1. A Fast and Scalable Nearest Neighbor Based Classification
Taufik Abidin and William Perrizo
Department of Computer Science
North Dakota State University

2. Outline Nearest Neighbors Classification Problems
SMART TV (SMall Absolute diffeRence of ToTal Variation): A Fast and Scalable Nearest Neighbors Classification Algorithm
SMART TV in Image Classification

3. Search for the K-Nearest Neighbors
Classification
Given a (large) TRAINING SET, R(A1,…,An, C), with C=CLASSES and (A1…An)=FEATURES
Classification task is: to label the unclassified objects based on the pre-defined class labels of objects in the training set
Prominent classification algorithms: SVM, KNN, Bayesian, etc.
Training Set
Search for the K-Nearest Neighbors
Vote the class
Unclassified Object

4. Problems with KNN
Finding k-nearest neighbors is expensive when the training set contains millions of objects (very large training set)
The classification time is linear to the size of the training set
Can we make it faster and scalable?

5. P-Tree Vertical Data Structure
A1 A2 A3 A4
R[A1] R[A2] R[A3] R[A4] = 
R11 R12 R13 R21 R22 R23 R31 R32 R33 R41 R42 R43
The construction steps of P-trees:
1. Convert the data into binary
2. Vertically project each attribute
3. Vertically project each bit position
4. Compress each bit slice into a P-tree
0 0
P11 P12 P13 P21 P22 P23 P31 P32 P33 P41 P42 P43
0 1 10
1 0 01
1 0
0 1 ^

6. Total Variation
The Total Variation of a set X about (the mean), , measures total squared separation of objects in X about , defined as follows:
TV(X,)=TV(X,x33) 1 2 3 4 5 X TV g
a- a  Y

7. Total Variation (Cont.)
21 x x 0 +
21 x x 1 = 5 2 3
1 0
1 1
21 x x 1 = 5

8. Total Variation (Cont.)

9. Total Variation (Cont.)

10. Total Variation (Cont.)

11. The Independency of RC
The root count operations are independence from , which allows us to run the operations once in advance and retain the count results
In classification task, the sets of classes are known and unchanged. Thus, the total variation of an object about its class can be pre-computed

12. Overview of SMART-TV Compute Root Count Store the root count
Measure TV of each object
Large
Training Set
Store the root count
and TV values
Preprocessing Phase
Unclassified Object
Approximate the candidate set of NNs
Search the K-nearest neighbors for the candidate set
Vote
Classifying Phase

13. Preprocessing Phase
Compute the root counts of each class Cj,  j  number of classes. Store the results.
Complexity: O(kdb2) where k is the number of classes, d is the total of dimensions, and b is the bit-width.
Compute , 1 j  number of classes.
Complexity: O(n) where n is the cardinality of the training set. Also, retain the results.

14. Classifying Phase Stored values of root count and TV Classifying Phase
Unclassified Object
Approximate the candidate set of NNs
Search the K-nearest neighbors from the candidate set
Vote
Classifying Phase

15. Classifying Phase
For each class Cj with nj objects, 1  j  number of classes, do the followings:
a. Compute , where is the unclassified object
Find hs objects in Cj such that the absolute difference between the total variation of the objects in Cj and the total variation of about Cj are the smallest, i.e.
Let A be an array and , where
Store all objectIDs in A into TVGapList

16. Classifying Phase (Cont.)
For each objectIDt, 1 t  Len(TVGapList) where Len(TVGapList) is equal to hs times the total number of classes, retrieve the corresponding object features from the training set and measure the pair-wise Euclidian distance between and , i.e.
and determine the k nearest neighbors of
Vote the class label for using the k nearest neighbors

