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Vector space model or term vector model is an algebraic model for representing text documents (or more generally, items) as vectors such that the distance between vectors represents the relevance between the documents. It is used in information filtering, information retrieval, indexing and relevancy rankings. Its first use was in the SMART Information Retrieval System[citation needed].

Each dimension corresponds to a separate term. If a term occurs in the document, its value in the vector is non-zero. Several different ways of computing these values, also known as (term) weights, have been developed. One of the best known schemes is tf-idf weighting (see the example below).

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The definition of term depends on the application. Typically terms are single words, keywords, or longer phrases. If words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary (the number of distinct words occurring in the corpus).

Candidate documents from the corpus can be retrieved and ranked using a variety of methods. Relevance rankings of documents in a keyword search can be calculated, using the assumptions of document similarities theory, by comparing the deviation of angles between each document vector and the original query vector where the query is represented as a vector with same dimension as the vectors that represent the other documents.

As all vectors under consideration by this model are element-wise nonnegative, a cosine value of zero means that the query and document vector are orthogonal and have no match (i.e. the query term does not exist in the document being considered). See cosine similarity for further information.[1]

Most of these advantages are a consequence of the difference in the density of the document collection representation between Boolean and term frequency-inverse document frequency approaches. When using Boolean weights, any document lies in a vertex in a n-dimensional hypercube. Therefore, the possible document representations are 2 n {\displaystyle 2^{n}} and the maximum Euclidean distance between pairs is n {\displaystyle {\sqrt {n}}} . As documents are added to the document collection, the region defined by the hypercube's vertices become more populated and hence denser. Unlike Boolean, when a document is added using term frequency-inverse document frequency weights, the inverse document frequencies of the terms in the new document decrease while that of the remaining terms increase. In average, as documents are added, the region where documents lie expands regulating the density of the entire collection representation. This behavior models the original motivation of Salton and his colleagues that a document collection represented in a low density region could yield better retrieval results.

Models that represent meaning as high-dimensional numerical vectors-such as latent semantic analysis (LSA), hyperspace analogue to language (HAL), bound encoding of the aggregate language environment (BEAGLE), topic models, global vectors (GloVe), and word2vec-have been introduced as extremely powerful machine-learning proxies for human semantic representations and have seen an explosive rise in popularity over the past 2 decades. However, despite their considerable advancements and spread in the cognitive sciences, one can observe problems associated with the adequate presentation and understanding of some of their features. Indeed, when these models are examined from a cognitive perspective, a number of unfounded arguments tend to appear in the psychological literature. In this article, we review the most common of these arguments and discuss (a) what exactly these models represent at the implementational level and their plausibility as a cognitive theory, (b) how they deal with various aspects of meaning such as polysemy or compositionality, and (c) how they relate to the debate on embodied and grounded cognition. We identify common misconceptions that arise as a result of incomplete descriptions, outdated arguments, and unclear distinctions between theory and implementation of the models. We clarify and amend these points to provide a theoretical basis for future research and discussions on vector models of semantic representation.

This is a blog post rewritten from a presentation at NYC Machine Learning on Sep 17. It covers a library called Annoy that I have built that helps you do nearest neighbor queries in high dimensional spaces. In the first part, I went through some examples of why vector models are useful. In the second part I will be explaining the data structures and algorithms that Annoy uses to do approximate nearest neighbor queries.

Let's start by going back to our point set. The goal is to find nearest neighbors in this space. Again, I am showing a 2 dimensional point set because computer screens are 2D, but in reality most vector models have much higher dimensionality.

