The document discusses alternative algebraic models for information retrieval, including the generalized vector model. The generalized vector model allows for index terms to be non-orthogonal, representing correlations between terms. It models term dependencies through "minterms" - binary patterns of term occurrence. While allowing representation of term correlations, the model has higher computational costs than the standard vector model and it is unclear when it performs better.

1. Information Retrieval : 15
Alternative Algebraic Models
Prof Neeraj Bhargava
Vaibhav Khanna
Department of Computer Science
School of Engineering and Systems Sciences
Maharshi Dayanand Saraswati University Ajmer

2. Alternative Algebraic Models
• Generalized Vector Model
• Latent Semantic Indexing
• Neural Network Model

3. Generalized Vector Model
• Classic models enforce independence of index
terms
• In the generalized vector space model, two
index term vectors might be non-orthogonal

4. Key Idea
• As before, let wi,j be the weight associated with [ki, dj ] and V =
{k1, k2, . . ., kt} be the set of all terms
• If the wi,j weights are binary, all patterns of occurrence of
terms within docs can be represented by minterms:

6. • Pairwise orthogonality among the ~mr vectors does
not imply independence among the index terms
• On the contrary, index terms are now correlated by the
~mr vectors
– For instance, the vector ~m4 is associated with the
minterm m4 = (1, 1, . . . , 0)
– This minterm induces a dependency between terms k1
and k2
– Thus, if such document exists in a collection, we say that
the minterm m4 is active
• The model adopts the idea that co-occurrence of terms
induces dependencies among these terms

8. Computation of ci,r

9. Computation of

10. Computation of Document Vectors

11. Conclusions
• Model considers correlations among index
terms
• Not clear in which situations it is superior to
the standard Vector model
• Computation costs are higher
• Model does introduce interesting new ideas

12. Assignment
• Explain the Generalized Vector Model of IR