Importance of Characteristic Features and Their Form for Data Exploration
Abstract
:1. Introduction
- Illustration of a research framework dedicated to a gradual discretisation procedure directed by selected rankings of features;
- Exploitation of multiple discretisation algorithms, with supervised and unsupervised interval construction;
- Comparison between domain transformations following rankings in ascending and descending directions;
- Analysis of trends in performance of state-of-the-art classifiers with varied operational backgrounds from the point of view of data representation and interpretation;
- Observation of the impact of considering information on the relevance of attributes during their discretisation on the performance of the selected classifiers;
- Application of the proposed methodology in the stylometric domain for authorship attribution tasks.
2. Background
2.1. Nature of Input Space
2.2. Data Transformations
- N—the number of training instances,
- —the number of training instances from the class ,
- —the number of instances with the x-th value of the given attribute,
- —the number of instances from class with the y-th value of the given attribute,
- —the number of possible cut-points.
2.3. Importance of Attributes
Algorithm 1 Pseudo-code for Relief |
Input: set of learning instances X, set A of all N attributes, set of classes Cl, probabilities of classes P(Cl), number of iterations m, number k of considered nearest instances from each class; Output: vector of weights w for all attributes; begin for i = 1 to N do w(i) = 0 end for for i = 1 to m do choose randomly an instance x ∈ X find k nearest hits Hj for each class Cl ≠ class(x) do find k nearest misses Mj(Cl) end for for l = 1 to N do end for end for end {algorithm} |
Algorithm 2 Pseudo-code for OneR classifier |
Input: set A of all attributes, set of learning instances X; Output: 1-rule 1-rB; begin CandidateRules←Ø for each attribute a ∈ A do for each value va of attribute a do count how often each class appears find the most frequent class ClF construct a rule IF a = va THEN ClF end for calculate classification accuracy for all rules choose the best rule rB CandidateRules←rB end for choose as 1-rB the best one from CandidateRules end {algorithm} |
2.4. Exploration of Input Space
3. Framework for Discretisation Controlled by Attribute Importance
3.1. Input Data and Attributes
3.2. Rankings
3.3. Discretisation Approaches
3.4. Inducers
3.5. Starting and Stopping Point
3.6. Intermediate Steps and Directions of Processing
Algorithm 3 Pseudo-code for ranking driven discretisation |
