Pattern Classification: Pattern Classification Pt.1
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Moreover, it can handle some overlap among classes.
Data Analysis and Pattern Classification (DATAPAC)
The distance between feature vectors was measured using log-euclidean distance. In this section, we discuss the average results obtained by following the approach presented in the Methodology Section, with the experiments repeated times with randomly selected learning and test sets. In the preprocessing step, we employed a feature standardization to avoid that attributes in larger numeric ranges dominate those in smaller ranges. We initialized each learning instance with 0.
However, final training sets were constructed from this learning set by each classifier. Given that sample selection is based on a fixed increment of 0. For instance, if the final training set contains 0.
Concerning the problem of overlapped training sets in cross-validation methodologies, as mentioned in the Background Section, we studied the correlation between each pair of training sets to evaluate the effectiveness of our methodology with respect to the choice of statistically different training sets see Fig 2. The training sets present correlation below 0. This indicates that our methodology really measures the generalization ability of the classifiers for different training sets. Cod-RNA a—d. Connect e—h. Covertype i—l.
IJCNN m—p. SensIT q—t. Tables 2 — 6 illustrate the effectiveness measure, namely the F 1 -score and the final training set size for each classification model, grouped by the learning-time constraint over different datasets. From the experimental results for Cod-RNA dataset Table 2 , we see that both SVM strategies are able to obtain relatively good accuracy even with small training sets. One of the main issues with SVM is its non-scalability with respect to the number of training samples. Our methodology allowed these methods to select their most representative samples for a reduced training set.
In Table 3 , we can see that faster techniques, such as OPF and k -NN, can acquire more samples within the time constraint as well as achieve higher mean accuracy. However, k -NN usually presents higher variance, being more sensitive to noise.
Data Analysis and Pattern Classification
Differently, OPF presents a more stable performance Tables 3 — 6 , in general, especially in multi-class problems. Some techniques can learn faster than others, building larger training sets. However, the ability of the technique in selecting the most informative samples is more important than its speed.
This makes an interesting point with respect to the proposed methodology. It is fair to all techniques in the sense that each one has the chance to mine the most informative samples for training. Note that, Tables 2 — 6 , show the final training set size of each technique and the best technique is not always the one with largest training set. Indeed, faster techniques obtained their maximal predictive performance only when they could effectively learn from their errors. To provide a statistical analysis of the results, we performed a Friedman test [ 56 ] for each pair of dataset and learning time constraint.
Figs 3 — 7 illustrate a graphical representation of the post-hoc Nemenyi test [ 58 ], since we rejected the null hypotheses that all the classifiers are equivalent.
Note that 1 represents the best technique, and while 4 stands for the worst one. Comparison of all classifiers against each other with the Nemenyi test and learning time constraint equals to 1, 5, 20, 60, , and seconds. It is worth noting the importance of the statistical test, since the mean and standard deviation see Tables 2 — 6 in some cases are not sufficient to indicate the best classifier.
The results presented by both tests Nemenyi test and mean-standard deviation , in general, are equivalents. According to the mean and standard deviation Table 2 , both SVMs are equivalent. However, the statistical tests show evidence that they are not. Such divergences can also be observed with the other datasets. They occur due to the fact that the standard deviation values are relatively high compared to the difference in performance of the classifiers.
However, the Nemenyi test indicates statistically significant differences between them, unlike the mean-standard deviation test. Sample selection methods do not account for time constraints. Methods based on clustering and statistical information learned from the data are usually time costly for large learning sets, which would make it very difficult to select and train a classifier within lower time limits.
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The simplest approach is random sample selection from each class. Even in this case, one has to estimate the maximum number of samples that a given model can use to train the classifier in a single iteration and within the given time limit. First, for some models, such as SVM, the training time also depends on the selected samples. Anyway, ignoring that, we have estimated that number for each classification model and compared to the proposed sample selection approach based on classification errors.
