an optimized approach for knn text categorization using p-trees imad rahal and william perrizo...

AN OPTIMIZED APPROACH FOR kNN TEXT CATEGORIZATION USING P-

TREES

Imad Rahal and William PerrizoComputer Science DepartmentNorth Dakota State University

Fargo, NDimad.rahal@ndsu.nodak.edu

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Outline The Text Categorization problem The P-tree technology Vector Space Model Proposed Solution

Intervalization (discretization) P-tree representation Similarity measures Categorization algorithm Performance analysis study

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Text categorization problem Text Categorization (topic spotting or text

classification) is the process of assigning categories or labels to documents based entirely on their contents

Problems text has no explicit structured unlike other data

(e.g. relational data) information is described freely in the documents (After introducing structure) huge number of

features

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Motivation Increase in the number of text documents (on

the Internet!) Medical articles Research Publications E-mails News reports (e.g. Reuters) others

Most algorithms fail to scale up because of the curse of dimensionality

Most algorithms suffer from relatively low accuracy

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The P-tree technology

Tree-like data structure that store numeric (and categorical) relational data in bit-compressed format by splitting each attribute into bits representing each bit position by a P-

tree

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Transformation to binary

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Each binary column will form a P-tree

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AND and OR operations

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Complement operation

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P-trees are characterized by 1-time creation cost Compression High speed processing (ANDing, no DB scans)

The latest bench mark on P-tree ANDing has shown a speed of 6 ms for two 1320x1320 images (i.e. two bit sequences each containing 1.6 million bits represented using P-trees)

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We have 8 P-trees in total for each attribute shown in the previous example: PA,7 PA,6 PA,5 PA,4 PA,3 PA,2 PA,1 and PA,0

To query for a certain attribute value, say Attribute A = 1110 0001, we do the following: PA,1110 0001 = PA,7 & PA,6 & PA,5 & P’A,4 & P’A,3 & P’A,2 & P’A,1 & PA,0

We can have varying bit precision. We query for A = 001, we do the following: PA,001 = P’A,3 & P’A,2 & PA,0

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Vector Space Model Each document is represented as a

vector whose dimensions are the terms in the initial document collection

Each vector coordinate is a term and has a numeric value which represents its relevance to the document. Usually higher values imply higher relevance

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Three popular weighting schemes are: Binary, TF, and TF*IDF.

The binary scheme uses the values 1 and 0 to reveal whether a term exists in the document or not

The term frequency (TF) scheme counts the occurrences of a term in a document. Usually measures are normalized to help overcome the problems associated with document length

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The TF*IDF scheme multiplies the coordinate measure derived by the TF scheme by a global weight called the IDF. The IDF measure for term t is defined as log(N/Nt) where N is the total number of documents and Nt is the total number of documents containing t. The cosine normalization is usually used

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Proposed solution Model 1: Classification over binary

representation is not accurate but fast

Model 2: Classification using exact counts (tf, idf, normalized tf…) more accurate but slower (very high dimensional space)

This can be viewed as a concept hierarchy

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Work along this hierarchy by using intervals Better speed than model 2

(approaching to Model1) Better accuracy than model 1

(approaching Model2)

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An example say we’re using TF (values normalized in the

range of [0,1]) divide range into 4 intervals: None, Low,

Medium, High Each interval will be represented by a string

of bits (we have four intervals so we need 2 bits)

None = “00”, Low =“01” , Medium = “10” and High=“11” (note the order among them)

Each bit position will be represented by a P-tree; so we have 2 P-trees for every dimension

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Term 1 Term 2 Term 3 Term 4 Term 5 Term 6 Term 7 C 1 C 2Doc 1 "00" "00" "00" "01" "01" "10" "11" 0 1

Doc 2 "00" "00" "00" "10" "01" "10" "11" 0 1

Doc 3 "00" "11" "00" "01" "00" "00" "11" 0 1

Doc 4 "00" "00" "00" "01" "01" "01" "00" 1 0

Doc 5 "11" "00" "00" "10" "01" "00" "11" 1 0

Doc 6 "11" "00" "11" "00" "01" "01" "00" 1 0

Doc 7 "01" "00" "11" "10" "00" "00" "11" 0 1

Doc 8 "10" "11" "01" "01" "01" "00" "00" 1 0

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kNN Algorithm Used to find the k most similar points

(referred to as k neighbours) to some given point P in some space and then assigning a proper class to P using the class labels of the k neighbours

Usually proceeds by the selecting the neighbours first (selection phase) and then assigning the class label (voting phase)

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Categorization Algorithm: Selection Phase Initialize a P-tree, Pnn, to contain only pure-1 quadrants

(i.e. all entries in it are 1’s) – identity P-tree Order the set of all term P-trees S in descending order from

term P-trees representing higher to lower interval values in dnew

For every term P-tree, Pt, in S do the following AND Pnn with Pt If root count of Pnn is less than k, expand Pt by removing the

rightmost bit from the interval value (i.e. interval 01 and 00 become 0 and intervals 10 and 11 become 1). This could be done by recalculating the Pt while disregarding the rightmost bit P-tree. Repeat this step until the root count of Pnn AND Pt is greater than k – this is guaranteed to happen at least when all the bits are disregarded.