Input: ranking of attributes RankingA, dataset in the continuous domain Data-R, direction Direction to pursue ranking RankingA, number of attributes N; begin TMP-Data←Data-R mine knowledge from TMP-Data evaluate performance for TMP-Data if Direction = Descending then k = 1 else k = N while (k > 0) AND (k < N + 1) do select attribute from the ranking attr = RankingA[k] discretise attr in TMP-Data mine knowledge from TMP-Data evaluate performance for TMP-Data if Direction = Descending then k = k + 1 else k = k − 1 end while end {algorithm} |
4. Experiments
4.1. Data Preparation
4.2. Rankings Employed
4.3. Discretisation Algorithms
4.4. Performance Evaluation for Classifiers
5. Results and Their Discussion
5.1. Reference Points
5.2. Performance Trends
5.3. Summary of Results
6. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Rank | F-Writers | M-Writers | |||
---|---|---|---|---|---|
Relief | OneR | Relief | OneR | ||
1 | on | to | by | by | |
2 | to | on | if | or | |
3 | of | of | so | in | |
4 | as | as | or | if | |
5 | by | by | in | at | |
6 | if | if | as | so | |
7 | or | in | at | as | |
8 | up | up | on | on | |
9 | at | so | no | no | |
10 | in | or | of | to | |
11 | so | at | up | of | |
12 | no | no | to | up |
Domain | F-Writers | M-Writers | Domain | F-Writers | M-Writers | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
NB | J48 | k-NN | NB | J48 | k-NN | NB | J48 | k-NN | NB | J48 | k-NN | ||||
Cont. | 93.33 | 89.79 | 85.56 | 84.03 | 75.63 | 77.29 | |||||||||
dsF | 50.00 | 87.78 | 62.22 | 69.44 | 80.76 | 83.54 | dsK | 62.22 | 93.40 | 62.22 | 68.89 | 80.76 | 82.43 | ||
duf02 | 91.18 | 91.18 | 83.89 | 75.35 | 73.82 | 68.47 | duw02 | 87.01 | 85.35 | 88.06 | 73.82 | 72.71 | 70.14 | ||
duf03 | 92.85 | 85.63 | 86.94 | 75.69 | 79.72 | 71.25 | duw03 | 89.38 | 83.68 | 85.83 | 78.68 | 77.29 | 72.36 | ||
duf04 | 93.40 | 86.46 | 88.61 | 81.60 | 69.31 | 75.21 | duw04 | 91.67 | 86.94 | 82.78 | 80.63 | 79.24 | 71.32 | ||
duf05 | 92.85 | 86.18 | 85.07 | 81.11 | 78.96 | 73.54 | duw05 | 90.56 | 80.42 | 84.10 | 79.38 | 75.76 | 69.51 | ||
duf06 | 94.10 | 88.19 | 89.17 | 80.35 | 74.79 | 73.47 | duw06 | 92.22 | 85.69 | 85.21 | 82.22 | 75.21 | 77.22 | ||
duf07 | 95.76 | 81.74 | 85.63 | 80.42 | 78.75 | 77.85 | duw07 | 91.11 | 89.65 | 86.46 | 81.04 | 71.94 | 72.29 | ||
duf08 | 92.29 | 88.19 | 88.47 | 80.49 | 77.92 | 75.28 | duw08 | 91.67 | 90.97 | 85.76 | 77.64 | 75.42 | 73.61 | ||
duf09 | 94.58 | 88.26 | 86.81 | 80.42 | 79.79 | 77.57 | duw09 | 90.56 | 90.35 | 88.68 | 81.53 | 76.46 | 74.58 | ||
duf10 | 93.47 | 87.15 | 86.88 | 79.86 | 80.90 | 75.35 | duw10 | 91.67 | 87.01 | 86.32 | 80.00 | 76.25 | 73.61 |
F-Writers | M-Writers | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
Ascending | Descending | Ascending | Descending | |||||||||
