Introduction: The VFDT (Very Fast Decision Tree) algorithm makes several modifications to the Hoeffding tree algorithm to improve both speed and memory utilization. The modifications include breaking near-ties during attribute selection more aggressively, computing the G function after a number of training examples, deactivating the least promising leaves whenever memory is running low, dropping poor splitting attributes, and improving the initialization method. VFDT works well on stream data and also compares extremely well to traditional classifiers in both speed and accuracy. However, it still cannot handle concept drift in data streams.
Basically, we need a way to identify in a timely manner those elements of the stream that are no longer consistent with the current concepts. A common approach is to use a sliding window. The intuition behind it is to incorporate new examples yet eliminate the effects of old ones. We can repeatedly apply a traditional classifier to the examples in the sliding window.
As new examples arrive, they are inserted into the beginning of the window; a corresponding number of examples is removed from the end of the window, and the classifier is reapplied. This technique, however, is sensitive to the window size, w. If w is too large, the model will not accurately represent the concept drift. On the other hand, if w is too small, then there will not be enough examples to construct an accurate model. Moreover, it will become very expensive to continually construct a new classifier model.
To adapt to concept-drifting data streams, the VFDT algorithm was further developed into the Concept-adapting Very Fast Decision Tree algorithm (CVFDT). CVFDT also uses a sliding window approach; however, it does not construct a new model from scratch each time. Rather, it updates statistics at the nodes by incrementing the counts associated with new examples and decrementing the counts associated with old ones. Therefore, if there is a concept drift, some nodes may no longer pass the Hoeffding bound. When this happens, an alternate subtree will be grown, with the new best splitting attribute at the root. As new examples stream in, the alternate subtree will continue to develop, without yet being used for classification. Once the alternate subtree becomes more accurate than the existing one, the old subtree is replaced.
Empirical studies show that CVFDT achieves better accuracy than VFDT with time-changing data streams. In addition, the size of the tree in CVFDT is much smaller than that in VFDT, because the latter accumulates many outdated examples.
A Classifier Ensemble Approach to Stream Data Classification
Let’s look at another approach to classifying concept drifting data streams, where we instead use a classifier ensemble. The idea is to train an ensemble or group of classifiers (using, say, C4.5, or naïve Bayes) from sequential chunks of the data stream. That is, whenever a new chunk arrives, we build a new classifier from it. The individual classifiers are weighted based on their expected classification accuracy in a time-changing environment. Only the top-k classifiers are kept. The decisions are then based on the weighted votes of the classifiers.
There are several reasons for involving more than one classifier. Decision trees are not necessarily the most natural method for handling concept drift. Specifically, if an attribute near the root of the tree in CVFDT no longer passes the Hoeffding bound, a large portion of the tree must be re-grown. Many other classifiers, such as naïve Bayes, are not subject to this weakness. In addition, naïve Bayesian classifiers also supply relative probabilities along with the class labels, which express the confidence of a decision. Furthermore, CVFDT’s automatic elimination of old examples may not be prudent. Rather than keeping only the most up-to-date examples, the ensemble approach discards the least accurate classifiers. Experimentation shows that the ensemble approach achieves greater accuracy than any one of the single classifiers.