In order to study the molecular pathways of Parkinson's disease (PD) and to develop novel therapeutic strategies, scientific investigators rely on animal models. The identification of PD-associated genes has led to the development of genetic PD models as an alternative to toxin-based models. Viral vector-mediated loco-regional gene delivery provides an attractive way to express transgenes in the central nervous system. Several vector systems based on various viruses have been developed. In this chapter, we give an overview of the different viral vector systems used for targeting the CNS. Further, we describe the different viral vector-based PD models currently available based on overexpression strategies for autosomal dominant genes such as -synuclein and LRRK2, and knockout or knockdown strategies for autosomal recessive genes, such as parkin, DJ-1, and PINK1. Models based on overexpression of -synuclein are the most prevalent and extensively studied, and therefore the main focus of this chapter. Many efforts have been made to increase the expression levels of -synuclein in the dopaminergic neurons. The best -synuclein models currently available have been developed from a combined approach using newer AAV serotypes and optimized vector constructs, production, and purification methods. These third-generation -synuclein models show improved face and predictive validity, and therefore offer the possibility to reliably test novel therapeutics.

GloVe is an unsupervised learning algorithm for obtaining vector representations for words. Training is performed on aggregated global word-word co-occurrence statistics from a corpus, and the resulting representations showcase interesting linear substructures of the word vector space.

In order to capture in a quantitative way the nuance necessary to distinguish man from woman, it is necessary for a model to associate more than a single number to the word pair. A natural and simple candidate for an enlarged set of discriminative numbers is the vector difference between the two word vectors. GloVe is designed in order that such vector differences capture as much as possible the meaning specified by the juxtaposition of two words.

The underlying concept that distinguishes man from woman, i.e. sex or gender, may be equivalently specified by various other word pairs, such as king and queen or brother and sister. To state this observation mathematically, we might expect that the vector differences man - woman, king - queen, and brother - sister might all be roughly equal. This property and other interesting patterns can be observed in the above set of visualizations.

As one might expect, ice co-occurs more frequently with solid than it does with gas, whereas steam co-occurs more frequently with gas than it does with solid. Both words co-occur with their shared property water frequently, and both co-occur with the unrelated word fashion infrequently. Only in the ratio of probabilities does noise from non-discriminative words like water and fashioncancel out, so that large values (much greater than 1) correlate well with properties specific to ice, and small values (much less than 1) correlate well with properties specific of steam. In this way, the ratio of probabilities encodes some crude form of meaning associated with the abstract concept of thermodynamic phase.

The training objective of GloVe is to learn word vectors such that their dot product equals the logarithm of the words' probability of co-occurrence. Owing to the fact that the logarithm of a ratio equals the difference of logarithms, this objective associates (the logarithm of) ratios of co-occurrence probabilities with vector differences in the word vector space. Because these ratios can encode some form of meaning, this information gets encoded as vector differences as well. For this reason, the resulting word vectors perform very well on word analogy tasks, such as those examined in the word2vec package.

The horizontal bands become more pronounced as the word frequency increases. Indeed, there are noticeable long-range trends as a function of word frequency, and they are unlikely to have a linguistic origin. This feature is not unique to GloVe -- in fact, I'm unaware of any model for word vector learning that avoids this issue.

Mr. Smith has biological complexity, with multiple newly recognized conditions. However, his personal, family, and community circumstances exert stabilizing and supportive forces along social, cultural and environmental axes, diminishing the overall complexity confronting his treating physicians. Mr. Smith has the means to find culturally concordant doctors whom he can trust, enhancing motivation to quit smoking, make lifestyle changes, and take his medicines. His overall complexity vector along the biological axis is low (Fig. 4), and his treating physicians need not modify their usual approach.

Complexity vectors for Mr. Smith and Mr. Jones. The arrows represent vector forces (V). In vector physics, these arrows can be added in space (for more details, see Appendix), and we propose an analogous relationship between the various domains of health determinants. The biological axis is a traditional focus, therefore it is dashed. Greater complexity along the biological axis is toward the top of the diagram, lesser complexity toward the bottom. For both patients, the biological complexity vector (VBIO) has the same magnitude and direction, but the other vectors differ markedly. The block arrows represent the summary vectors along the biological axis, which for Mr. Smith indicate less overall complexity compared with the biological complexity vector alone (arrow points down). However, for Mr. Jones, the summary vector indicates greater overall complexity compared with the biological complexity vector alone (arrow points up). BIOL biological, SES socioeconomic, CUL cultural, ENV environmental, BEH behavioral ff782bc1db