PIRST Presentation
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The document provides an introduction to various mathematical concepts commonly used in information retrieval and summarizes several models including vector space models, inductive models like probabilistic and neural networks, and hybrid models. It gives examples of how vector space and probabilistic models can be used for applications like document clustering, targeted advertising, and part-of-speech tagging. It also notes some uncertainties and pitfalls with these models.
PIRST Presentation
- 1. Mathematical Roadmap for IR Introduction to the mathematical concepts commonly used in IR/ST - Abhay Shete, 42
- 2. Why bother about the maths ? Lots of open source libraries out there General approach for external software Include it Build it Forget it !!
- 3. IR is fuzzy Consider the following sentences India beat Pakistan Sachin has scored over 10,000 runs in Test cricket Sachin Tendulkar was unable to run to the non- striker's end How do we humans interpret this information ? How do machines interpret it ?
- 4. What excites me about IR ? Its all about indulging and flirting with sexy models !!!!
- 5. Models of interest Vector space models Inductive models Probabilistic Neural networks, decision trees Hybrid vector space and inductive Others...
- 6. Vector Space Model Recall junior college mathematics Dot-product, cross-product, projections, etc..
- 7. Vector Space Model A1, A2 are articles about animals P1 contains politics To find similarity scores between a) A1, A2 ==> assume score is S1 b) A1, P1 ==> assume score is S2 Intuitively S1 > S2 How do u create a model around this ?
- 8. Vector Space Model A1 = {dog(1), cat(2), lion(1), rhino(1), tiger(2)} A2 = {eagle(1), cat(1), tiger(1), fox, hyena N Dimensional Space !!! d1 = 1(dog) + 2(cat) + 1(lion) + 1(rhino) + 2(tiger) + 0(eagle) + 0(fox) + 0(hyena) d2 = 0(dog) + 1(cat) + 0(lion) + 0(rhino) + 1(tiger) + 1(eagle) + 1(fox) + 1(hyena) Similarity is measured by the angle between the two vectors !!
- 9. Similarity measured by the angle between two vectors !! If X and Y are two n-dimensional vectors <xi> and <yi>, the angle 慮 between them satisfies: X Y = |X| |Y| cos 慮 cos 慮 = X Y / (|X||Y|)
- 11. Linear Algebra Vectors and matrices are equivalent Important Linear Algebra concepts: Singular Value Decomposition EigenVectors Latent Semantic Indexing (LSI) Face recognition
- 12. Latent Semantic Indexing Exact keyword match not required No predfined semantic knowledge base Demo http://lsi.research.telcordia.com/lsi-bin/lsiQuery How does it work ? Fish Tank Analogy
- 13. Uncertainities, Pitfalls Not suitable for fine grained search Web Scale corpus !! Does anybody find Google suggestions really helpful ?
- 14. Face recognition application EigenValues, covariance and SVD Intuitive Understanding Create a vector space from the pixels modelling the face Find average face vector Find the specific features of every face by computing the variance from the average vector Take the top N specific features of this vector space and create the classifier vector
- 15. Document Clustering Clusty.com demo Clustering approaches
- 16. Inductive Models Require prior information (Training set) to extrapolate to future unseen cases. Create a function from the input training data which is applied on test data to produce output.
- 17. Bag 1 Bag 2 Bag 3 Ball drawn at random from a bag and found to be white. What are the chances of it being drawn from Bag 3?
- 18. Bag 1 Bag 2 Bag 3 Ball drawn at random from a bag and found to be green. What are the chances that it is from Bag 2 ?
- 20. Sachin, Pilot, Rock, band, Sachin, cricket, political, career, took, crowd, Tendulkar, drew, crowds, storm, elected run, wicket, , year, centre, grammy crowd government, cheered elections Cricket Bag Politics Bag Music Bag Test sentence:- Sachin's 10,000th run was highly appreciated by the crowd What chances this is from Bag Cricket ?
- 21. Other applications on probabilistic models Targeted Advertising Demo POS Tagging http://www.infogistics.com/posdemo.htm Named Entity Recognition
- 22. Neural Networks Demo video (5 minutes) Machine learns how to steer the vehicle by observing the driver After training, capable of steering the vehicle on its own.
- 23. Uncertainities, Pitfalls Depends on the training set Training set may not be in line with the application for which it is being used. POS Tagging done on Wall Street Corpus Like Applying the same for like analyzing teen text !! dove makes my skin smooth. Can you deal with The Black Swan!! Is inductive learning really needed ? Combine with other features/approaches ? More data better than a good algorithm.