The detextion of antonymy has been studied in a number of previous papers. These methods consist of two main steps:

1. Detecting contrasting word categories and then determining the degree of antonymy.
2. Determining the degree of antonymy

The automatic detecting of synonyms has been more extensively studied.

This is a widely used method for representing words and documents in a low dimensional vector space. The method is based on applying singular value decomposition (SVD) to a matrix $W$ which indicates the occurrence of words in documents. A $dtimes n$ document-term matrix $W$ is formed. Its $ij^{th}$ entry can be term frequency or a TF-IDF weighting. The similarity between two documents can be computed using the cosine similarity of their corresponding row vectors. The similarity between two words can be computed using the cosine similarity of their corresponding column vectors. Finally, to obtain a subspace representation of dimension $k$, $W$ is decomposed as

where $U$ is $xtimes k$, $V^T$ is $k times n$, and $S$ is a $k times k$ diagonal matrix. In applications, $k ll n$ and $k ll d$.

LSA is also confuse antonyms and synonyms. This paper want to make the least-similar words to a given a word be its opposites instead of words without relationship at all.

Words with opposite meaning will lie at opposite axes.

First, some lexical analysis are conducted to try to match an unknown word to one or more in-thesaurus words in their lemmatized forms. If now such match can be found, we then attempt to find semantically related inthesaurus words by leveraging co-occurrence statistics from general text data.

The problem, the size of vocabulary is not big enough. Because the thesaurus may contain enough words.

They propose a discriminvative training method to obtain a model used as a matrix $A$. The neural network transforms a $d time 1$ vector $f$ into $k times 1$ vector $g$.

When a target word is not included in a thesaurus, it is quite often that some of its morphological variations are covered.

First, apply a morphological analyzer for English developed by Minnen. It not match, apply Porter’s stemmer. If both fails, removing hyphens is considered.

If there are more than one matched words, the centroid of their PILSA vectors is used to represent the target word.

If no words in the thesaurus can be linked to the target word through the simple lexical analysis procedure, they try to find matched words by creating a context vector space model from a large document collection, and then mapping from this space to the PILSA space.

For each target word, a bag of words is created by collecting all the terms within a windows of [-10,+10] centered at each occurrence of the target word in the corpus. Using its TF-IDF value to build context-word matrix. Then LSA is performed on the context-word matrix.

A revised k-nearest neighbors approach is proposed. Given an out-of-thesaurus word $w$, K-nearest in-thesaurus neighbors are found in the context space. A subset of k members of these K words such that the pairwise similarity of each of the k members with every other is positive. The thesaurus-space centroid of these k items is computed as w’s representation.