Classification.NET: Efficient and Accurate Classification in C# Jamie Shotton Toshiba Corporate...

Classification.NET: Efficient and Accurate Classification in C#

Jamie Shotton

Toshiba Corporate Research & Development Center, Japan

http://jamie.shotton.org/work/code/Classification.NET.zip

Introduction This tutorial gives

brief introduction to classification theory ideas for practical design and implementation of

classifiers examples of classifiers in Vision

Main technical reference [Bishop, 2006]

Programming references [Murach, 2005] [Liberty, 2005]

Structure

1) Introduction to classification

2) Library Design

3) Implementing classifiers

4) Real vision research

Infer discrete class label y from a set of measurements x

Mapping from a data point to a class label

This tutorial considers D-dimensional feature space binary labels

Supervised learning labeled training set

N training examples

Classification

Vending machine

Measurements x: material, diameter, weight

Class labels y : coin value

[Bishop, 2006]

Probabilistic Interpretation Discriminative models

model conditional probability directly

Generative models are an alternative use Bayes’ theorem to infer conditional probability

Decision theory is used to choose a single y e.g. maximum a-posteriori (MAP)

[Bishop, 2006]

Example Classifiers Nearest neighbour

[Shakhnarovich, 2006]

Linear discriminants decision stumps Fisher’s linear discriminant perceptrons

Decision trees

[Bishop, 2006]

Example Classifiers Boosting

http://www.boosting.org/

Support Vector Machines (SVMs) a ‘kernel’ method

http://www.kernel-machines.org/

And many more!DEMO

TIME

[Bishop, 2006]

Structure

1) Introduction to classification

2) Library Design

3) Implementing classifiers

4) Real vision research

Classification.NET Framework for classification in C#

general purpose extensible

A few example classifiers

Download library, demo, and slides from http://jamie.shotton.org/work/code/Classification

.NET.zip many thanks to Matthew Johnson for the demo

Why C#? Modern, object-oriented language

combines best of C++ and Java pointers, interpreted or compiled, garbage collected

.NET libraries rapid development and re-use of code

Freely available IDEs http://msdn.microsoft.com/vstudio/express/visualc

sharp/

http://www.mono-project.com/

[Scientific C#]

Representing Data

accuratedouble

fast, memory efficientfloat

flexibleno performance hit

<T>

generics

IDataPoint<T>flexible

v low performance hit

T[]fast, easy, but inflexible

double[] or float[]

Representing Data

fast, easyextensible to multi-class

int

Representing Data Sets

dim

en

sio

n d…

…

matrix

row vector…

…

……

……

……

example i

So just use T[,] or T[][] arrays? Not flexible

e.g. on-the-fly computation

Representing Custom class DataSet<T>

no interface changes needed for: on-the-fly computation sparse arrays sparse data points

void Increment(DataSet<double> dataSet){

for(int i = 0; i < dataSet.Count; i++) for(int d = 0; d < dataSet.Dimensionality; d++)

dataSet.Data[i][d] ++;}

Representing Data – Summary

IDataPoint<T>

DataSet<T>

LabeledDataSet<T>

int

Classifier<T> –Classifier Base Class

public abstract class Classifier<T>

{

// Train the classifier

public abstract void Train(LabeledTrainingSet<T> trainingSet);

// Return the classification for the data point

public abstract int Classify(IDataPoint<T> dataPoint);

…

}

Structure

1) Introduction to classification

2) Library Design

3) Implementing classifiers

4) Real vision research

Nearest-Neighbour Classification (NN) Find the nearest point in training set

distance metric (e.g. Euclidean)

Classify the point as

[Shakhnarovich, 2006]

Nearest-Neighbour Classification (NN)

[Shakhnarovich, 2006]

x1

x2

‘decision boundary’

Nearest-Neighbour Classification (NN)

[Shakhnarovich, 2006]

‘Voronoi’diagram

x1

x2

Implementing NN Classification

So let’s implement NN in Classification.NET

Naïve implementation very memory hungry training is instantaneous testing is very slow

Improvements to NN Classification Distance computation ‘trick’

