SLIDE 25 Overview Discourse segmentation Discourse coherence theories Penn Discourse Treebank 2.0 Unsupervised coherence Conclusion
Divisive clustering (Choi 2000)
1 Compare all sentences pairwise for cosine similarity, to
create a matrix of similarity values.
is computed using the cosine measure as shown in equation 1. This is applied to all sentence pairs to generate a similarity matrix.
E:, f.~., x :~.,
sim(x,y) = ~_~., .~., ,,,
f2.xEjf2. (1)
Figure 1 shows an example of a similarity matrix ~ . High similarity values are represented by bright pix-
- els. The bottom-left and top-right pixel show the
self-similarity for the first and last sentence, respec-
- tively. Notice the matrix is symmetric and contains
bright square regions along the diagonal. These re- gions represent cohesive text segments. Each value in the similarity matrix is replaced by its rank in the local region. The rank is the num- ber of neighbouring elements with a lower similarity
- value. Figure 2 shows an example of image ranking
using a 3 x 3 rank mask with output range {0, 8}. For segmentation, we used a 11 x 11 rank mask. The
- utput is expressed as a ratio r (equation 2) to cir-
cumvent normalisation problems (consider the cases when the rank mask is not contained in the image).
Similarity matrix Rank matrix I 5 4 ~7 1~
i7 8,6 3 i 7
Step 1
i2.1' ~t
LTl~ '6,, ~ 7 ,
Step 2
12 14
Similarity matrix Rank matrix
2 3 2 I
;
4, 7
a
I
Step 3 Step 4
Figure 2: A working example of image ranking. Figure 1: An example similarity matrix. 3.2 Ranking For short text segments, the absolute value of
sire(x, y) is unreliable. An additional occurrence of
a common word (reflected in the numerator) causes a disproportionate increase in sim(x,y) unless the denominator (related to segment length) is large. Thus, in the context of text segmentation where a segment has typically < 100 informative tokens, one can only use the metric to estimate the order of sim- ilarity between sentences, e.g. a is more similar to b than c. Furthermore, language usage varies throughout a
- document. For instance, the introduction section of
a document is less cohesive than a section which is about a particular topic. Consequently, it is inap- propriate to directly compare the similarity values from different regions of the similarity matrix. In non-parametric statistical analysis, one com- pares the rank of data sets when the qualitative be- haviour is similar but the absolute quantities are un-
- reliable. We present a ranking scheme which is an
adaptation of that described in (O'Neil and Denos, 1992). 1The contrast of the image has been adjusted to highlight the image features. # of elements with a lower value
r = (2)
# of elements examined To demonstrate the effect of image ranking, the process was applied to the matrix shown in figure 1 to produce figure 32 . Notice the contrast has been improved significantly. Figure 4 illustrates the more subtle effects of our ranking scheme, r(x) is the rank (1 x 11 mask) of f(x) which is a sine wave with decaying mean, amplitude and frequency (equation 3). Figure 3: The matrix in figure 1 after ranking. 2The process was applied to the original matrix, prior to contra.st enhancement. The output image has not been en- hanced. :97
2
For each value s, find the n ⇥ n submatrix Ns with s at its center and replace s with the value |{s0 2 Ns : s0 < s}| n2
is computed using the cosine measure as shown in equation 1. This is applied to all sentence pairs to generate a similarity matrix.
E:, f.~., x :~.,
sim(x,y) = ~_~., .~., ,,,
f2.xEjf2. (1)
Figure 1 shows an example of a similarity matrix ~ . High similarity values are represented by bright pix-
- els. The bottom-left and top-right pixel show the
self-similarity for the first and last sentence, respec-
- tively. Notice the matrix is symmetric and contains
bright square regions along the diagonal. These re- gions represent cohesive text segments. Each value in the similarity matrix is replaced by its rank in the local region. The rank is the num- ber of neighbouring elements with a lower similarity
- value. Figure 2 shows an example of image ranking
using a 3 x 3 rank mask with output range {0, 8}. For segmentation, we used a 11 x 11 rank mask. The
- utput is expressed as a ratio r (equation 2) to cir-
cumvent normalisation problems (consider the cases when the rank mask is not contained in the image).
