You are provided with the abstract of a scientific paper and the abstracts of the papers it references. Your task is to write a Related Work section for the main paper. This section should concisely summarize and integrate the key points from the cited abstracts, reflecting how they relate to the main paper's contributions and context. In your summary, use numerical citation markers like [1], [2], etc., to refer to the corresponding papers.

Main Abstract:
We analyze a word embedding method in supervised tasks. It maps words on a sphere such that words co-occurring in similar contexts lie closely. The similarity of contexts is measured by the distribution of substitutes that can fill them. We compared word embeddings, including more recent representations, in Named Entity Recognition (NER), Chunking, and Dependency Parsing. We examine our framework in multilingual dependency parsing as well. The results show that the proposed method achieves as good as or better results compared to the other word embeddings in the tasks we investigate. It achieves state-of-the-art results in multilingual dependency parsing. Word embeddings in 7 languages are available for public use.

Cited Abstract(s):
[1]: Motivated by an application to unsupervised part-of-speech tagging, we present an algorithm for the Euclidean embedding of large sets of categorical data based on co-occurrence statistics. We use the CODE model of but constrain the embedding to lie on a high-dimensional unit sphere. This constraint allows for efficient optimization, even in the case of large datasets and high embedding dimensionality. Using k-means clustering of the embedded data, our approach efficiently produces state-of-the-art results. We analyze the reasons why the sphere constraint is beneficial in this application, and conjecture that these reasons might apply quite generally to other large-scale tasks.

[2]: We investigate paradigmatic representations of word context in the domain of unsupervised syntactic category acquisition. Paradigmatic representations of word context are based on potential substitutes of a word in contrast to syntagmatic representations based on properties of neighboring words. We compare a bigram based baseline model with several paradigmatic models and demonstrate significant gains in accuracy. Our best model based on Euclidean co-occurrence embedding combines the paradigmatic context representation with morphological and orthographic features and achieves 80 many-to-one accuracy on a 45-tag 1M word corpus.

[3]: Embedding algorithms search for a low dimensional continuous representation of data, but most algorithms only handle objects of a single type for which pairwise distances are specified. This paper describes a method for embedding objects of different types, such as images and text, into a single common Euclidean space, based on their co-occurrence statistics. The joint distributions are modeled as exponentials of Euclidean distances in the low-dimensional embedding space, which links the problem to convex optimization over positive semidefinite matrices. The local structure of the embedding corresponds to the statistical correlations via random walks in the Euclidean space. We quantify the performance of our method on two text data sets, and show that it consistently and significantly outperforms standard methods of statistical correspondence modeling, such as multidimensional scaling, IsoMap and correspondence analysis.
SCODE Word Embeddings: [1] introduce the SCODE framework, an extension of the CODE [3] framework. [1] obtains word type representations from co-occurrence data generated by using neighbors of words. [2] extend this work by generating co-occurrence data using probable substitutes of words. In Section , we explain this framework in detail. Here, we review studies extending that work.