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On Oblique Random Forests
"... Abstract. In his original paper on random forests, Breiman proposed two different decision tree ensembles: one generated from “orthogonal” trees with thresholds on individual features in every split, and one from “oblique ” trees separating the feature space by randomly oriented hyperplanes. In spit ..."
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Abstract. In his original paper on random forests, Breiman proposed two different decision tree ensembles: one generated from “orthogonal” trees with thresholds on individual features in every split, and one from “oblique ” trees separating the feature space by randomly oriented hyperplanes. In spite of a rising interest in the random forest framework, however, ensembles built from orthogonal trees (RF) have gained most, if not all, attention so far. In the present work we propose to employ “oblique ” random forests (oRF) built from multivariate trees which explicitly learn optimal split directions at internal nodes using linear discriminative models, rather than using random coefficients as the original oRF. This oRF outperforms RF, as well as other classifiers, on nearly all data sets but those with discrete factorial features. Learned node models perform distinctively better than random splits. An oRF feature importance score shows to be preferable over standard RF feature importance scores such as Gini or permutation importance. The topology of the oRF decision space appears to be smoother and better adapted to the data, resulting in improved generalization performance. Overall, the oRF propose here may be preferred over standard RF on most learning tasks involving numerical and spectral data. 1
Building classification models from microarray data with treebased classification algorithms
"... Abstract. Building classification models plays an important role in DNA mircroarray data analyses. An essential feature of DNA microarray data sets is that the number of input variables (genes) is far greater than the number of samples. As such, most classification schemes employ variable selection ..."
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Abstract. Building classification models plays an important role in DNA mircroarray data analyses. An essential feature of DNA microarray data sets is that the number of input variables (genes) is far greater than the number of samples. As such, most classification schemes employ variable selection or feature selection methods to preprocess DNA microarray data. This paper investigates various aspects of building classification models from microarray data with treebased classification algorithms by using Partial LeastSquares (PLS) regression as a feature selection method. Experimental results show that the Partial LeastSquares (PLS) regression method is an appropriate feature selection method and treebased ensemble models are capable of delivering high performance classification models for microarray data. 1
Potential Properties of Turing Machines
, 2012
"... In this paper we investigate the notion of potential properties for Turing machines, focussing especially on universality and intelligence. We consider several machine characterisations (noninteractive and interactive) and give definitions for each case, considering permanent and transitory potentia ..."
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In this paper we investigate the notion of potential properties for Turing machines, focussing especially on universality and intelligence. We consider several machine characterisations (noninteractive and interactive) and give definitions for each case, considering permanent and transitory potentials. From these definitions, we analyse the relation between some potential abilities, we bring out the dependency on the environment distribution and we suggest some ideas on how potential abilities can be measured.
Algebraic properties of ωtrees (I)
"... Abstract. This paper is a starting point for a possible research line to study the theoretical aspects of the answer function for a masterslave system based on semantic schemas. We define the concept of ωlabeled tree as a binary, ordered and labeled tree with several features concerning the labels ..."
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Abstract. This paper is a starting point for a possible research line to study the theoretical aspects of the answer function for a masterslave system based on semantic schemas. We define the concept of ωlabeled tree as a binary, ordered and labeled tree with several features concerning the labels and order between the direct descendants of a node. The labeling operation of the nodes is guided by the mapping ω which defines the splitting operation for labels. An embedding operation of an ωtree into another ωtree is introduced. We prove that this operation is performed by means of an injective mapping. Based on this operation some binary relation between ωlabeled trees is defined. This is a reflexive and transitive relation, but is not antisymmetric. All the results proved in this paper and in [15] constitute the algebraic background of a forthcoming paper as we mention in the last section.
Algebraic properties of ωtrees (II)
"... Abstract. In [16] we defined the concept of ωlabeled tree as a binary, ordered and labeled tree with several features concerning the labels and order between the direct descendants of a node. This paper includes several further results concerning these structures. The main results presented in this ..."
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Abstract. In [16] we defined the concept of ωlabeled tree as a binary, ordered and labeled tree with several features concerning the labels and order between the direct descendants of a node. This paper includes several further results concerning these structures. The main results presented in this paper are the following: we introduce an equivalence relation ' on the set OBT (ω) of ωtrees and a partial order on the factor set OBT (ω)/'.
Local Greatest Equivalence Classes of!trees
"... Abstract. In [18] we defined the concept of!labeled tree as a binary, ordered and labeled tree with several features concerning the labels and order between the direct descendants of a node. In [19] we introduced an equivalence relation ≃ on the set OBT (!) of!trees and a partial order on the fact ..."
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Abstract. In [18] we defined the concept of!labeled tree as a binary, ordered and labeled tree with several features concerning the labels and order between the direct descendants of a node. In [19] we introduced an equivalence relation ≃ on the set OBT (!) of!trees and a partial order on the factor set OBT (!)=≃. In this paper we decompose the factor set OBT (!)= ≃ into disjoint ”local ” subsets K, we show that if the relation defined by the mapping! is a noetherian one then every local subset K has a greatest element, we define an increasing operator on the set OBT (!)=≃, which allows to obtain the greatest element of a local subset. In order to relieve the local features of a subset K we give an example which shows that the greatest element of K is not necessarily a maximal element of the factor set.