Slides for paper
Reconstructing Textual Documents from n-grams
KDD 2015 (Knowledge Discovery and Data Mining)
http://dl.acm.org/citation.cfm?id=2783361
Pedagogy of Mathematics (Part II) - Set language introduction and Ex.1.4, Set Language, Maths, IX std Maths, Samacheerkalvi maths, II year B.Ed., Pedagogy,
Pedagogy of Mathematics (Part II) - Set language introduction and Ex.1.4, Set Language, Maths, IX std Maths, Samacheerkalvi maths, II year B.Ed., Pedagogy,
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and its applications such as coding theory, communication networks, and block design. An important tool
for investigation of such graphs is their spectra, which is the set of eigenvalues of adjacency matrix of a
graph. Let G be a finite simple group of Lie type and X be the set homogeneous elements of the associated
geometry.
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Cancer cell metabolism: special Reference to Lactate PathwayAADYARAJPANDEY1
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IN CANCER CELL:
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introduction to WARBERG PHENOMENA:
WARBURG EFFECT Usually, cancer cells are highly glycolytic (glucose addiction) and take up more glucose than do normal cells from outside.
Otto Heinrich Warburg (; 8 October 1883 – 1 August 1970) In 1931 was awarded the Nobel Prize in Physiology for his "discovery of the nature and mode of action of the respiratory enzyme.
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2. Motivation: Privacy-preserving data mining
Share textual data for mutual benefit, general good or contractual reasons
But not all of it:
text analytics on private documents
1
3. Motivation: Privacy-preserving data mining
Share textual data for mutual benefit, general good or contractual reasons
But not all of it:
text analytics on private documents
marketplace scenarios [Cancedda ACL 2012]
1
4. Motivation: Privacy-preserving data mining
Share textual data for mutual benefit, general good or contractual reasons
But not all of it:
text analytics on private documents
marketplace scenarios [Cancedda ACL 2012]
copyright concerns
1
5. Problem
1 Given n-gram information of a document d, how well can we
reconstruct d?
2 If I want/have to share n-gram statistics, what is a good strategy to
avoid reconstruction, while preserving utility of data?
2
7. Example
s = $ a rose rose is a rose is a rose #
2-grams:
$ a 1
a rose 3
rose rose 1
rose is 2
is a 2
rose # 1
3
8. Example
s = $ a rose rose is a rose is a rose #
2-grams:
$ a 1
a rose 3
rose rose 1
rose is 2
is a 2
rose # 1
Note that the same 2-grams are obtained starting from:
s = $ a rose is a rose rose is a rose #
s = $ a rose is a rose is a rose rose #
3
9. Example
s = $ a rose rose is a rose is a rose #
2-grams:
$ a 1
a rose 3
rose rose 1
rose is 2
is a 2
rose # 1
Note that the same 2-grams are obtained starting from:
s = $ a rose is a rose rose is a rose #
s = $ a rose is a rose is a rose rose #
=⇒ Find large chunks of text of whose presence we are
certain
3
10. Problem Encoding
An n-gram corpus is encoded as a graph, subgraph of the de Bruijn graph, where
edges correspond to n-grams
0
1
$ a , 1
2
a rose , 3
rose rose , 1
3
rose is , 2
4
rose # , 1
is a , 2
4
11. Problem Encoding
[2, 2, 3, 1] → rose rose is a
0
1
$ a , 1
2
a rose , 3
rose rose , 1
3
rose is , 2
4
rose # , 1
is a , 2
4
13. Problem encoding
Given such a graph, each Eulerian path gives a plausible reconstruction
Problem: Find those parts that are common in all of them
14. Problem encoding
Given such a graph, each Eulerian path gives a plausible reconstruction
Problem: Find those parts that are common in all of them
BEST Theorem, 1951
Given an Eulerian graph G = (V , E), the number of different Eulerian
cycles is
Tw (G)
v∈V
(d(v) − 1)!
Tw (G) is the number of trees directed towards the root at a fixed node w
5
15. Problem Encoding
[0, 1, 2] → $ a rose
0
1
$ a , 1
2
a rose , 3
rose rose , 1
3
rose is , 2
4
rose # , 1
is a , 2
6
16. Definitions
ec(G): the set of all Eulerian paths of G
given the path c = e1, . . . , en; (c) = [label(e1), . . . , label(en)]
s(c) = label(e1).label(e2). . . . .label(en) (overlapping concatenation)
17. Definitions
ec(G): the set of all Eulerian paths of G
given the path c = e1, . . . , en; (c) = [label(e1), . . . , label(en)]
s(c) = label(e1).label(e2). . . . .label(en) (overlapping concatenation)
Given G, we want G∗ st:
1 is equivalent:
{s(c) : c ∈ ec(G)} = {s(c) : c ∈ ec(G∗
)}
2 is irreducible:
∃e1, e2 ∈ E∗
: [label(e1), label(e2)] appears in all (c), c ∈ ec(G∗
)
18. Definitions
ec(G): the set of all Eulerian paths of G
given the path c = e1, . . . , en; (c) = [label(e1), . . . , label(en)]
s(c) = label(e1).label(e2). . . . .label(en) (overlapping concatenation)
Given G, we want G∗ st:
1 is equivalent:
{s(c) : c ∈ ec(G)} = {s(c) : c ∈ ec(G∗
)}
2 is irreducible:
∃e1, e2 ∈ E∗
: [label(e1), label(e2)] appears in all (c), c ∈ ec(G∗
)
Given G∗ we can just read maximal blocks from the labels.
7
19. Example
s = $ a rose rose is a rose is a rose #
2
rose rose , 1
rose is a rose , 2
4
rose # , 1
0
$ a rose , 1
8
39. Conclusions
How well can textual documents be reconstructed from their list of
n-grams
Resilience to standard noisifying approach
Better noisifying by adding (instead of removing) n-grams
18
42. Rule 1 (Pigeonhole rule)
Incoming edges of x: ( v1, x, 1 , p1), . . . , ( vn, x, n , pn)
Outgoing edges ( x, w1, t1 , k1) . . . , ( x, wm, tm , km).
If ∃i, j such that pi > d(x) − kj .
then
E = E ({ vi , x, i , a), (x, wj , tj , a)}) ∪ { vi , wj , i .tj , a)} where
a = pi − (d(x) − kj ).
if a = d(x) then V = V {x}, else V = V
21
43. Rule 2: non-local information
x division point dividing G in components G1, G2. If ˆdinG1
(x) = 1 and
ˆdoutG2
(x) = 1 (( v, x, , p) and ( x, w, t , k)), then
E = (E {( v, x, , 1), ( x, w, t , 1)}) ∪ {( v, w, .t , 1)}
V = V
22
