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Machine Learning workshop by GDSC Amity University Chhattisgarh

Clustering Strategies
? K-means
�C Iteratively re-assign points to the nearest cluster
center
? Agglomerative clustering
�C Start with each point as its own cluster and iteratively
merge the closest clusters
? Mean-shift clustering
�C Estimate modes of pdf
? Spectral clustering
�C Split the nodes in a graph based on assigned links with
similarity weights
As we go down this chart, the clustering strategies
have more tendency to transitively group points
even if they are not nearby in feature space

The machine learning framework
? Apply a prediction function to a feature representation of
the image to get the desired output:
f( ) = ��apple��
f( ) = ��tomato��
f( ) = ��cow��
�ݺ�ߣ credit: L. Lazebnik

Prediction
Steps
Training
Labels
Training
Images
Training
Training
Image
Features
Image
Features
Testing
Test Image
Learned
model
Learned
model
�ݺ�ߣ credit: D. Hoiem and L. Lazebnik

Features
? Raw pixels
? Histograms
? GIST descriptors
? �� ݺ�ߣ credit: L. Lazebnik

Classifiers: Nearest neighbor
f(x) = label of the training example nearest to x
? All we need is a distance function for our inputs
? No training required!
Test
example
Training
examples
from class 1
Training
examples
from class 2

Classifiers: Linear
? Find a linear function to separate the classes:
f(x) = sgn(w ? x + b)

? Images in the training set must be annotated with the
��correct answer�� that the model is expected to produce
Contains a motorbike
Recognition task and supervision

Unsupervised ��Weakly�� supervised Fully supervised
Definition depends on task

Generalization
? How well does a learned model generalize from
the data it was trained on to a new test set?
Training set (labels known) Test set (labels
unknown)

Bias-Variance Trade-off
? Models with too few
parameters are
inaccurate because of a
large bias (not enough
flexibility).
? Models with too many
parameters are
inaccurate because of a
large variance (too much
sensitivity to the sample).
�ݺ�ߣ credit: D. Hoiem

Generative vs. Discriminative Classifiers
Generative Models
Represent both the data and
the labels
Often, makes use of
conditional independence
and priors
Examples
? Na?ve Bayes classifier
? Bayesian network
Models of data may apply to
future prediction problems
Discriminative Models
? Learn to directly predict the
labels from the data
? Often, assume a simple
boundary (e.g., linear)
? Examples
�C Logistic regression
�C SVM
�C Boosted decision trees
? Often easier to predict a
label from the data than to
model the data

Classification
Assign input vector to one of two or more classes
Any decision rule divides input space into decision
regions separated by decision boundaries

K-nearest neighbor
x x
x
x
x
x
x
x
o
o
o
o
o
o
o
x2
x1
+
+

1-nearest neighbor
x x
x
x
x
x
x
x
o
o
o
o
o
o
o
x2
x1
+
+

3-nearest neighbor
x x
x
x
x
x
x
x
o
o
o
o
o
o
o
x2
x1
+
+

5-nearest neighbor
x x
x
x
x
x
x
x
o
o
o
o
o
o
o
x2
x1
+
+

Classifiers: Linear SVM
x x
x
x
x
x
x
x
o
o
o
o
o
x2
x1
f(x) = sgn(w ? x + b)

Classifiers: Linear SVM
x x
x
x
x
x
x
x
o
o
o
o
o
o
x2
x1
f(x) = sgn(w ? x + b)

? Datasets that are linearly separable work out great:
? But what if the dataset is just too hard?
? We can map it to a higher-dimensional space:
0 x
0 x
0 x
x2
Nonlinear SVMs
�ݺ�ߣ credit: Andrew Moore

��: x �� (x)
Nonlinear SVMs
? General idea: the original input space can
always be mapped to some higher-dimensional
feature space where the training set is
separable:
�ݺ�ߣ credit: Andrew Moore

Nonlinear SVMs
b
K
y
b
y
i
i
i
i
i
i
i
i ?
?
?
? ?
? )
,
(
)
(
)
( x
x
x
x ?
?
?
?
? The kernel trick: instead of explicitly computing
the lifting transformation ��(x), define a kernel
function K such that
K(xi,xj) = ��(xi ) �� (xj)
(to be valid, the kernel function must satisfy
Mercer��s condition)
? This gives a nonlinear decision boundary in the
original feature space:
C. Burges, A Tutorial on Support Vector Machines for Pattern Recognition, Data Mining
and Knowledge Discovery, 1998

Nonlinear kernel: Example
? Consider the mapping )
,
(
)
( 2
x
x
x ?
?
2
2
2
2
2
2
)
,
(
)
,
(
)
,
(
)
(
)
(
y
x
xy
y
x
K
y
x
xy
y
y
x
x
y
x
?
?
?
?
?
?
??
?
x2

Kernels for bags of features
?
?
?
N
i
i
h
i
h
h
h
I
1
2
1
2
1 ))
(
),
(
min(
)
,
(
? Histogram intersection kernel:
? Generalized Gaussian kernel:
? D can be (inverse) L1 distance, Euclidean distance, ��2
distance, etc.
?
?
?
?
?
?
?
? 2
2
1
2
1 )
,
(
1
exp
)
,
( h
h
D
A
h
h
K
J. Zhang, M. Marszalek, S. Lazebnik, and C. Schmid, Local Features and Kernels for
Classifcation of Texture and Object Categories: A Comprehensive Study, IJCV 2007

Summary: SVMs for image classification
1. Pick an image representation (in our case, bag
of features)
2. Pick a kernel function for that representation
3. Compute the matrix of kernel values between
every pair of training examples
4. Feed the kernel matrix into your favorite SVM
solver to obtain support vectors and weights
5. At test time: compute kernel values for your test
example and each support vector, and combine
them with the learned weights to get the value of
the decision function

What about multi-class SVMs?
? Unfortunately, there is no ��definitive�� multi-class SVM
formulation
? In practice, we have to obtain a multi-class SVM by combining
multiple two-class SVMs
? One vs. others
? Traning: learn an SVM for each class vs. the others
? Testing: apply each SVM to test example and assign to it the class of the SVM that
returns the highest decision value
? One vs. one
? Training: learn an SVM for each pair of classes
? Testing: each learned SVM ��votes�� for a class to assign to the test example

SVMs: Pros and cons
? Pros
? Many publicly available SVM packages:
http://www.kernel-machines.org/software
? Kernel-based framework is very powerful, flexible
? SVMs work very well in practice, even with very small
training sample sizes
? Cons
? No ��direct�� multi-class SVM, must combine two-class SVMs
? Computation, memory
�C During training time, must compute matrix of kernel values for
every pair of examples
�C Learning can take a very long time for large-scale problems

What to remember about classifiers
No free lunch: machine learning algorithms are tools, not
dogmas
Try simple classifiers first
Better to have smart features and simple classifiers than simple
features and smart classifiers
Use increasingly powerful classifiers with more training data
(bias-variance tradeoff)

Some Machine Learning References
General
? Tom Mitchell, Machine Learning, McGraw Hill, 1997
? Christopher Bishop, Neural Networks for Pattern Recognition, Oxford
University Press, 1995
Adaboost
? Friedman, Hastie, and Tibshirani, ��Additive logistic regression: a
statistical view of boosting��, Annals of Statistics, 2000
SVMs
? http://www.support-vector.net/icml-tutorial.pdf

�ݺ�ߣ

Machine Learning workshop by GDSC Amity University Chhattisgarh

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