What is Vector space models

Understanding Vector Space Models

Vector space model (VSM) is a mathematical framework that is used to represent text documents as vectors in a high-dimensional space. This framework is used in natural language processing (NLP) tasks such as information retrieval, text classification, and sentiment analysis. In this article, we explore the basics of vector space models, their applications, and implementation.

The Idea behind Vector Space Model

Vector space models are based on the idea that words or terms often occur together in similar contexts. For example, the words "dog" and "puppy" often occur together in texts that describe animals. Similarly, the words "bank" and "loan" often appear together in texts that discuss financial matters. Based on this idea, we represent texts as a set of terms, and then each term is assigned a weight that indicates its importance in the text. Thus, each text is represented as a vector in a high-dimensional space, where each dimension represents a term, and the magnitude of each dimension represents the importance of the term in the text.

Applications of Vector Space Models
  • Information Retrieval: Vector space models are widely used in information retrieval applications such as search engines. In this application, the query entered by the user is represented as a vector, and then compared with the vectors of documents in a corpus. The similarity between the query and documents is measured using similarity measures such as cosine similarity.
  • Text Classification: VSMs are also used for text classification tasks such as categorization of news articles or emails. In this application, each category is represented as a vector, and a new text is assigned to the category with the closest vector.
  • Sentiment Analysis: Vector space models are used in sentiment analysis tasks to classify texts as positive, negative or neutral. In this application, a sentiment lexicon is used to assign weights to words, and then the sentiment of the text is determined based on the weights of the words in the text.
Implementation of Vector Space Models

The implementation of vector space models involves the following steps:

  • Text preprocessing: The first step in implementing VSMs is to preprocess the text. This involves tokenization, stop word removal, stemming, and other text normalization techniques.
  • Term weighting: Once the text has been preprocessed, the next step is to assign weights to each term. There are several term weighting schemes such as term frequency-inverse document frequency (tf-idf) that can be used to assign weights to each term in the text.
  • Vector representation: After the terms have been weighted, the text is represented as a vector. Each term in the text is given a dimension in the vector space, and the weight of the term is the magnitude of the dimension.
  • Similarity measure: Finally, a similarity measure is used to compare the vectors of different texts. Cosine similarity is one of the most commonly used similarity measures in vector space models.
Challenges with Vector Space Models

One of the main challenges with vector space models is handling the sparsity of the vectors. Since most texts contain only a small subset of the terms in the corpus, the vectors are often sparse, with most dimensions being zero. This sparsity poses a challenge when computing similarity measures between vectors. Another challenge with vector space models is the curse of dimensionality. As the number of dimensions increases, the density of the data decreases, making it difficult to compute accurate similarity measures.


In conclusion, vector space models are a fundamental concept in natural language processing and have applications in many areas such as information retrieval, text classification, and sentiment analysis. The implementation of vector space models involves preprocessing the text, assigning weights to terms, constructing vectors, and using a similarity measure to compare vectors. Despite their usefulness, vector space models pose several challenges such as sparsity and the curse of dimensionality.