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--- assignments:assignment3 [2013/10/04 21:08]
asa [Part 3: Using the SVM]
+++ assignments:assignment3 [2013/10/06 13:33]
asa
@@ Line 10: / Line 10: @@
 Hint:  consider the difference in the constraints.
-Discuss the merit of the bias-less formulation as the dimensionality
+===== Part 2:  Closest Centroid Algorithm =====
-of the data (or the feature space) is varied.
-When using this SVM formulation it may be useful to add a constant to the
-kernel matrix.  Explain why this can be beneficial.
+Express the closest centroid algorithm in terms of kernels, i.e. determine how the coefficients $\alpha_i$ will be computed using a given labeled dataset.
-===== Part 3:  Using the SVM =====
+===== Part 3:  Using SVMs =====
-Download the dataset associated with this assignment from the homework
+The data for this question comes from a database called SCOP (structural
-page of the course.
+classification of proteins), which classifies proteins into classes
-In this assignment we will explore the dependence of classifier accuracy on
+according to their structure (download it from {{assignments:scop_motif.data|here}}).
-the kernel, kernel parameters, kernel normalization, and SVM parameter.
+The data is a two-class classification
-The use of the SVM class is discussed in the PyML [[http://pyml.sourceforge.net/tutorial.html#svms|tutorial]].
+problem
+of distinguishing a particular class of proteins from a selection of
+examples sampled from the rest of the SCOP database.
+I chose to represent the proteins in
+terms of their motif composition.  A sequence motif is a
+pattern of nucleotides/amino acids that is conserved in evolution.
+Motifs are usually associated with regions of the protein that are
+important for its function, and are therefore useful in differentiating between classes of proteins.
+A given protein will typically contain only a handful of motifs, and
+so the data is very sparse.  It is also very high dimensional, since
+the number of conserved patterns in the space of all proteins is
+large.
+The data was constructed as part of the following analysis of detecting distant relationships between proteins:
+  * A. Ben-Hur and D. Brutlag. [[http://bioinformatics.oxfordjournals.org/content/19/suppl_1/i26.abstract | Remote homology detection: a motif based approach]]. In: Proceedings, eleventh international conference on intelligent systems for molecular biology. Bioinformatics 19(Suppl. 1): i26-i33, 2003.
+In this part of the assignment we will explore the dependence of classifier accuracy on
+the kernel, kernel parameters, kernel normalization, and SVM parameter soft-margin parameter.
+The use of the SVM class is discussed in the PyML [[http://pyml.sourceforge.net/tutorial.html#svms|tutorial]], and by using help(SVM) in the python interpreter.
-By default a dataset is instantiated with a linear kernel attached to it.
+By default, a dataset is instantiated with a linear kernel attached to it.
 To use a different kernel you need to attach a new kernel to the dataset:
 <code python>
@@ Line 35: / Line 51: @@
 >>> data.attachKernel(ker.Polynomial(degree = 3))
 </code>
+Alternatively, you can instantiate an SVM with a given kernel:
+<code python>
+>>> classifier = SVM(ker.Gaussian(gamma = 0.1))
+</code>
+This will override the kernel the data is associated with.
 In this question we will consider both the Gaussian and polynomial kernels:
 $$
-K_{gaus}(\mathbf{x}, \mathbf{x'}) = \exp(-\gamma || \mathbf{x} - \mathbf{x}' ||^2)
+K_{gauss}(\mathbf{x}, \mathbf{x'}) = \exp(-\gamma || \mathbf{x} - \mathbf{x}' ||^2)
 $$
 $$
 K_{poly}(\mathbf{x}, \mathbf{x'}) = (1 + \mathbf{x}^T \mathbf{x}') ^{p}
 $$
-Plot the accuracy of the classifier, measured using the success rate and the area under the ROC curve
+Plot the accuracy of the SVM, measured using the balnced success rate
-as a function of both the ridge parameter of the classifier, and the free parameter
+as a function of both the soft-margin parameter of the SVM, and the free parameter
 of the kernel function.
 Show a couple of representative cross sections of this plot for a given value
@@ Line 49: / Line 71: @@
 Comment on the results.  When exploring the values of a continuous
 classifier/kernel parameter it is
-useful use values that are distributed on an exponential grid,
+useful to use values that are distributed on an exponential grid,
 i.e. something like 0.01, 0.1, 1, 10, 100 (note that the degree of the
 polynomial kernel is not such a parameter).
-The data for this question comes from a database called SCOP (structural
+For this type of sparse dataset it is useful to normalize the input features.
-classification of proteins), which classifies proteins into classes
-according to their structure.  The data is a two-class classification
-problem
-of distinguishing a particular class of proteins from a selection of
-examples sampled from the rest of the SCOP database.
-I chose to represent the proteins in
-terms of their motif composition.  A sequence motif is a
-pattern of nucleotides/amino acids that is conserved in evolution.
-Motifs are usually associated with regions of the protein that are
-important for its function, and are therefore useful in predicting protein
-function.
-A given protein will typically contain only a handful of motifs, and
-so the data is very sparse.  It is also very high dimensional, since
-the number of conserved patterns in the space of all proteins is
-large.
-More information about motifs and their usefulness in classifying
-proteins can be found in the following paper:
-  * A. Ben-Hur and D. Brutlag. Protein sequence motifs: Highly predictive features of protein function. In: Feature extraction, foundations and applications. I. Guyon, S. Gunn, M. Nikravesh, and L. Zadeh (eds.) Springer Verlag, 2006.
-For this type of sparse dataset it is useful to normalize the input features before
-training and testing your classifier.
 One way to do so is to divide each input example by its norm.  This is
 accomplished in PyML by:
@@ Line 91: / Line 91: @@
 Explain the structure that you are seeing in the plot (it is more
 interesting when the data is normalized).

CS545 fall 2016

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