Similarity matrix Rank matrix I 5 4 ~7 1~
i7 8,6 3 i 7
Step 1
i2.1' ~t
LTl~ '6,, ~ 7 ,
Step 2
12 14
Similarity matrix Rank matrix
2 3 2 I
;
4, 7
a
I
Step 3 Step 4
Figure 2: A working example of image ranking. Figure 1: An example similarity matrix. 3.2 Ranking For short text segments, the absolute value of
sire(x, y) is unreliable. An additional occurrence of
a common word (reflected in the numerator) causes a disproportionate increase in sim(x,y) unless the denominator (related to segment length) is large. Thus, in the context of text segmentation where a segment has typically < 100 informative tokens, one can only use the metric to estimate the order of sim- ilarity between sentences, e.g. a is more similar to b than c. Furthermore, language usage varies throughout a
- document. For instance, the introduction section of
a document is less cohesive than a section which is about a particular topic. Consequently, it is inap- propriate to directly compare the similarity values from different regions of the similarity matrix. In non-parametric statistical analysis, one com- pares the rank of data sets when the qualitative be- haviour is similar but the absolute quantities are un-
- reliable. We present a ranking scheme which is an
adaptation of that described in (O'Neil and Denos, 1992). 1The contrast of the image has been adjusted to highlight the image features. # of elements with a lower value
r = (2)
# of elements examined To demonstrate the effect of image ranking, the process was applied to the matrix shown in figure 1 to produce figure 32 . Notice the contrast has been improved significantly. Figure 4 illustrates the more subtle effects of our ranking scheme, r(x) is the rank (1 x 11 mask) of f(x) which is a sine wave with decaying mean, amplitude and frequency (equation 3). Figure 3: The matrix in figure 1 after ranking. 2The process was applied to the original matrix, prior to contra.st enhancement. The output image has not been en- hanced. :97
3
Apply something akin to Reynar’s algorithm to find the cluster boundaries (which are clearer as a result of the local smoothing
is computed using the cosine measure as shown in equation 1. This is applied to all sentence pairs to generate a similarity matrix.
E:, f.~., x :~.,
sim(x,y) = ~_~., .~., ,,,
f2.xEjf2. (1)
Figure 1 shows an example of a similarity matrix ~ . High similarity values are represented by bright pix-
- els. The bottom-left and top-right pixel show the
self-similarity for the first and last sentence, respec-
- tively. Notice the matrix is symmetric and contains
bright square regions along the diagonal. These re- gions represent cohesive text segments. Each value in the similarity matrix is replaced by its rank in the local region. The rank is the num- ber of neighbouring elements with a lower similarity
- value. Figure 2 shows an example of image ranking
using a 3 x 3 rank mask with output range {0, 8}. For segmentation, we used a 11 x 11 rank mask. The
- utput is expressed as a ratio r (equation 2) to cir-
cumvent normalisation problems (consider the cases when the rank mask is not contained in the image).
Similarity matrix Rank matrix I 5 4 ~7 1~
i7 8,6 3 i 7
Step 1
i2.1' ~t
LTl~ '6,, ~ 7 ,
Step 2
12 14
Similarity matrix Rank matrix
2 3 2 I
;
4, 7
a
I
Step 3 Step 4
Figure 2: A working example of image ranking. Figure 1: An example similarity matrix. 3.2 Ranking For short text segments, the absolute value of
sire(x, y) is unreliable. An additional occurrence of
a common word (reflected in the numerator) causes a disproportionate increase in sim(x,y) unless the denominator (related to segment length) is large. Thus, in the context of text segmentation where a segment has typically < 100 informative tokens, one can only use the metric to estimate the order of sim- ilarity between sentences, e.g. a is more similar to b than c. Furthermore, language usage varies throughout a
- document. For instance, the introduction section of
a document is less cohesive than a section which is about a particular topic. Consequently, it is inap- propriate to directly compare the similarity values from different regions of the similarity matrix. In non-parametric statistical analysis, one com- pares the rank of data sets when the qualitative be- haviour is similar but the absolute quantities are un-
- reliable. We present a ranking scheme which is an
adaptation of that described in (O'Neil and Denos, 1992). 1The contrast of the image has been adjusted to highlight the image features. # of elements with a lower value
r = (2)
# of elements examined To demonstrate the effect of image ranking, the process was applied to the matrix shown in figure 1 to produce figure 32 . Notice the contrast has been improved significantly. Figure 4 illustrates the more subtle effects of our ranking scheme, r(x) is the rank (1 x 11 mask) of f(x) which is a sine wave with decaying mean, amplitude and frequency (equation 3). Figure 3: The matrix in figure 1 after ranking. 2The process was applied to the original matrix, prior to contra.st enhancement. The output image has not been en- hanced. :97
Choi (2000) reports substantial accuracy gains over both TextTiling and dotplotting.
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