Random indexing:On space and meaning

Simon Belak

Order of the day

• Meaning– Philosophy– Neuroscience– Computer science

• Space– Words as points in space– On dimensionality

• Random indexing

What’s the meaning of meaning?

Philosophers say:

“Meaning just is use.”– Wittgenstein

Neuroscientists say:

• Episodic memory semantic memory(concrete event abstract concept)

• Hebbian process

Computer scientists say:

LSA semantic networks

HALTLC

SAMACT-R

ontology

Projecting meaning into space

Adjacent words closely related

Movement

• Co-occurrences

• Hebbian process– Self-organisation– Clustering

• Evolution of language– Coach (Kocs carriage train car)

Problem: homonymsTable1. a. An article of furniture supported by one or more vertical legs and having a flat horizontal

surface.b. The objects laid out for a meal on this article of furniture.

2. The food and drink served at meals; fare: kept an excellent table.3. The company of people assembled around a table, as for a meal.4 A plateau or tableland.5. a. A flat facet cut across the top of a precious stone.

b. A stone or gem cut in this fashion.6. Music

a. The front part of the body of a stringed instrument.b. The sounding board of a harp.

7. Architecture a. A raised or sunken rectangular panel on a wall.b. A raised horizontal surface or continuous band on an exterior wall; a stringcourse.

8. A part of the human palm framed by four lines, analyzed in palmistry.9. An orderly arrangement of data, especially one in which the data are arranged in columns and rows

in an essentially rectangular form.10. An abbreviated list, as of contents; a synopsis.11. An engraved slab or tablet bearing an inscription or a device.12. Anatomy The inner or outer flat layer of bones of the skull separated by the dipole.

Solution: high dimensionality

• One dimension per word • Table extends into food, furniture, music,... dimensions

Problem: synonyms

amazing, stupefying, staggering, awesome, awful, awe-inspiring, awing, astonishing, astounding

Solution: latent meaning

• Reduced dimensionality

• Closely related words fold into one

• “Higher-order” meaning

Random indexing

The idea

• Word is the sum of it’s contexts

• Context is the sum of it’s words

• Grounding?

The algorithm

1) Take a context of words

2) Generate a context index vector

3) Add index to all the word vectors

4) Go to 1)

Episodic memory (2) + Hebbian process (3)

Dimensionality reduction

• Sparse high-dimensional ternary index

(a small number of randomly distributed +1s and -1s)

• Nearly orthogonal– Distances approximately preserved

The good

• Fast, scalable

• Trivially parallelised– Per word– Addition is associative, commutative

• Stable– Words are independent– Integer arithmetics

• Incremental

The bad

• Memory hungry– Caching (Zipf’s law)

Uses

• Comparing words to words– Query expnasion

• Comparing documents to documents – Clustering– Search– Recomendations

• Comparing documents to words– Keyword extraction

Key points

1. Meaning is use

2. Words in space

3. Many meanings, many dimensions

4. Random indexing

• Cognitive rationale

• Simple

• Fast, scalable

Key points

1. Meaning is use

2. Words in space

3. Many meanings, many dimensions

4. Random indexing– Cognitive rationale– Simple– Fast, scalable

Questions?

References• http://www.sics.se/~mange/papers/KarlgrenSahlgren2001.pdf• http://www.kfs.org/~jonathan/witt/tlph.html• http://www.mtsu.edu/~sschmidt/Cognitive/semantic/semantic.html• http://memory.syr.edu/marc/papers/HowaAddiJingKaha-LSAChap-doc.pdf• http://memory.psych.upenn.edu/research/research_episodic_memory.php• http://www.rni.org/kanerva/cogsci2k-poster.txt• http://www.sics.se/~mange/papers/RI_intro.pdf

• http://code.google.com/p/cl-random-indexing