarities across categories. We perform a thorough empirical validation on non-curated tables, a problem seldom studied in machine learning. Results on seven real-world datasets show that similarity encoding brings significant gains in predictive performance in comparison with known encoding methods for categories or strings, notably one-hot encoding and bag of character n-grams. We draw practical recommendations for encoding dirty categories: 3-gram similarity appears to be a good choice to capture morphological resemblance. For very high-cardinalities, dimensionality reduction significantly reduces the computational cost with little loss in performance: random projections or choosing a subset of prototype categories still outperform classic encoding approaches. A typical recommender setting is based on two kinds of relations: similarity between users (or between objects) and the taste of users towards certain objects. In environments such as online dating websites, these two relations are difficult to separate, as the users can be similar to each other, but also have preferences towards other users, i.e., rate other users. In this paper, we present a novel and unified way to model this duality of the relations by using split-complex numbers, a number system related to the complex numbers that is used in mathematics, physics and other fields. We show that this unified representation is capable of modeling both notions of relations between users in a joint expression and apply it for recommending potential partners. In experiments with the Czech dating website Libimseti.cz we show that our modeling approach leads to an improvement over baseline recommendation methods in this scenario. We consider learning representations of entities and relations in KBs using the neural-embedding approach. We show that most existing models, including NTN (, 2013) and TransE (, 2013b), can be generalized under a unified learning framework, where entities are low-dimensional vectors learned from a neural network and relations are bilinear and or linear mapping functions. Under this framework, we compare a variety of embedding models on the link prediction task. We show that a simple bilinear formulation achieves new state-of-the-art results for the task (achieving a top-10 accuracy of 73.2 vs. 54.7 by TransE on Freebase). Furthermore, we introduce a novel approach that utilizes the learned relation embeddings to mine logical rules such as "BornInCity(a,b) and CityInCountry(b,c) => Nationality(a,c)". We find that embeddings learned from the bilinear objective are particularly good at capturing relational semantics and that the composition of relations is characterized by matrix multiplication. More interestingly, we demonstrate that our embedding-based rule extraction approach successfully outperforms a state-of-the-art confidence-based rule mining approach in mining Horn rules that involve compositional reasoning. We present an approach named JSFusion (Joint Sequence Fusion) that can measure semantic similarity between any pairs of multimodal sequence data (e.g. a video clip and a language sentence). Our multimodal matching network consists of two key components. First, the Joint Semantic Tensor composes a dense pairwise representation of two sequence data into a 3D tensor. Then, the Convolutional Hierarchical Decoder computes their similarity score by discovering hidden hierarchical matches between the two sequence modalities. Both modules leverage hierarchical attention mechanisms that learn to promote well-matched representation patterns while prune out misaligned ones in a bottom-up manner. Although the JSFusion is a universal model to be applicable to any multimodal sequence data, this work focuses on video-language tasks including multimodal retrieval and video QA. We evaluate the JSFusion model in three retrieval and VQA tasks in LSMDC, for which our model achieves the best performance reported so far. We also perform multiple-choice and movie retrieval tasks for the MSR-VTT dataset, on which our approach outperforms many state-of-the-art methods.