Else, put the result in Pnn Loop

End of selection phase

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Term 1 Term 2 Term 3 Term 4 Term 5 Term 6 Term 7 C 1 C 2Doc 1 "00" "00" "00" "01" "01" "10" "11" 0 1

Doc 2 "00" "00" "00" "10" "01" "10" "11" 0 1

Doc 3 "00" "11" "00" "01" "00" "00" "11" 0 1

Doc 4 "00" "00" "00" "01" "01" "01" "00" 1 0

Doc 5 "11" "00" "00" "10" "01" "00" "11" 1 0

Doc 6 "11" "00" "11" "00" "01" "01" "00" 1 0

Doc 7 "01" "00" "11" "10" "00" "00" "11" 0 1

Doc 9 "10" "11" "01" "01" "01" "00" "00" 1 0

dnew "00" "00" "11" "01" "01" "10" "11"

Pnn P3 P7 P6 P4 P5 P1 P2

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Categorization Algorithm: Voting Phase For every class ci, loop through dnew vector and

do the following for every term tj in dnew vector:

Get the P-tree representing the neighboring documents (Pnn from the selection phase) having the same value for t (Pt) and class ci (Pi). This could be done by calculating Presult = Ptj AND Pnn AND Pi

If the term under consideration has a value Ij then multiply the root count of Presult by (Ij+1)

//if we want to neglect Ij=“00” then don’t add 1 Add the result to the counter of ci, w(ci). Loop

Select the class ck having the largest counter w(ck) as the respective class of dnew

End of voting phase

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Performance analysis study

Compared accuracy and speed to cosine-similarity KNN and accuracy to string kernels approach by Lodhi et al. (Journal of Machine Learning Feb. 2002)

Speed Used synthetic document x term

matrices with different sizes

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Accuracy: Followed the sampling approach depicted in the

string kernels approach Tested over a subset of the Reuters-21578 collection

(analysis over the whole dataset if still underway) Experimented on four classes namely:

acquisition, earn, corn, and crude. We used k=3 and a 4-interval value set, I0=[0,0], I1=(0,0.25], I2=(0.25,0.75] and I3=(0.75,1].

Averaged precision (not shown), recall (not shown) and F1-measures (2pr/(p+r)) for our approach and cosine KNN and compared with string kernels

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F-1 Measure values Class/Method P-tree based KNN String kernels

Earn 95.4 85.5 94.4

Acq 90.2 80.8 87.2

Crude 87.3 73.8 94.9

Corn 88.7 66.0 83.1

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Compared to the KNN approach, we show much better results in terms of speed and accuracy The reason for the improvement in speed

is mainly related to the complexity of the selection phases: O(n)

VS O(mn) where m is the size of the dataset – number of rows – and n is the number of dimensions.

and P-tree ANDing speed.

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As for accuracy, the KNN approach uses the angle

between the vectors and considers all terms

Our approach uses ANDing to compare the closeness of the value of each term and to ignore unneeded terms (those whose ANDing renders a less than k neighbors)

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As for the kernels approach, it would not be appropriate to compare speeds here because the two approaches are fundamentally different. Example-based VS Eager Context sensitive VS Context insensitive

In general, results were very comparable results

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The range for the precision, recall and F1 measurements in the other two approaches spreads over a wider range than they do in ours which indicates that our P-tree based approach’s accuracy is less variable across categories or classes thus leading to more stable results in general

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Drawsbacks

Needs tuning We need to decide upon the

number of intervals and their ranges ahead of time (analysis for varying those is still underway)

Since this is a KNN algorithm, K must also be known ahead of time

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Conclusion

We have shown Higher accuracy

the use of sequential ANDing in selection

Very fair voting Use of closed neighbourhood (in case

root count is greater than K) – refer to Maleq Khan’s thesis (Dec. 2001) for previous work

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Better space utilization reduced compressed space

Reduced space due to intervalization (from 8 bits to 2 bits reduction by a factor of 4)

Compression due to the use of P-trees Higher speed

Due to P-trees No DB scans Based on the AND operation which is among the

fastest computer instructions

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Future direction Solve the problem of random

ANDing for term P-trees having the same values? Information gain?

Test the effects of varying the number of intervals and their values over different datasets

Analyze speed and accuracy results over large datasets (all Reuters collection)