17. Dataset KDDCUP-99 Dataset (Network Intrusion Dataset)
4.8 millions records, 32 numerical attributes
6 classes, each contains >10,000 records
Class distribution:
Testing set: 120 records, 20 per class
4 synthetic datasets (randomly generated):
10,000 records (SS-I)
100,000 records (SS-II)
1,000,000 records (SS-III)
2,000,000 records (SS-IV)
Normal
972,780
IP sweep
12,481
Neptune
1,072,017
Port sweep
10,413
Satan
15,892
Smurf
2,807,886

18. Dataset (Cont.) OPTICS dataset
8,000 points, 8 classes (CL-1, CL-2,…,CL-8)
2 numerical attributes
Training set: 7,920 points
Testing set: 80 points, 10 per class

19. Dataset (Cont.) IRIS dataset 150 samples
3 classes (iris-setosa, iris-versicolor, and iris-virginica)
4 numerical attributes
Training set: 120 samples
Testing set: 30 samples, 10 per class

20. Speed and Scalability Speed and Scalability Comparison (k=5, hs=25)
Algorithm
x 1000 cardinality 10
100
1000
2000
4891
SMART-TV
0.14
0.33
2.01
3.88
9.27
P-KNN
0.89
1.06
3.94
12.44
30.79
KNN
0.39
2.34
23.47
49.28
　NA
Machine used:
Intel Pentium 4 CPU 2.6 GHz machine, 3.8GB RAM, running Red Hat Linux

21. Classification Accuracy (Cont.)
Classification Accuracy Comparison (SS-III), k=5, hs=25
Algorithm
Class TP FP P R F
SMART-TV
normal 18
1.00
0.90
0.95
ipsweep 20 1
0.98
neptune
portsweep
satan 17 2
0.85
0.87
smurf 4
0.83
0.91
P-KNN 15
0.75
0.86 14
0.93
0.70
0.80 5
0.89
KNN 3
0.94

22. Overall Classification Accuracy Comparison
Overall Accuracy
Overall Classification Accuracy Comparison
Datasets
SMART-TV
PKNN
KNN
IRIS
0.97
0.71
OPTICS
0.96
0.99
SS-I
0.72
0.89
SS-II
0.92
0.91
SS-III
0.94
SS-IV NI
0.93 NA

23. Outline Nearest Neighbors Classification Problems
SMART TV (SMall Absolute diffeRence of ToTal Variation): A Fast and Scalable Nearest Neighbors Classification Algorithm
SMART TV in Image Classification

24. Image Preprocessing
We extracted color and texture features from the original pixel of the images
Color features: We used HVS color space and quantized the images into 52 bins i.e. (6 x 3 x 3) bins
Texture features: we used multi-resolutions Gabor filter with two scales and four orientation (see B.S. Manjunath, IEEE Trans. on Pattern Analysis and Machine Intelligence, 1996)

25. Image Dataset - 54 from color features - 16 from texture features
Corel images (
10 categories
Originally, each category has 100 images
Number of feature attributes:
- 54 from color features
- 16 from texture features
We randomly generated several bigger size datasets to evaluate the speed and scalability of the algorithms.
50 images for testing set, 5 for each category

26. Image Dataset

27. Example on Corel Dataset

28. Results Class SMART-TV KNN k=3 k=5 k=7 hs=15 hs=25 hs=35 C1 0.69 0.72
0.75
0.74
0.73
0.78
0.81
0.77
0.79 C2
0.64
0.60
0.59
0.62
0.68
0.63
0.66 C3
0.65
0.67
0.76
0.57
0.70 C4
0.84
0.87
0.90
0.88 C5
0.91
0.92
0.93
0.89
0.94 C6
0.61
0.71 C7
0.85 C8
0.96 C9
0.52
0.43
0.45
0.54
C10
0.82

29. Results
Classification Time

30. Results
Preprocessing Time

31. Summary
A nearest-based classification algorithm that starts its classification steps by approximating a number of candidates of nearest neighbors
The absolute difference of total variation between data points in the training set and the unclassified point is used to approximate the candidates
The algorithm is fast, and it scales well in very large dataset. The classification accuracy is very comparable to that of KNN algorithm.