Compositional semantic aims at constructing the meaning of phrases or sentences according to the compositionality of word meanings. In this paper, we propose to synchronously learn the representations of individual words and extracted high-frequency phrases. Representations of extracted phrases are considered as gold standard for constructing more general operations to compose the representation of unseen phrases. We propose a grammatical type specific model that improves the composition flexibility by adopting vector-tensor-vector operations. Our model embodies the compositional characteristics of traditional additive and multiplicative model. Empirical result shows that our model outperforms state-of-the-art composition methods in the task of computing phrase similarities.
Tensor networks are linear algebraic representations of quantum many-body states based on their entanglement structure. People are exploring their applications to machine learning. Deep convolutional neural networks achieve state of the art results in computer vision and other areas. Supposedly this happens because of parameter sharing, locality, and deepness. We devise a novel tensor network based model called Deep convolutional tensor network (DCTN) for image classification, which has parameter sharing, locality, and deepness. It is based on the Entangled plaquette states (EPS) tensor network. We show how Entangled plaquette states can be implemented as a backpropagatable layer which can be used in neural networks. We test our model on FashionMNIST dataset and find that deepness increases overfitting and decreases test accuracy. Also, we find that the shallow version performs well considering its low parameter count. We discuss how hyperparameters of DCTN affect its training and overfitting.
Hypergraphs have gained increasing attention in the machine learning community lately due to their superiority over graphs in capturing super-dyadic interactions among entities. In this work, we propose a novel approach for the partitioning of k-uniform hypergraphs. Most of the existing methods work by reducing the hypergraph to a graph followed by applying standard graph partitioning algorithms. The reduction step restricts the algorithms to capturing only some weighted pairwise interactions and hence loses essential information about the original hypergraph. We overcome this issue by utilizing the tensor-based representation of hypergraphs, which enables us to capture actual super-dyadic interactions. We prove that the hypergraph to graph reduction is a special case of tensor contraction. We extend the notion of minimum ratio-cut and normalized-cut from graphs to hypergraphs and show the relaxed optimization problem is equivalent to tensor eigenvalue decomposition. This novel formulation also enables us to capture different ways of cutting a hyperedge, unlike the existing reduction approaches. We propose a hypergraph partitioning algorithm inspired from spectral graph theory that can accommodate this notion of hyperedge cuts. We also derive a tighter upper bound on the minimum positive eigenvalue of even-order hypergraph Laplacian tensor in terms of its conductance, which is utilized in the partitioning algorithm to approximate the normalized cut. The efficacy of the proposed method is demonstrated numerically on simple hypergraphs. We also show improvement for the min-cut solution on 2-uniform hypergraphs (graphs) over the standard spectral partitioning algorithm.
Word embedding is a powerful tool in natural language processing. In this paper we consider the problem of word embedding composition \--- given vector representations of two words, compute a vector for the entire phrase. We give a generative model that can capture specific syntactic relations between words. Under our model, we prove that the correlations between three words (measured by their PMI) form a tensor that has an approximate low rank Tucker decomposition. The result of the Tucker decomposition gives the word embeddings as well as a core tensor, which can be used to produce better compositions of the word embeddings. We also complement our theoretical results with experiments that verify our assumptions, and demonstrate the effectiveness of the new composition method.
In many real-world applications, data are often unlabeled and comprised of different representations/views which often provide information complementary to each other. Although several multi-view clustering methods have been proposed, most of them routinely assume one weight for one view of features, and thus inter-view correlations are only considered at the view-level. These approaches, however, fail to explore the explicit correlations between features across multiple views. In this paper, we introduce a tensor-based approach to incorporate the higher-order interactions among multiple views as a tensor structure. Specifically, we propose a multi-linear multi-view clustering (MMC) method that can efficiently explore the full-order structural information among all views and reveal the underlying subspace structure embedded within the tensor. Extensive experiments on real-world datasets demonstrate that our proposed MMC algorithm clearly outperforms other related state-of-the-art methods.