## 4 Results and Discussion
### High-Dimensional Multi-Category Classification  
KLSVM is a supervised learning multi-category classification technique. It learns a linear kernel function from training data consisting of pairs of pre-processed packet traces, as input features, and link quality estimates, as categorical output. The linear kernel function is used to predict a class label of any valid input feature. Interestingly, within the research field of multi-category classification, there exist two types of existing methods for handling multi-category classification problem that can be distinguished: pairwise classifiers and one-versus-all approach. Whereas the former seeks to solve a series of binary classifications, the latter considers all the classes simultaneously. In our technique, we considered one-versus-all because we required training \(X\) distinct binary classifiers to separate one class from all others and each binary classifier uses all training samples. For the pairwise approach, there are \(X(X-1)/2\) binary classifiers to be trained with one for each pair of classes. Compared to the one-versus-all approach, the number of classifiers is much larger for the pairwise approach but each one involves only a subsample of the training data and thus is easier to train.  
The remarkable recent development of sense computing, powerful state-of-the-art technology and massive storage technology has allowed scientists to collect data of unprecedented size and complexity. When the dimensionality of the input feature space is too large, things become complicated, for instance, if the raw packet traces were used for training. Another difficulty of high dimensional classification is caused by the existence of many noise features such as outliers that do not contribute to the reduction of classification error. Although individually each extracted feature from the examined packet traces can be estimated accurately, aggregated estimation error over the raw packet traces (if they were to be used as features) can be very large and this could significantly increase the misclassification rate, which places more emphasis on misclassification rates rather than the accuracy of estimated categorical output. Even though in high dimensional classification, the focus is much more about the misclassification rate instead of the accuracy of the estimated parameters. This characteristic makes the LSVM incline to be sensitive to training noisy data. When there exist outliers within their own classes, LSVM classifier inclines to be vigorously affected by such far away points due to the unboundedness of the hinge loss. Figure 8 shows, the directions found by the KLSVM technique puts much more weight on link features that provide large classification power.  
Figure 7: KLSVM’s training and prediction model. The inputs are the pre-processed packet traces.  
Generally, linear prediction methods are likely to perform poorly unless the prediction vector \(\hat{y}\) is sparse, that is, the effective number of selected features is small. This is due to, as earlier mentioned, the noise accumulation to a large extent as a high-dimensional problem. Classification technique using all features do not necessarily perform well due to the noise accumulation when estimating a large number of noise features. Dealing with high dimensionality and small sample size mitigates the \"curse-of-dimensionality\". The \"curse-of-dimensionality\" refers to a phenomena that arises when analyzing and organizing the dataset in high-dimensional spaces with very large-dimensional settings that does not occur in low dimensions such as the \(3D\) physical space.