Distances.Euclidean( IDataPoint<double> a,IDataPoint<double> b,double minDistance )

exact

kd-trees [Beis, 1997] class NearestNeighbourFast { … } exact or approximate

Parameter sensitive hashing [Shakhnarovich, 2006] approximate

Divide space into two halves division is axis-aligned classify each half differently

Examples

2D

3D

Decision Stumps (DS)

Classifier compares value xd

with threshold µ

Returns +1 or -1 based on sign s

Decision Stumps (DS)

x1

x2

x3

µ µ

Training Decision Stumps (DS)

x1

x2

x1

x2

x1-value threshold x2-value threshold

or

Training DS

But not always this easy! not usually linearly separable D dimensions

Search for best decision stump H dimensions d thresholds µ signs

Training set error

Training DS Efficiently Project onto each dimension successively

x1

x2

projection onto x1 axis

projectiononto x2 axis

Which Thresholds To Try? Fixed discrete set

perhaps wasteful does not adapt to data

Adaptive discrete set calculate mid-points between pairs of points

Efficient calculation of training set error ² algorithm

Efficient computation of error ² Recall

Consider decision stump with sign

Trivially,

decision stump training set error

Efficient computation of error ² Linear search over µ with update

4

µ

Efficient computation of error ² Linear search over µ with update

4 5

µ

Efficient computation of error ² Linear search over µ with update

4 5 6

µ

Efficient computation of error ² Linear search over µ with update

4 5 6 5

µ

Efficient computation of error ² Linear search over µ with update

4 5 6 5 4 3 2 3

µ

Efficient computation of error ² Linear search over µ with update

µ

4 5 6 5 4 3 2 34 4 5 6 7 65 3

DS Implementationpublic class DecisionStump : Classifier<double>

{private int _d; // The data dimensionprivate double _threshold; // The thresholdprivate int _sign; // The sign (+1 or -1)

// Train the classifier

public override void Train(LabeledTrainingSet<T> trainingSet) { … }

// Return the classification for the data point

public override int Classify(IDataPoint<T> dataPoint)

{

return dataPoint[_d] > _threshold ? _sign : -_sign;

}

…

DEMO

TIME

DS Summary Complexity

reasonable training time very low memory instantaneous classification time

Classification accuracy individually, not very powerful but in combination, much more powerful…

Boosting Many variants, e.g.

AdaBoost [Freund, 1999] LogitBoost & GentleBoost [Friedman, 1998] Cascade [Viola, 2001]

super-fast JointBoost [Torralba, 2007]

multi-class with shared features

Core ideas1. combine many simple classifiers2. weight the training data points

Core Idea 1 – Classifier Combine many simple classifiers (‘weak’ or

‘base’ learners)

1. computes classification score of weak learner2. multiplies by learned confidence value3. sums over T rounds4. compares sum to zero

gives discrete classification value, +1 or -1

Core Idea 2 – Training Weight the training data points

normalised distribution emphasise poorly classified examples

Learning is greedy iteration

At round (iteration) t choose optimal weak learner

under distribution

calculateto reflect updated accuracy

Weak Learners Can use almost any type of classifier

must adapt to weights distribution must give some classification advantage

Simple change allows DS to learn with weights:

AdaBoost Learning Algorithm

Initialise weights For

train weak learner using distribution

compute training set error

calculate confidence

update weights

[Freund, 1999]

AdaBoost with DS Example

1 round2 rounds3 rounds4 rounds5 rounds50 rounds

public class AdaBoost<WeakLearner>: Classifier<double>

where WeakLearner : Classifier<double>, IWeightedLearner

{

private List<WeakLearner> _h = new List<WeakLearner>(); // The learned weak learners

private List<double> _alpha = new List<double>(); // The learned alpha values

// Return the classification for the data point

public override int Classify(IDataPoint<T> dataPoint)

{

double classification = 0.0;

// Call the weak learner Classify() method and combine results

for (int t = 0; t < _h.Count; t++)

classification += _alpha[t] * _h[t].Classify(dataPoint);

// Return the thresholded classification

return classification > 0.0 ? +1 : -1;

}

…

AdaBoost Implementation DEMO

TIME

AdaBoost Summary Complexity

complexity of weak learners x T

Weak Learners stumps, trees, even AdaBoost classifiers

e.g. AdaBoost<AdaBoost<DecisionStump>>

Classification accuracy very flexible decision boundary good generalization

Support Vector Machines (SVMs) Maximize the margin

good generalization

Kernels allow complex decision boundaries linear, Gaussian, etc.