Avg. ± St.dev. | Min | Max | Avg. ± St.dev. | Min | Max | Avg. ± St.dev. | Min | Max | Avg. ± St.dev. | Min | Max | |
Domain | Relief ranking | |||||||||||
dsF | 80.38 ± 12.94 | 56.18 | 95.14 | 60.18 ± 14.52 | 50.00 | 88.61 | 83.74 ± 1.79 | 81.53 | 87.08 | 76.60 ± 4.13 | 72.29 | 82.85 |
dsK | 83.67 ± 07.50 | 74.17 | 95.14 | 78.57 ± 11.70 | 61.11 | 90.56 | 83.15 ± 1.29 | 81.32 | 84.79 | 75.96 ± 4.71 | 70.83 | 82.85 |
duf | 94.07 ± 00.19 | 92.71 | 95.76 | 93.00 ± 00.49 | 89.38 | 95.21 | 82.73 ± 1.80 | 77.43 | 85.21 | 80.95 ± 1.84 | 73.13 | 85.76 |
duf02 | 94.58 ± 00.58 | 93.89 | 95.76 | 90.16 ± 00.60 | 89.38 | 91.11 | 81.98 ± 2.33 | 77.43 | 84.51 | 77.14 ± 3.64 | 73.13 | 83.54 |
duf03 | 94.35 ± 00.50 | 93.89 | 95.21 | 93.20 ± 00.98 | 91.67 | 94.58 | 82.64 ± 1.49 | 79.93 | 84.03 | 79.07 ± 3.28 | 74.03 | 83.40 |
duf04 | 94.34 ± 00.63 | 93.89 | 95.76 | 93.16 ± 00.81 | 92.29 | 94.51 | 83.13 ± 2.12 | 79.93 | 85.21 | 81.76 ± 1.47 | 79.79 | 84.65 |
duf05 | 93.67 ± 00.40 | 92.71 | 93.89 | 92.34 ± 01.00 | 90.49 | 93.96 | 82.68 ± 1.93 | 79.24 | 84.65 | 82.96 ± 1.69 | 80.56 | 85.21 |
duf06 | 93.95 ± 00.32 | 93.33 | 94.51 | 93.54 ± 00.47 | 92.85 | 94.51 | 82.80 ± 2.00 | 79.38 | 85.21 | 80.90 ± 1.22 | 79.79 | 83.40 |
duf07 | 94.12 ± 00.49 | 93.33 | 95.14 | 94.53 ± 00.44 | 93.33 | 95.21 | 82.69 ± 1.85 | 79.93 | 85.14 | 81.52 ± 1.61 | 79.24 | 84.65 |
duf08 | 93.73 ± 00.38 | 92.71 | 93.89 | 93.11 ± 00.94 | 91.74 | 95.07 | 82.60 ± 1.93 | 79.31 | 85.21 | 81.87 ± 1.69 | 80.35 | 84.58 |
duf09 | 93.90 ± 00.27 | 93.33 | 94.51 | 94.00 ± 00.57 | 93.33 | 95.14 | 82.73 ± 1.92 | 79.86 | 85.21 | 82.14 ± 1.43 | 80.42 | 84.58 |
duf10 | 94.00 ± 00.38 | 93.89 | 95.14 | 93.01 ± 00.82 | 92.29 | 94.51 | 83.33 ± 1.44 | 80.49 | 85.21 | 81.18 ± 1.88 | 79.24 | 85.76 |
duw | 93.15 ± 00.61 | 90.69 | 95.76 | 91.12 ± 00.97 | 85.21 | 93.89 | 83.30 ± 1.11 | 79.86 | 86.46 | 81.01 ± 0.92 | 76.88 | 84.17 |
duw02 | 93.88 ± 00.92 | 92.22 | 95.76 | 88.17 ± 02.26 | 85.21 | 92.22 | 83.67 ± 0.79 | 82.71 | 85.14 | 78.87 ± 1.19 | 77.29 | 80.76 |
duw03 | 92.99 ± 01.05 | 91.04 | 94.51 | 89.64 ± 01.22 | 88.13 | 92.08 | 83.42 ± 2.03 | 79.93 | 86.46 | 79.65 ± 1.89 | 76.88 | 82.85 |
duw04 | 93.24 ± 00.66 | 91.67 | 94.03 | 91.46 ± 00.84 | 90.56 | 93.33 | 82.66 ± 1.26 | 80.00 | 84.51 | 81.75 ± 1.09 | 80.00 | 83.96 |
duw05 | 92.84 ± 00.94 | 90.69 | 93.89 | 91.18 ± 01.60 | 89.38 | 93.89 | 83.24 ± 2.05 | 79.86 | 85.28 | 81.11 ± 1.00 | 79.86 | 83.47 |
duw06 | 93.25 ± 00.54 | 91.74 | 93.96 | 92.17 ± 00.87 | 91.04 | 93.33 | 83.48 ± 1.09 | 81.04 | 84.58 | 81.22 ± 1.32 | 79.44 | 84.10 |
duw07 | 93.05 ± 00.86 | 91.11 | 94.03 | 92.01 ± 00.52 | 91.53 | 92.78 | 83.40 ± 1.03 | 80.49 | 84.51 | 82.59 ± 0.90 | 81.11 | 84.17 |
