As a fundamental problem of natural language processing, it is important to measure the distance between different documents. Among the existing methods, the Word Mover's Distance (WMD) has shown remarkable success in document semantic matching for its clear physical insight as a parameter-free model. However, WMD is essentially based on the classical Wasserstein metric, thus it often fails to robustly represent the semantic similarity between texts of different lengths. In this paper, we apply the newly developed Wasserstein-Fisher-Rao (WFR) metric from unbalanced optimal transport theory to measure the distance between different documents. The proposed WFR document distance maintains the great interpretability and simplicity as WMD. We demonstrate that the WFR document distance has significant advantages when comparing the texts of different lengths. In addition, an accelerated Sinkhorn based algorithm with GPU implementation has been developed for the fast computation of WFR distances. The KNN classification results on eight datasets have shown its clear improvement over WMD.
(a) Representation of documents. There have been many ways for documents representation. Latent Semantic Indexing @cite_4 and Latent Dirichlet Allocation @cite_31 are based on inferred latent variables generated by the graphical model. However, most of those models are lack of the semantic information in word embedding space @cite_18 . Stack denoising auto encoders @cite_11 , Doc2Vec @cite_19 and skip-thoughts @cite_26 are neural network based similarities. Despite their numerical success, those models are difficult to explain, and the performance always relies on the training samples.
@cite_18 @cite_26 @cite_4 @cite_19 @cite_31 @cite_11
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Latent Dirichlet Allocation (LDA) mining thematic structure of documents plays an important role in nature language processing and machine learning areas. However, the probability distribution from LDA only describes the statistical relationship of occurrences in the corpus and usually in practice, probability is not the best choice for feature representations. Recently, embedding methods have been proposed to represent words and documents by learning essential concepts and representations, such as Word2Vec and Doc2Vec. The embedded representations have shown more effectiveness than LDA-style representations in many tasks. In this paper, we propose the Topic2Vec approach which can learn topic representations in the same semantic vector space with words, as an alternative to probability. The experimental results show that Topic2Vec achieves interesting and meaningful results. Models such as latent semantic analysis and those based on neural embeddings learn distributed representations of text, and match the query against the document in the latent semantic space. In traditional information retrieval models, on the other hand, terms have discrete or local representations, and the relevance of a document is determined by the exact matches of query terms in the body text. We hypothesize that matching with distributed representations complements matching with traditional local representations, and that a combination of the two is favourable. We propose a novel document ranking model composed of two separate deep neural networks, one that matches the query and the document using a local representation, and another that matches the query and the document using learned distributed representations. The two networks are jointly trained as part of a single neural network. We show that this combination or 'duet' performs significantly better than either neural network individually on a Web page ranking task, and significantly outperforms traditional baselines and other recently proposed models based on neural networks. We consider the problem of modeling annotated data---data with multiple types where the instance of one type (such as a caption) serves as a description of the other type (such as an image). We describe three hierarchical probabilistic mixture models which aim to describe such data, culminating in correspondence latent Dirichlet allocation, a latent variable model that is effective at modeling the joint distribution of both types and the conditional distribution of the annotation given the primary type. We conduct experiments on the Corel database of images and captions, assessing performance in terms of held-out likelihood, automatic annotation, and text-based image retrieval. This paper presents a series of new latent semantic models based on a convolutional neural network (CNN) to learn low-dimensional semantic vectors for search queries and Web documents. By using the convolution-max pooling operation, local contextual information at the word n-gram level is modeled first. Then, salient local fea-tures in a word sequence are combined to form a global feature vector. Finally, the high-level semantic information of the word sequence is extracted to form a global vector representation. The proposed models are trained on clickthrough data by maximizing the conditional likelihood of clicked documents given a query, us-ing stochastic gradient ascent. The new models are evaluated on a Web document ranking task using a large-scale, real-world data set. Results show that our model significantly outperforms other se-mantic models, which were state-of-the-art in retrieval performance prior to this work.