Classification.NET class SVM wrapper for [SVM.NET] library

[Bishop, 2006], [Burges, 1998]

smaller margin larger margin

DEMO

TIME

Structure

1) Introduction to classification

2) Library Design

3) Implementing classifiers

4) Real vision research

Contour Fragments for Object Detection We can recognise objects based fragments of

contour:

Can a computer?

[Shotton, 2007a]

Contour Fragments for Object Detection Clustering learns fragments

Labeled training data object bounding boxes

Boosted classifier learns is the object centre here?

[Shotton, 2007a]

sparse image locations

ears

hin

d legs

rear

tors

o

head

head

belly

contour fragmentsexample i

dim

en

sion

d…

……

……

……

……

DEMO

TIME

TextonBoost

Goal: semantically segment an image using texture (via ‘textons’) layout context

bicycle

road

building

TextonBoost Patterns of textons

‘texture-layout filters’

Labeled training data hand-drawn segmentations

Multi-class boosted classifier [Torralba, 2007] what class is this pixel?

[Shotton, 2007b]

dense image pixels

patterns of textons

dim

en

sion

d…

……

……

……

……

example i

sheep

gra

ss

TextonBoost

[Shotton, 2007b]

cow

grass grass

tree

body road

sky

airplane

sky

grass

building

object

classes

building grass tree cow sheep sky airplane water face car

bicycle flower sign bird book chair road cat dog body boat

Summary Classifiers very powerful for Vision research

many different options available

Classification.NET gives you AdaBoost, SVMs, Decision Stumps, Nearest

Neighbour

Careful high-level library design allows rapid classifier implementation quick experimentation

References [Beis, 1997]

J.S. Beis and D.G. Lowe.Shape Indexing Using Approximate Nearest-Neighbour Search in High-Dimensional Spaces.CVPR.

[Bishop, 2006]

C.M. Bishop.Pattern Recognition and Machine Learning.

[Burges, 1998]

C.J.C. Burges.A Tutorial on Support Vector Machines for Pattern Recognition. Data Mining and Knowledge Discovery.

[Freund, 1999]

Y. Freund and R.E. Schapire.A Short Introduction to Boosting.Journal of Japanese Society for Artificial Intelligence.

[Friedman, 1998]

J. Friedman, T. Hastie, and R. Tibshirani.Additive Logistic Regression: A Statistical View of Boosting.The Annals of Statistics.

[SVM.NET]

M. Johnson.http://mi.eng.cam.ac.uk/~mj293/software_svm.html

[Liberty, 2005]

J. Liberty.Programming C#.

[Murach, 2005]

J. Murach.Murach’s C# 2005.

[Scientific C#]

F. Gilani.http://msdn.microsoft.com/msdnmag/issues/04/03/ScientificC/default.aspx

[Shakhnarovich, 2006]

G. Shakhnarovich, T. Darrel, and P. Indyk [Eds.].Nearest-Neighbor Methods in Learning and Vision.

[Shotton, 2007a]

J. Shotton, A. Blake, and R. Cipolla.Multi-Scale Categorical Object Recognition Using Contour Fragments.PAMI to appear (available on request).

[Shotton, 2007b]

J. Shotton, J.Winn, C. Rother, and A. Criminisi.TextonBoost for Image Understanding: Multi-Class Object Recognition and Segmentation by Jointly Modeling Texture, Layout, and Context.IJCV to appear (available on request).

[Torralba, 2007]

A. Torralba, K.P. Murphy, and W.T. Freeman.Sharing Visual Features for Multiclass and Multiview Object Detection.PAMI.

[Viola, 2001]

P. Viola and M. Jones.Robust Real-time Object Detection.ICCV.

Thank You!jamie@shotton.org

code and slides available at

http://jamie.shotton.org/work/code/Classification.NET.zip