assignments:assignment3
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assignments:assignment3 [2013/10/04 21:06] asa |
assignments:assignment3 [2013/10/06 11:54] asa |
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| Hint: consider the difference in the constraints. | 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 $alpha_i$ coefficients will be determined using a given labeled dataset. | ||
| - | ===== Part 3: Using the SVM ===== | + | ===== Part 3: Using SVMs ===== |
| + | |||
| + | The data for this question comes from a database called SCOP (structural | ||
| + | classification of proteins), which classifies proteins into classes | ||
| + | according to their structure (download it from {{assignments:scop_motif.data|here}}. | ||
| + | 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 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. | ||
| Download the dataset associated with this assignment from the homework | Download the dataset associated with this assignment from the homework | ||
| Line 37: | Line 55: | ||
| In this question we will consider both the Gaussian and polynomial kernels: | 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_{gaus}(\mathbf{x}, \mathbf{x'}) = \exp(-\gamma || \mathbf{x} - \mathbf{x}' ||^2) |
| $$ | $$ | ||
| $$ | $$ | ||
| - | K_{poly}(\mathbf{x}, \mathbf{x'} = (1 + \mathbf{x}^T \mathbf{x}') ^{p} | + | 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 classifier, measured using the success rate and the area under the ROC curve | ||
| Line 53: | Line 71: | ||
| polynomial kernel is not such a parameter). | polynomial kernel is not such a parameter). | ||
| - | The data for this question comes from a database called SCOP (structural | ||
| - | 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 | For this type of sparse dataset it is useful to normalize the input features before | ||
| Line 79: | Line 77: | ||
| accomplished in PyML by: | accomplished in PyML by: | ||
| <code python> | <code python> | ||
| - | data.normalize() | + | >>> data.normalize() |
| </code> | </code> | ||
| Compare the results under this normalization with what you obtain | Compare the results under this normalization with what you obtain | ||
| Line 91: | Line 89: | ||
| Explain the structure that you are seeing in the plot (it is more | Explain the structure that you are seeing in the plot (it is more | ||
| interesting when the data is normalized). | interesting when the data is normalized). | ||
| - | |||
assignments/assignment3.txt · Last modified: 2016/09/20 09:34 by asa
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