A new metric splitting criterion for decision trees

Abstract

We examine a new approach to building decision tree by introducing a geometric splitting criterion, based on the properties of a family of metrics on the space of partitions of a finite set. This criterion can be adapted to the characteristics of the data sets and the needs of the users and yields decision trees that have smaller sizes and fewer leaves than the trees built with standard methods and have comparable or better accuracy.

On the Axiomatization of Generalized Entropic Metrics

“…We have shown in [14] that the conditional β-entropy enjoys the property specified next. Theorem 2.3 Let π, σ, σ ′ be three partitions of a finite set…”

“…These metrics are used for a variety of data mining tasks ranging from clustering [7,15] to classification [13,14] and discretization [10].…”

Detecting phylogenetic relations out from sparse context trees

“…Before defining the distance between sparse context trees we introduce the notion of β-entropy of a tree τ . Following Simovici and Szymon (2006) we define, for all β > 0,…”

Cadeias estocásticas parcimoniosas com aplicações à classificação e filogenia das seqüências de proteínas.

“…Com a noção de entropia e a definição de partição máxima entre duas partições, deriva-se a definição de distância introduzida em (Simovici & Szymon, 2006). Essa será a distância que utilizaremos para estudar a similaridade entre as seqüências de proteínas.…”

“…Para issoé utilizada uma distância entre asárvores de contextos, introduzida em Simovici & Szymon (2006). O estudoé feito em seqüências de globinas e de fatores de crescimento de fibroblastos (FGF).…”