Decision tree learning

Decision tree learning, used in statistics, data mining and machine learning, uses a decision tree as a predictive model which maps observations about an item to conclusions about the item's target value. More descriptive names for such tree models are classification trees or regression trees. In these tree structures, leaves represent class labels and branches represent conjunctions of features that lead to those class labels.

In decision analysis, a decision tree can be used to visually and explicitly represent decisions and decision making. In data mining, a decision tree describes data but not decisions; rather the resulting classification tree can be an input for decision making. This page deals with decision trees in data mining.

Contents

General

Decision tree learning is a method commonly used in data mining. The goal is to create a model that predicts the value of a target variable based on several input variables. An example is shown on the right. Each interior node corresponds to one of the input variables; there are edges to children for each of the possible values of that input variable. Each leaf represents a value of the target variable given the values of the input variables represented by the path from the root to the leaf.

A tree can be "learned" by splitting the source set into subsets based on an attribute value test. This process is repeated on each derived subset in a recursive manner called recursive partitioning. The recursion is completed when the subset at a node all has the same value of the target variable, or when splitting no longer adds value to the predictions.

In data mining, decision trees can be described also as the combination of mathematical and computational techniques to aid the description, categorisation and generalisation of a given set of data.

Data comes in records of the form:

(\textbf{x},Y) = (x_1, x_2, x_3, ..., x_k, Y)

The dependent variable, Y, is the target variable that we are trying to understand, classify or generalise. The vector x is composed of the input variables, x1, x2, x3 etc., that are used for that task.

Types

Decision trees used in data mining are of two main types:

The term Classification And Regression Tree (CART) analysis is an umbrella term used to refer to both of the above procedures, first introduced by Breiman et al.[1] Trees used for regression and trees used for classification have some similarities - but also some differences, such as the procedure used to determine where to split.[1]

Some techniques use more than one decision tree for their analysis:

There are many specific decision-tree algorithms. Notable ones include:

Formulae

The algorithms that are used for constructing decision trees usually work top-down by choosing a variable at each step that is the next best variable to use in splitting the set of items.[6] "Best" is defined by how well the variable splits the set into homogeneous subsets that have the same value of the target variable. Different algorithms use different formulae for measuring "best". This section presents a few of the most common formulae. These formulae are applied to each candidate subset, and the resulting values are combined (e.g., averaged) to provide a measure of the quality of the split.

Gini impurity

Main article: Gini coefficient

Used by the CART algorithm, Gini impurity is a measure of how often a randomly chosen element from the set would be incorrectly labeled if it were randomly labeled according to the distribution of labels in the subset. Gini impurity can be computed by summing the probability of each item being chosen times the probability of a mistake in categorizing that item. It reaches its minimum (zero) when all cases in the node fall into a single target category.

To compute Gini impurity for a set of items, suppose y takes on values in {1, 2, ..., m}, and let fi = the fraction of items labeled with value i in the set.

I_{G}(f) = \sum_{i=1}^{m} f_i (1-f_i) = \sum_{i=1}^{m} (f_i - {f_i}^2) = \sum_{i=1}^m f_i - \sum_{i=1}^{m} {f_i}^2 = 1 - \sum^{m}_{i=1} {f_i}^{2}

Information gain

Main article: Information gain in decision trees

Used by the ID3, C4.5 and C5.0 tree generation algorithms. Information gain is based on the concept of entropy used in information theory.

I_{E}(f) = - \sum^{m}_{i=1} f_i \log^{}_2 f_i

Decision tree advantages

Amongst other data mining methods, decision trees have various advantages:

Limitations

Extensions

Decision graphs

In a decision tree, all paths from the root node to the leaf node proceed by way of conjunction, or AND. In a decision graph, it is possible to use disjunctions (ORs) to join two more paths together using Minimum Message Length (MML).[12] Decision graphs have been further extended to allow for previously unstated new attributes to be learnt dynamically and used at different places within the graph.[13] The more general coding scheme results in better predictive accuracy and log-loss probabilistic scoring. In general, decision graphs infer models with fewer leaves than decision trees.

Search through Evolutionary Algorithms

Evolutionary algorithms have been used to avoid local optimal decisions and search the decision tree space with little a priori bias.[14] [15]

See also

Implementations

References

  1. ^ a b Breiman, Leo; Friedman, J. H., Olshen, R. A., & Stone, C. J. (1984). Classification and regression trees. Monterey, CA: Wadsworth & Brooks/Cole Advanced Books & Software. ISBN 978-0412048418. 
  2. ^ Friedman, J. H. (1999). Stochastic gradient boosting. Stanford University.
  3. ^ Hastie, T., Tibshirani, R., Friedman, J. H. (2001). The elements of statistical learning : Data mining, inference, and prediction. New York: Springer Verlag.
  4. ^ Rodriguez, J.J. and Kuncheva, L.I. and Alonso, C.J. (2006), Rotation forest: A new classifier ensemble method, IEEE Transactions on Pattern Analysis and Machine Intelligence, 28(10):1619-1630.
  5. ^ Kass, G. V. (1980). "An exploratory technique for investigating large quantities of categorical data". Applied Statistics 29 (2): 119–127. doi:10.2307/2986296. JSTOR 2986296. 
  6. ^ Rokach, L.; Maimon, O. (2005). "Top-down induction of decision trees classifiers-a survey". IEEE Transactions on Systems, Man, and Cybernetics, Part C 35 (4): 476–487. doi:10.1109/TSMCC.2004.843247. 
  7. ^ Hyafil, Laurent; Rivest, RL (1976). "Constructing Optimal Binary Decision Trees is NP-complete". Information Processing Letters 5 (1): 15–17. doi:10.1016/0020-0190(76)90095-8. 
  8. ^ Murthy S. (1998). Automatic construction of decision trees from data: A multidisciplinary survey. Data Mining and Knowledge Discovery
  9. ^ Principles of Data Mining. 2007. doi:10.1007/978-1-84628-766-4. ISBN 978-1-84628-765-7.  edit
  10. ^ Horváth, Tamás; Yamamoto, Akihiro, eds (2003). Inductive Logic Programming. Lecture Notes in Computer Science. 2835. doi:10.1007/b13700. ISBN 978-3-540-20144-1.  edit
  11. ^ Deng,H.; Runger, G.; Tuv, E. (2011). "Bias of importance measures for multi-valued attributes and solutions". Proceedings of the 21st International Conference on Artificial Neural Networks (ICANN). pp. 293–300. http://enpub.fulton.asu.edu/hdeng3/MultiICANN2011.pdf. 
  12. ^ http://citeseer.ist.psu.edu/oliver93decision.html
  13. ^ Tan & Dowe (2003)
  14. ^ Papagelis A., Kalles D.(2001). Breeding Decision Trees Using Evolutionary Techniques, Proceedings of the Eighteenth International Conference on Machine Learning, p.393-400, June 28-July 01, 2001
  15. ^ Barros, Rodrigo C., Basgalupp, M. P., Carvalho, A. C. P. L. F., Freitas, Alex A. (2011). A Survey of Evolutionary Algorithms for Decision-Tree Induction. IEEE Transactions on Systems, Man and Cybernetics, Part C: Applications and Reviews

External links