6 Sparse Coding for feature selection
6.4 Conclusion sparse coding
In the first part of this thesis we explored different classification approaches for risk prediction on large numbers of SNPs (see Chapters 4and5). The number of SNPs in most GWA data sets is expected by far to exceed the number of SNPs truly associ-ated with the disease. Hence, classification may be improved if we exclude irrelevant SNPs to reduce the amount of noise. There are several strategies for excluding disease-unspecific SNPs. One strategy is to select SNPs that are individually associated with the disease. However, we do not expect all disease-specific SNPs to have an individual effect; SNPs that only have an appreciable effect when they occur together may also be important for classification.
Disease-specific patterns are however not straightforward to identify. In this chapter, we have evaluated whether principal component analysis (PCA) and sparse coding are suitable tools for this task. Both PCA and sparse coding are approaches that identify structures in data on the premise that structures correspond to the directions of great-est variance. We use the PCA and sparse coding to score SNPs; the larger the influence of a SNP is on a direction of variance identified by the algorithm, the larger is the so-called pcascore or scscore.
To test whether SNP patterns can be identified using the pcascore and scscore, we first evaluated the algorithms on simulated data sets. We also evaluated the p-value ranking and svmscore on these data sets. We simulated data sets with a pattern specific for the disease phenotype and tested whether the algorithms identify these SNPs and to which extent. Whereas the p-value ranking and svmscore clearly fail to identify the SNPs, the relevant SNPs scored high on both the pcascore and scscore. However, the
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performance for these two latter algorithms does decrease with increasing numbers of unspecific patterns in the data. The size of the patterns also strongly influences the performance: If the size of the pattern is too small, the algorithm fails to identify it. The scscore performs consistently better than the pcascore and is thus the most suitable feature selection approach on the simulated data.
We then proceeded to evaluate the four feature selection strategies on real data.
Whereas on simulated data sets, we can assess the quality of the results by counting the number of disease-specific SNPs identified by the algorithms, on real GWA data, we do not know these SNPs. Hence, we evaluated the algorithms by the performance of the SVM on the selected subsets. We obtain different results for the IBD and CAD data.
On the IBD data, the scscore ranking yields a subset that improves the classification over that on all SNPs. On the CAD data, however, the scscore fails to select a suitable subset; except on very large numbers of SNPs, its performance is equal to that obtained by chance.
As discussed above, there are probably many reasons why scscore selection fails to identify disease-specific patterns on the CAD data set. As we experienced on the simulated data set, the algorithm clearly struggles to identify patterns that consist only of a small number of SNPs. Hence, if the patterns are too small, the algorithm cannot identify them.
In the simulated data set, we incorporated a defined number of disease-unspecific patterns to test how they influence the performance of the algorithms. However, we do not know how many such patterns exist in real data sets and how large they are. In the simulated data set, we saw that more disease-unspecific patterns decrease the per-formance. The more unspecific patterns there are in the data, the more the algorithm struggles to identify the disease-specific ones. We conclude that one possible reason why the scscore fails on the CAD data may be that the number of unspecific patterns is large. In such cases, the dictionary that is learned by the sparse coding algorithm may not be large enough to contain all structures and may hence miss the disease-specific ones. One possible solution is to increase the number of basis vectors in the learned dictionary. A drawback of this solution is, however, that this further increases the computational effort of an already computationally demanding algorithm.
A further weakness of the sparse coding selection strategy is that we apply the al-gorithm to the two groups (cases and controls) separately. If we have strong unspecific patterns in the data, the sparse coding algorithm will select these in both groups. If we then determine the difference between the two groups, we only find small random differences and the scscore is hence of no use.
A major difference between the IBD and CAD data is that the CAD data is LD-pruned (see Chapter2.2.1). LD-pruning aims to eliminate redundant SNPs that carry the same information as neighbouring SNPs. One possible explanation why sparse coding selection fails on the CAD data could be that by eliminating these SNPs, we
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also miss some disease-specific patterns. Hence, it would be interesting to see whether the performance of sparse coding selection improves if we omit the LD-pruning.
To sum up, the proposed sparse coding algorithm can be used to identify a subset of SNPs that improves classification over the set of all SNPs, as shown on the IBD data set. However, as we have seen on the CAD data, the algorithm may also fail. This underlines the need to explore the performance on further data sets.
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