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Tables 7 — 11 present the corresponding results using a single learning iteration with the maximum number of randomly selected samples. Comparing the results achieved by the proposed method Tables 2 — 6 with the ones by the randomized method Tables 7 — 11 , one can observe that in general, the proposed methodology is capable to select the most representative samples for the training set, holding higher accuracy results see Tables 2 and 7 with time constraint equal to 1 sec for all classifiers.
Even in some cases, when it was possible to train with the entire dataset for instance, see Table 7 with time constraint equal to sec for k -NN and OPF, as well as with time constraint equal to sec for k -NN, OPF and LSVM , it seems that some randomly selected training samples impaired the performance of the classifier, while our methodology is capable to avoid them in the training set see Table 2 with the same time constraints and classifiers.
Note also that the proposed methodology can output considerably smaller training sets, which matters in some approaches, such as the OPF and k -NN classifiers, to speed up classification of large test sets. The comparison of methods using randomized sample selection is not suitable, because these samples capture the geometry of the classes.
Besides, as they increase in number, all classification models become equivalent. Fig 8 shows randomly selected samples by each classification model within a given time constraint 1 and 1. Samples that were not selected are highlighted in gray. It is noteworthy that faster techniques with a larger training set do not always achieve higher accuracy.
It relies on the effective learning from their errors. Each classification model defines decision boundaries regions in a different way in the feature space. By selecting classification errors as training samples, the learning process converges faster to the corresponding decision boundaries. The errors tend to be samples close to the decision boundaries rather than outliers, as long as outliers are minority.
If this is not the case, outlier removal should be applied before the learning process. In order to better clarify this issue, we have added Fig 9 with samples not selected from the learning set in gray and samples selected by the classifiers to the training set in color. Fig 9 shows the selected samples for 1 second of time limit using the 2D Cone-Torus dataset. In order to analyze the performance of each classifier using the entire learning set, Table 13 shows the accuracy and the time required for training each dataset.
All classifiers presented similar accuracies. We presented a methodology to compare multiple classifiers under a learning-time constraint, which is useful to select the best classifier for a given application. In this paper, the applications were represented by different datasets with unbalancing of classes, distinct number of classes and feature space dimensions.
The proposed methodology allows each classifier to select its most representative samples from a learning set during the training phase. The experiments allowed us to reach several conclusions. Although it was not possible to assert which is the most effective classification model under a given time constraint, due to the variability of results on each application domain, experiments obtained using the proposed methodology allowed us to arrive at some relevant observations. Larger training sets do not necessarily lead to higher predictive performance on unseen test sets, which indicates the effectiveness of some classifiers in learning from their own errors.
The methodology is able to produce statistically independent training sets as observed by the low correlations between each pair of training set obtained for a given dataset-classifier pair, following executions. This demonstrates the advantage of our approach with respect to the regular cross-validation procedure, largely used in related works. It is also very common in the literature for the presentation of experimental results to rely solely on the mean and standard deviation of accuracy values.
The statistical test shows that this approach is not always reliable, due to the relative variations of the standard deviation. Browse Subject Areas? Click through the PLOS taxonomy to find articles in your field. Abstract Nowadays, large datasets are common and demand faster and more effective pattern analysis techniques. This is an open access article distributed under the terms of the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited Data Availability: All relevant data are within the paper.
Introduction Advances in digital technologies make large datasets commonly available, which demands faster and more effective pattern analysis techniques. Download: PPT. Background Many works have presented pattern classification models based on discriminant analysis, nearest neighbors, neural networks, support vector machines and decision trees, among other techniques. Methodology In this section, we present the proposed evaluation methodology that considers efficacy and efficiency at the same time. Output : A supervised classifier.
Experiments In this section, we describe the overall experimental methodology, including datasets, effectiveness measure, classification models and the computational environment used. Dataset Description For the experiments, we selected commonly available datasets of modest sizes with feature spaces of various dimensions. Effectiveness Measure Description It is important to highlight that the proposed methodology can be used with any effectiveness measure appropriate to the specific domain of application.
Learning-Time Constraints For each dataset, we used four different learning-time limits, which were empirically chosen to simulate potential applications with different response times, so named: very interactive , interactive , nearly interactive and non-interactive. Support Vector Machines. Optimum-Path Forest.