duw08 | 93.08 ± 00.46 | 92.22 | 93.33 | 92.08 ± 00.87 | 91.04 | 93.89 | 82.38 ± 1.26 | 79.93 | 83.96 | 80.64 ± 1.47 | 78.75 | 82.85 |
duw09 | 92.89 ± 00.59 | 91.67 | 93.89 | 91.28 ± 01.28 | 89.93 | 93.26 | 83.43 ± 1.10 | 81.53 | 84.58 | 81.72 ± 0.83 | 80.49 | 83.47 |
duw10 | 93.09 ± 00.67 | 91.11 | 93.33 | 92.07 ± 01.06 | 91.11 | 93.89 | 83.99 ± 1.21 | 81.67 | 85.76 | 81.55 ± 1.00 | 79.38 | 82.85 |
OneR ranking | ||||||||||||
dsF | 78.54 ± 12.29 | 52.22 | 93.33 | 60.61 ± 15.34 | 50.00 | 92.78 | 84.32 ± 1.58 | 81.46 | 87.08 | 76.06 ± 3.87 | 71.67 | 83.33 |
dsK | 81.07 ± 08.04 | 61.88 | 93.33 | 82.92 ± 08.32 | 61.11 | 92.78 | 83.59 ± 0.94 | 81.94 | 84.72 | 75.56 ± 4.49 | 68.33 | 83.33 |
duf | 93.88 ± 00.19 | 92.22 | 95.76 | 93.14 ± 00.51 | 89.38 | 95.21 | 83.09 ± 1.60 | 79.24 | 85.28 | 80.81 ± 1.73 | 73.06 | 85.76 |
duf02 | 94.42 ± 00.73 | 93.33 | 95.76 | 90.33 ± 01.12 | 89.38 | 93.33 | 82.47 ± 1.64 | 79.65 | 84.51 | 77.28 ± 3.84 | 73.06 | 83.54 |
duf03 | 94.02 ± 00.44 | 93.47 | 95.14 | 93.54 ± 00.73 | 92.22 | 94.58 | 82.78 ± 1.67 | 79.93 | 84.65 | 78.00 ± 3.24 | 74.03 | 83.40 |
duf04 | 94.02 ± 00.45 | 93.40 | 95.14 | 93.43 ± 00.79 | 92.29 | 94.51 | 83.54 ± 1.68 | 80.42 | 85.28 | 81.76 ± 1.37 | 79.79 | 84.65 |
duf05 | 93.52 ± 00.58 | 92.22 | 93.89 | 92.23 ± 01.26 | 90.49 | 93.96 | 83.25 ± 1.92 | 79.24 | 84.72 | 82.80 ± 1.46 | 81.04 | 84.58 |
duf06 | 93.90 ± 00.04 | 93.89 | 94.03 | 93.50 ± 00.73 | 92.29 | 94.51 | 83.43 ± 1.44 | 80.42 | 85.21 | 81.22 ± 1.36 | 79.79 | 83.47 |
duf07 | 93.91 ± 00.27 | 93.33 | 94.51 | 94.80 ± 00.44 | 93.89 | 95.21 | 82.68 ± 1.80 | 79.93 | 85.14 | 81.35 ± 1.64 | 79.24 | 84.65 |
duf08 | 93.63 ± 00.59 | 92.22 | 93.89 | 93.15 ± 01.19 | 91.67 | 95.07 | 83.14 ± 1.35 | 80.49 | 85.21 | 81.70 ± 1.17 | 80.35 | 83.96 |
duf09 | 93.74 ± 00.34 | 92.85 | 93.89 | 94.01 ± 00.55 | 93.47 | 95.14 | 83.06 ± 1.95 | 79.86 | 85.21 | 81.76 ± 1.22 | 80.42 | 84.58 |
duf10 | 93.79 ± 00.31 | 92.85 | 93.89 | 93.29 ± 00.70 | 92.29 | 94.51 | 83.42 ± 1.57 | 80.49 | 85.21 | 81.44 ± 1.83 | 79.24 | 85.76 |
duw | 93.11 ± 00.81 | 89.44 | 95.76 | 91.42 ± 01.04 | 86.39 | 94.51 | 83.05 ± 1.19 | 79.86 | 86.46 | 81.11 ± 1.03 | 74.38 | 84.17 |
duw02 | 93.51 ± 01.52 | 89.44 | 95.76 | 88.83 ± 02.21 | 86.39 | 93.89 | 83.32 ± 1.34 | 80.90 | 85.14 | 78.48 ± 1.90 | 74.38 | 80.63 |
duw03 | 92.94 ± 01.11 | 90.63 | 93.89 | 90.25 ± 01.30 | 88.13 | 92.78 | 83.91 ± 1.71 | 79.93 | 86.46 | 80.16 ± 1.75 | 77.50 | 82.85 |
duw04 | 93.39 ± 00.90 | 91.04 | 94.03 | 91.20 ± 01.14 | 89.93 | 93.89 | 82.18 ± 1.57 | 80.35 | 84.51 | 82.17 ± 1.18 | 81.18 | 84.10 |
duw05 | 92.82 ± 00.99 | 90.49 | 93.89 | 91.69 ± 01.54 | 89.38 | 93.89 | 83.15 ± 1.81 | 79.86 | 85.28 | 81.25 ± 1.60 | 78.75 | 83.47 |
duw06 | 93.24 ± 00.58 | 91.60 | 93.96 | 92.27 ± 00.83 | 91.04 | 93.33 | 83.37 ± 0.88 | 81.04 | 84.03 | 81.37 ± 0.84 | 80.00 | 82.36 |
