Volume 25, Issue 3 (2014), pp. 385–399
Background: In the area of artificial learners, not much research on the question of an appropriate description of artificial learner's (empirical) performance has been conducted. The optimal solution of describing a learning problem would be a functional dependency between the data, the learning algorithm's internal specifics and its performance. Unfortunately, a general, restrictions-free theory on performance of arbitrary artificial learners has not been developed yet.
Objective: The objective of this paper is to investigate which function is most appropriately describing the learning curve produced by C4.5 algorithm.
Methods: The J48 implementation of the C4.5 algorithm was applied to datasets (n=121) from publicly available repositories (e.g. UCI) in step wise k-fold cross-validation. First, four different functions (power, linear, logarithmic, exponential) were fit to the measured error rates. Where the fit was statistically significant (n=86), we measured the average mean squared error rate for each function and its rank. The dependent samples T-test was performed to test whether the differences between mean squared error are significantly different, and Wilcoxon's signed rank test was used to test whether the differences between ranks are significant.
Results: The decision trees error rate can be successfully modeled by an exponential function. In a total of 86 datasets, exponential function was a better descriptor of error rate function in 64 of 86 cases, power was best in 13, logarithmic in 3, and linear in 6 out of 86 cases. Average mean squared error across all datasets was 0.052954 for exponential function, and was significantly different at P=0.001 from power and at P=0.000 from linear function. The results also show that exponential function's rank is significantly different at any reasonable threshold (P=0.000) from the rank of any other model.
Conclusion: Our findings are consistent with tests performed in the area of human cognitive performance, e.g. with works by Heathcote et al. (2000), who were observing that the exponential function is best describing an individual learner. In our case we did observe an individual learner (C4.5 algorithm) at different tasks. The work can be used to forecast and model the future performance of C4.5 when not all data have been used or there is a need to obtain more data for better accuracy.
Volume 23, Issue 4 (2012), pp. 521–536
In a supervised learning, the relationship between the available data and the performance (what is learnt) is not well understood. How much data to use, or when to stop the learning process, are the key questions.
In the paper, we present an approach for an early assessment of the extracted knowledge (classification models) in the terms of performance (accuracy). The key questions are answered by detecting the point of convergence, i.e., where the classification model's performance does not improve any more even when adding more data items to the learning set. For the learning process termination criteria we developed a set of equations for detection of the convergence that follow the basic principles of the learning curve. The developed solution was evaluated on real datasets. The results of the experiment prove that the solution is well-designed: the learning process stopping criteria are not subjected to local variance and the convergence is detected where it actually has occurred.
Volume 18, Issue 3 (2007), pp. 343–362
One of the tasks of data mining is classification, which provides a mapping from attributes (observations) to pre-specified classes. Classification models are built by using underlying data. In principle, the models built with more data yield better results. However, the relationship between the available data and the performance is not well understood, except that the accuracy of a classification model has diminishing improvements as a function of data size. In this paper, we present an approach for an early assessment of the extracted knowledge (classification models) in the terms of performance (accuracy), based on the amount of data used. The assessment is based on the observation of the performance on smaller sample sizes. The solution is formally defined and used in an experiment. In experiments we show the correctness and utility of the approach.
Volume 13, Issue 3 (2002), pp. 333–344
In the paper two methods for data structure analysis and visualisation are presented: the simultaneous nonlinear mapping (Sammon, 1969) and the sequential one (Montvilas, 1995). These two methods were compared according ability to map the data on the plane, mapping accuracy and a mapping time. It was showed that the sequential nonlinear mapping has some bigger total mapping error but needs considerable less calculation time than that of the simultaneous one. Examples are given.