ENN: Extended Nearest Neighbor Method for …...ENN: A New Approach Define generalized class-wise...

ENN: Extended Nearest Neighbor Method for Pattern Recognition

This lecture notes is based on the following paper: B. Tang and H. He, "ENN: Extended Nearest Neighbor Method for Pa@ern RecogniBon," IEEE

Computa+onal Intelligence Magazine, vol.10, no.3, pp.52 -‐ 60, Aug. 2015

Prof. Haibo He Electrical Engineering

University of Rhode Island, Kingston, RI 02881

ComputaBonal Intelligence and Self-‐AdapBve Systems (CISA) Laboratory h@p://www.ele.uri.edu/faculty/he/

Email: [email protected]

Extended Nearest Neighbor for Pa3ern Recogni6on

1.  Limita6ons of K-‐Nearest Neighbors (KNN)

2.  “Two-‐way communica-on”: Extended Nearest

Neighbors (ENN)

3.  Experimental Analysis

4.  Conclusion

Pattern Recognition ü  Parametric Classifier

§  Class-‐wise density es6ma6on, including naive Bayes, mixture Gaussian, etc.

ü  Non-‐Parametric Classifier §  Nearest Neighbors §  Neural Network §  Support Vector Machine

Nonparametric nature

Easy implementa6on

Powerfulness

Robustness

Consistency

Scale-‐SensiBve Problem: The class 1 samples dominate their near neighborhood with higher density (i.e., more concentrated distribuBon). The class 2 samples are distributed in regions with lower density (i.e., more spread out distribuBon).

Limitations of traditional KNN

Those class 2 samples which are close to the region of class 1 may be easily misclassified.

ENN: A New Approach

Define generalized class-wise statistic for each class:

Si denotes the samples in class i, and NNr(x, S) denotes the r-th nearest neighbor of x in S.

Ti measures the coherence of data from the same class. 0 ≤ Ti ≤ 1 with Ti = 1 when all the nearest neighbors of class i data are also from the same class i, and with Ti = 0 when all the nearest neighbors are from other classes.

Intra-class coherence:

Given an unknown sample Z to be classified, we iteratively assign it to class 1 and class 2, respectively, to obtain two new generalized class-wise statistics Ti

j, where j=1,2. Then, the sample Z is classified according to:

ENN Classification Rule: Maximum Gain of Intra-class Coherence.

For N-class classification:

To avoid the recalculation of generalized class-wise statistics in testing stage, an Equivalent Version of ENN is proposed:

The equivalent version has the same result as the original one, but avoids the recalculation of Ti

j

How this simple rule works better than KNN The ENN method makes a prediction in a “two-way communication” style: it considers not only who are the nearest neighbors of the test sample, but also who consider the test sample as their nearest neighbors.

Experimental Results and Analysis

Sampling methods

Synthetic Data Set: A 3-dimensional Gaussian data with 3 classes:

Considering the following four models, their error rates are:

Model 2 Class 1 Class 2 Class 3

KNN ENN KNN ENN KNN ENN k = 3 32 31.9 39.3 34.4 31.4 30.5 k = 5 31.2 29.7 40.5 33.7 28.6 26.7 k = 7 28.5 28.3 40.8 33.6 25 24.3 Model 3 Class 1 Class 2 Class 3 KNN ENN KNN ENN KNN ENN k = 3 33.2 31 27 26.8 38.8 33.7 k = 5 30.3 27.3 24 23.2 40.2 33.5 k = 7 26.7 25.1 20.8 20.8 40.6 33

2 2 21 2 35, 20, 5σ σ σ= = =

2 2 21 2 35, 5, 20σ σ σ= = =

• MNIST Handwri3en Digit Recogni6on

Sampling methods

Real-life Data Sets:

Data Examples

Sampling methods

Real-life Data Sets:

t-‐test shows that ENN can significantly improve the classifica6on performance in 17 out of 20 datasets, in comparison with KNN.

•  20 data sets from UCI Machine Learning Repository

B. Tang and H. He, "ENN: Extended Nearest Neighbor Method for Pa3ern Recogni6on," IEEE Computa6onal Intelligence Magazine, vol.10, no.3, pp.52 -‐ 60, Aug. 2015

ENN

Summary: Three versions of ENN

ENN.V1





ENN.V2



Online Resources

h@p://www.ele.uri.edu/faculty/he/research/ENN/ENN.html

Supplementary materials and Matlab source code implementaBon available at:

1.  A new ENN classifica6on methodology based on the maximum gain of

intra-‐class coherence.

2.  “Two-‐way communica-on”: ENN considers not only who are the nearest

neighbors of the test sample, but also who consider the test sample as

their nearest neighbors.

3.  Important and useful for many other machine learning and data mining

problems, such as density es6ma6on, clustering, regression, among

others.

Conclusion


ENN: Extended Nearest Neighbor Method for …...ENN: A New Approach Define generalized class-wise...

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