Search Engine Technology #7 http://www.cs.columbia.edu/~radev/SET07.html October 18, 2007
Prof. Dragomir R. Radev
radev@umich.edu

Slide2:

SET – Fall 2007 …
11. Lexical semantics and wordnet
…

Lexical Networks:

Lexical Networks Used to represent relationships between words
Example: WordNet - created by George Miller’s team at Princeton
Based on synsets (synonyms, interchangeable words) and lexical matrices

Lexical matrix:

Lexical matrix

Synsets:

Synsets Disambiguation
{board, plank}
{board, committee}
Synonyms
substitution
weak substitution
synonyms must be of the same part of speech

Slide6:

$ ./wn board -hypen
Synonyms/Hypernyms (Ordered by Frequency) of noun board
9 senses of board
Sense 1
board
=> committee, commission
=> administrative unit
=> unit, social unit
=> organization, organisation
=> social group
=> group, grouping
Sense 2
board
=> sheet, flat solid
=> artifact, artefact
=> object, physical object
=> entity, something
Sense 3
board, plank
=> lumber, timber
=> building material
=> artifact, artefact
=> object, physical object
=> entity, something

Antonymy “x” vs. “not-x”
“rich” vs. “poor”?
{rise, ascend} vs. {fall, descend}

Other relations:

Other relations Meronymy: X is a meronym of Y when native speakers of English accept sentences similar to “X is a part of Y”, “X is a member of Y”.
Hyponymy: {tree} is a hyponym of {plant}.
Hierarchical structure based on hyponymy (and hypernymy).

Other features of WordNet:

Other features of WordNet Index of familiarity
Polysemy

Familiarity and polysemy:

board used as a noun is familiar (polysemy count = 9)
bird used as a noun is common (polysemy count = 5)
cat used as a noun is common (polysemy count = 7)
house used as a noun is familiar (polysemy count = 11)
information used as a noun is common (polysemy count = 5)
retrieval used as a noun is uncommon (polysemy count = 3)
serendipity used as a noun is very rare (polysemy count = 1) Familiarity and polysemy

Compound nouns:

Compound nouns advisory board
appeals board
backboard
backgammon board
baseboard
basketball backboard
big board
billboard
binder's board
binder board blackboard
board game
board measure
board meeting
board member
board of appeals
board of directors
board of education
board of regents
board of trustees

Overview of senses:

Overview of senses 1. board -- (a committee having supervisory powers; "the board has seven members")
2. board -- (a flat piece of material designed for a special purpose; "he nailed boards across the windows")
3. board, plank -- (a stout length of sawn timber; made in a wide variety of sizes and used for many purposes)
4. display panel, display board, board -- (a board on which information can be displayed to public view)
5. board, gameboard -- (a flat portable surface (usually rectangular) designed for board games; "he got out the board and set up the pieces")
6. board, table -- (food or meals in general; "she sets a fine table"; "room and board")
7. control panel, instrument panel, control board, board, panel -- (an insulated panel containing switches and dials and meters for controlling electrical devices; "he checked the instrument panel"; "suddenly the board lit up like a Christmas tree")
8. circuit board, circuit card, board, card -- (a printed circuit that can be inserted into expansion slots in a computer to increase the computer's capabilities)
9. dining table, board -- (a table at which meals are served; "he helped her clear the dining table"; "a feast was spread upon the board")

SET – Fall 2007 …
12. Latent semantic indexing
Singular value decomposition
…

Problems with lexical semantics:

Problems with lexical semantics Polysemy (sim < cos)
Bar, bank, jaguar, hot
Synonymy (sim > cos)
Building/edifice, Large/big, Spicy/hot
Relatedness
Doctor/patient/nurse/treatment
Sparse matrix
Need: dimensionality reduction

Techniques for dimensionality reduction:

Techniques for dimensionality reduction Based on matrix decomposition (goal: preserve clusters, explain away variance)
A quick review of matrices
Vectors
Matrices
Matrix multiplication

Eigenvectors and eigenvalues:

Eigenvectors and eigenvalues An eigenvector is an implicit “direction” for a matrix where v (eigenvector) is non-zero, though λ (eigenvalue) can be any complex number in principle
Computing eigenvalues:

Eigenvectors and eigenvalues:

Eigenvectors and eigenvalues Example:
Det (A-lI) = (-1-l)*(-l)-3*2=0
Then: l+l2-6=0; l1=2; l2=-3
For l1=2:
Solutions: x1=x2

Matrix decomposition:

Matrix decomposition If S is a square matrix, it can be decomposed into ULU-1
where
U = matrix of eigenvectors
L = diagonal matrix of eigenvalues
SU = UL
U-1SU = L
S = ULU-1

Example:

Example

Example:

Example Eigenvalues are 3, 2, 0 x is an arbitrary vector, yet Sx depends
on the eigenvalues and eigenvectors

SVD: Singular Value Decomposition:

SVD: Singular Value Decomposition A=USVT
U is the matrix of orthogonal eigenvectors of AAT
V is the matrix of orthogonal eigenvectors of ATA
The components of S are the eigenvalues of ATA
This decomposition exists for all matrices, dense or sparse
If A has 5 columns and 3 rows, then U will be 5x5 and V will be 3x3
In Matlab, use [U,S,V] = svd (A)

Example (Berry and Browne) T1: baby
T2: child
T3: guide
T4: health
T5: home
T6: infant
T7: proofing
T8: safety
T9: toddler D1: infant & toddler first aid
D2: babies & children’s room (for your home)
D3: child safety at home
D4: your baby’s health and safety: from infant to toddler
D5: baby proofing basics
D6: your guide to easy rust proofing
D7: beanie babies collector’s guide

Readings For October 11: MRS18
For October 18: MRS17, MRS19
For October 25: MRS20

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