Rank discrimination measures for enforcing monotonicity in decision tree induction

Marsala, Christophe; Petturiti, Davide

doi:10.1016/j.ins.2014.08.045

Cited by 28 publications

(25 citation statements)

References 29 publications

(79 reference statements)

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“…Some quantification of non‐monotonicity in a data set has been investigated in the works of Marsala and Petturiti and Milstein et al Suppose a data set

X = {false{x_{i} false}}_{i = 1}^{N}

contains n condition attributes

{false{A_{k} false}}_{k}^{n}

and one decision attribute D . X is not monotone consistent if it contains at least a pair x i , x h ∈Ω satisfying one of following conditions: ( i )( v ( A 1 , x i ),…, v ( A k , x i ))≤( v ( A 1 , x h ),…, v ( A k , x h )) and v ( D , x i )> v ( D , x h ); ( ii )( v ( A 1 , x i ),…, v ( A k , x i ))≥( v ( A 1 , x h ),…, v ( A k , x h )) and v ( D , x i )< v ( D , x h ). …”

Section: A Fast Rank Mutual Information Based Decision Treementioning

confidence: 99%

“…For monotonic classification problems, in order to make some comparisons with several different splitting rule based monotonic decision trees described in the work of Marsala and Petturiti, we employ the same data sets, that is, 7 pre‐processed UCI benchmark data sets with N M I 1 less than 12 %, as shown in Table . In the work of Marsala and Petturiti, all these data sets are pre‐processed by removing all the instances with missing values and applying WEKA filter Discretize to discretize real attributes; moreover, integer attributes have been converted to ordinal ones by using WEKA filter NumericToNominal , both contained in weka.filters.unsupervised.attribute .…”

Section: Experimental Studiesmentioning

confidence: 99%

“…In this section, we use the results in the work of Marsala and Petturiti to make comparative analysis with the proposed FRMIDT algorithm. In the work of Marsala and Petturiti, there are several different splitting criteria based monotonic decision trees such as rank Gini discrimination measure (

H_{G}^{*}

), rank Shannon discrimination measure (

H_{S}^{*}

), pessimistic rank discrimination measure (

H_{p}^{*}

) and rank Gini measure H G , rank Shannon measure H S , total ambiguity score measure

H_{M I D}^{10}

, and a modified Gini measure H I C T (see the work of Marsala and Petturiti for a careful discussion of quoted measures). The comparisons mainly focus on the testing accuracy, the number of leaves, and the monotonicity of constructed trees.…”

Section: Experimental Studiesmentioning

confidence: 99%

“…In the work of Makino et al, the Positive Decision Tree (P‐DT) algorithm was presented, which could always produce a monotonic decision tree for any positive data set. Other most known monotonic decision trees such as the Monotone Decision Tree (MDT), the Isotonic Classification Tree (ICT), and the Rank Discrimination Measure Tree (RDMT) have been developed over the years.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

A fast rank mutual information based decision tree and its implementation via Map‐Reduce

Wang

Liu

2018

Concurrency and Computation

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Summary To address the time‐consuming problem for the confirmation of splitting attributes and splitting points in classic rank mutual information based decision trees, this paper establishes a fast rank mutual information based decision tree (FRMIDT) for classification problems. First, the proposed FRMIDT algorithm improves the velocity by a max‐relevance and min‐redundancy criterion to remove the redundant attributes in each tree node building. Then, the fuzzy c‐means algorithm is employed to confirm the splitting points for further acceleration. Meanwhile, a parallel implementation is developed in the framework of Map‐Reduce (MR‐FRMIDT) for medium or large‐scale data classification. Several comparative studies are conducted on UCI benchmark data sets. In contrast to the classic rank mutual information based decision tree on 12 data sets, the proposed FRMIDT model effectively reduces the computational time on the premise of keeping testing accuracy. Furthermore, the proposed FRMIDT algorithm is comparable through comparing FRMIDT with other traditional decision tree classifiers including BFT, C4.5, LAD, NBT, and SC. Meanwhile, the comparison with 7 different popular splitting measures based monotonic decision trees on several data sets illustrates the effectiveness of FRMIDT in monotonic classification. At last, the experimental analysis on other 6 data sets shows that the proposed MR‐FRMIDT is feasible and has a good parallel performance on reducing execution time and avoiding memory restrictions.

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“…Some quantification of non‐monotonicity in a data set has been investigated in the works of Marsala and Petturiti and Milstein et al Suppose a data set

X = {false{x_{i} false}}_{i = 1}^{N}

contains n condition attributes

{false{A_{k} false}}_{k}^{n}

Section: A Fast Rank Mutual Information Based Decision Treementioning

confidence: 99%

Section: Experimental Studiesmentioning

confidence: 99%

H_{G}^{*}

), rank Shannon discrimination measure (

H_{S}^{*}

), pessimistic rank discrimination measure (

H_{p}^{*}

) and rank Gini measure H G , rank Shannon measure H S , total ambiguity score measure

H_{M I D}^{10}

Section: Experimental Studiesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A fast rank mutual information based decision tree and its implementation via Map‐Reduce

Wang

Liu

2018

Concurrency and Computation

View full text Add to dashboard Cite

show abstract

“…The other algorithms are all supervised algorithms and have different advantages and disadvantages: LDA is effective in many classification problems [31]; GMSS is more robust than LDA when the subspace dimension is less than C À 1 (C is the number of categories) [44]; and DLA and SLPP are top-level manifold learning algorithms that consider both local geometric structure and discriminative information preservation from different perspectives.…”

Section: Baselines and Performance Evaluationmentioning

confidence: 99%

Local structure preserving discriminative projections for RGB-D sensor-based scene classification

Tao

Cheng

et al. 2015

Information Sciences

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Discovering Ordinal Attributes Through Gradual Patterns, Morphological Filters and Rank Discrimination Measures

Marsala

Laurent

Lesot

et al. 2018

Lecture Notes in Computer Science

Self Cite

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This paper proposes to exploit heterogeneous data, i.e. data described by both numerical and categorical features, so as to gain knowledge about the categorical attributes from the numerical ones. More precisely, it aims at discovering whether, according to a given data set, based on information provided by the numerical attributes, some categorical attributes actually are ordinal ones and, additionally, at establishing ranking relations between the category values. To that aim, the paper proposes the 3-step methodology OSACA, standing for Order Seeking Algorithm for Categorical Attributes: it first consists in extracting gradual patterns from the numerical attributes, to identify rich ranking information about the data; it then applies mathematical morphology tools, more precisely alternated filters, to induce an associated order on the categorical attributes. The third step evaluates the quality of the candidate rankings through measures derived from the rank entropy discrimination.

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Rank discrimination measures for enforcing monotonicity in decision tree induction

Cited by 28 publications

References 29 publications

A fast rank mutual information based decision tree and its implementation via Map‐Reduce

A fast rank mutual information based decision tree and its implementation via Map‐Reduce

Local structure preserving discriminative projections for RGB-D sensor-based scene classification

Discovering Ordinal Attributes Through Gradual Patterns, Morphological Filters and Rank Discrimination Measures

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