Given appropriate representations of the semantic relations between carpenter and wood and between mason and stone (for example, vectors in a vector space model), a suitable algorithm should be able to recognize that these relations are highly similar (carpenter is to wood as mason is to stone; the relations are analogous). Likewise, with representations of dog, house, and kennel, an algorithm should be able to recognize that the semantic composition of dog and house, dog house, is highly similar to kennel (dog house and kennel are synonymous). It seems that these two tasks, recognizing relations and compositions, are closely connected. However, up to now, the best models for relations are significantly different from the best models for compositions. In this paper, we introduce a dual-space model that unifies these two tasks. This model matches the performance of the best previous models for relations and compositions. The dual-space model consists of a space for measuring domain similarity and a space for measuring function similarity. Carpenter and wood share the same domain, the domain of carpentry. Mason and stone share the same domain, the domain of masonry. Carpenter and mason share the same function, the function of artisans. Wood and stone share the same function, the function of materials. In the composition dog house, kennel has some domain overlap with both dog and house (the domains of pets and buildings). The function of kennel is similar to the function of house (the function of shelters). By combining domain and function similarities in various ways, we can model relations, compositions, and other aspects of semantics.
Let @math be a phrase, such as a noun-modifier phrase, and assume that we have vectors @math and @math that represent the component words @math and @math . One of the earliest proposals for semantic composition is to represent @math by the vector @math that is the average of @math and @math @cite_56 . If we are using a cosine measure of vector similarity, taking the average of a set of vectors (or their centroid) is the same as adding the vectors, @math . Vector addition works relatively well in practice @cite_38 @cite_5 , although it lacks order sensitivity, adaptive capacity, and information scalability. Regarding order sensitivity and adaptive capacity, mitchell08,mitchell10 suggest using weights, @math , and tuning the weights to different values for different syntactic relations. In their experiments @cite_5 , weighted addition performed better than unweighted addition.
@cite_38 @cite_5 @cite_56
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Additive composition ( in Discourse Process 15:285---307, 1998; Landauer and Dumais in Psychol Rev 104(2):211, 1997; Mitchell and Lapata in Cognit Sci 34(8):1388---1429, 2010) is a widely used method for computing meanings of phrases, which takes the average of vector representations of the constituent words. In this article, we prove an upper bound for the bias of additive composition, which is the first theoretical analysis on compositional frameworks from a machine learning point of view. The bound is written in terms of collocation strength; we prove that the more exclusively two successive words tend to occur together, the more accurate one can guarantee their additive composition as an approximation to the natural phrase vector. Our proof relies on properties of natural language data that are empirically verified, and can be theoretically derived from an assumption that the data is generated from a Hierarchical Pitman---Yor Process. The theory endorses additive composition as a reasonable operation for calculating meanings of phrases, and suggests ways to improve additive compositionality, including: transforming entries of distributional word vectors by a function that meets a specific condition, constructing a novel type of vector representations to make additive composition sensitive to word order, and utilizing singular value decomposition to train word vectors. We propose a framework of word-vector adaptation, which makes vectors of visually similar concepts close to each other. Here, word vectors are real-valued vector representation of words, e.g., word2vec representation. Our basic idea is to assume that each concept has some hypernyms that are important to determine its visual features. For example, for a concept Swallow with hypernyms Bird, Animal and Entity, we believe Bird is the most important since birds have common visual features with their feathers etc. Adapted word vectors are obtained for each word by taking a weighted sum of a given original word vector and its hypernym word vectors. Our weight optimization makes vectors of visually similar concepts close to each other, by giving a large weight for such important hypernyms. We apply the adapted word vectors to zero-shot learning on the TRECVID 2014 semantic indexing dataset. We achieved 0.083 of Mean Average Precision, which is the best performance without using TRECVID training data to the best of our knowledge. We present an algorithm for learning from unlabeled text, based on the Vector Space Model (VSM) of information retrieval, that can solve verbal analogy questions of the kind found in the SAT college entrance exam. A verbal analogy has the form A:B::C:D, meaning "A is to B as C is to D"; for example, mason:stone::carpenter:wood. SAT analogy questions provide a word pair, A:B, and the problem is to select the most analogous word pair, C:D, from a set of five choices. The VSM algorithm correctly answers 47 of a collection of 374 college-level analogy questions (random guessing would yield 20 correct; the average college-bound senior high school student answers about 57 correctly). We motivate this research by applying it to a difficult problem in natural language processing, determining semantic relations in noun-modifier pairs. The problem is to classify a noun-modifier pair, such as "laser printer", according to the semantic relation between the noun (printer) and the modifier (laser). We use a supervised nearest-neighbour algorithm that assigns a class to a given noun-modifier pair by finding the most analogous noun-modifier pair in the training data. With 30 classes of semantic relations, on a collection of 600 labeled noun-modifier pairs, the learning algorithm attains an F value of 26.5 (random guessing: 3.3 ). With 5 classes of semantic relations, the F value is 43.2 (random: 20 ). The performance is state-of-the-art for both verbal analogies and noun-modifier relations. We propose an approach to adjective-noun composition (AN) for corpus-based distributional semantics that, building on insights from theoretical linguistics, represents nouns as vectors and adjectives as data-induced (linear) functions (encoded as matrices) over nominal vectors. Our model significantly outperforms the rivals on the task of reconstructing AN vectors not seen in training. A small post-hoc analysis further suggests that, when the model-generated AN vector is not similar to the corpus-observed AN vector, this is due to anomalies in the latter. We show moreover that our approach provides two novel ways to represent adjective meanings, alternative to its representation via corpus-based co-occurrence vectors, both outperforming the latter in an adjective clustering task.