duw07 | 93.10 ± 00.74 | 91.67 | 94.03 | 92.49 ± 00.63 | 91.67 | 93.89 | 83.30 ± 1.26 | 80.49 | 84.65 | 82.27 ± 1.04 | 81.04 | 84.17 |
duw08 | 93.08 ± 00.46 | 92.22 | 93.33 | 92.17 ± 00.92 | 91.04 | 93.89 | 81.79 ± 1.86 | 79.86 | 84.58 | 80.56 ± 1.75 | 77.64 | 83.47 |
duw09 | 92.97 ± 00.85 | 91.04 | 93.89 | 91.54 ± 01.48 | 89.93 | 94.51 | 83.11 ± 1.26 | 81.53 | 84.58 | 81.81 ± 0.86 | 80.56 | 83.47 |
duw10 | 92.93 ± 00.90 | 91.11 | 93.33 | 92.32 ± 00.96 | 91.11 | 93.89 | 83.30 ± 1.18 | 81.60 | 84.58 | 81.94 ± 1.04 | 80.00 | 83.47 |
F-Writers | M-Writers | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
Ascending | Descending | Ascending | Descending | |||||||||
Avg. ± St.dev. | Min | Max | Avg. ± St.dev. | Min | Max | Avg. ± St.dev. | Min | Max | Avg. ± St.dev. | Min | Max | |
Domain | Relief ranking | |||||||||||
dsF | 91.45 ± 1.57 | 89.79 | 94.65 | 74.36 ± 19.08 | 50.00 | 90.28 | 77.53 ± 2.36 | 72.01 | 79.51 | 78.59 ± 1.64 | 76.32 | 80.76 |
dsK | 91.16 ± 1.17 | 89.79 | 92.78 | 92.41 ± 01.93 | 87.50 | 93.40 | 76.76 ± 2.69 | 71.88 | 80.14 | 78.59 ± 1.64 | 76.32 | 80.76 |
duf | 89.95 ± 0.92 | 82.64 | 93.33 | 87.54 ± 00.73 | 82.85 | 92.22 | 76.37 ± 0.71 | 70.83 | 80.90 | 74.77 ± 0.81 | 66.67 | 82.08 |
duf02 | 90.55 ± 1.77 | 85.69 | 92.78 | 88.43 ± 02.42 | 84.79 | 91.81 | 73.64 ± 1.84 | 72.01 | 77.85 | 71.87 ± 3.92 | 66.74 | 77.92 |
duf03 | 90.24 ± 1.48 | 86.81 | 93.33 | 85.73 ± 00.58 | 85.28 | 87.43 | 76.52 ± 1.31 | 74.44 | 78.89 | 77.54 ± 2.48 | 72.15 | 81.46 |
duf04 | 90.38 ± 0.82 | 89.24 | 91.53 | 89.36 ± 02.56 | 86.46 | 92.22 | 77.07 ± 1.29 | 75.63 | 79.58 | 72.97 ± 4.56 | 66.67 | 79.51 |
duf05 | 89.35 ± 2.36 | 83.47 | 92.78 | 84.68 ± 01.01 | 83.75 | 87.01 | 78.43 ± 1.54 | 75.63 | 80.14 | 71.27 ± 0.82 | 69.86 | 72.64 |
duf06 | 88.77 ± 2.75 | 82.64 | 90.42 | 90.75 ± 01.15 | 88.19 | 91.88 | 75.13 ± 1.99 | 70.83 | 77.92 | 75.00 ± 1.57 | 72.22 | 77.43 |
duf07 | 90.34 ± 0.76 | 89.79 | 92.15 | 84.36 ± 02.42 | 82.85 | 90.49 | 75.64 ± 0.74 | 74.58 | 76.88 | 78.05 ± 2.14 | 73.26 | 80.42 |
duf08 | 90.32 ± 0.60 | 89.79 | 91.53 | 88.42 ± 00.67 | 87.64 | 90.00 | 77.54 ± 2.57 | 73.89 | 80.90 | 76.84 ± 1.90 | 72.64 | 78.47 |
duf09 | 90.13 ± 0.41 | 89.79 | 90.97 | 88.09 ± 00.57 | 86.53 | 88.33 | 77.51 ± 1.01 | 75.63 | 78.75 | 74.43 ± 2.79 | 69.65 | 79.79 |
duf10 | 89.48 ± 0.91 | 86.88 | 90.35 | 88.04 ± 01.27 | 87.15 | 91.81 | 75.81 ± 1.13 | 72.92 | 77.36 | 74.94 ± 4.14 | 69.38 | 82.08 |
duw | 89.83 ± 1.22 | 83.68 | 92.85 | 87.63 ± 00.83 | 80.35 | 94.51 | 76.73 ± 1.13 | 68.13 | 81.32 | 74.42 ± 0.98 | 63.19 | 79.86 |
duw02 | 90.73 ± 1.19 | 88.61 | 92.22 | 84.22 ± 03.09 | 80.35 | 89.38 | 76.67 ± 1.57 | 73.68 | 78.96 | 69.15 ± 3.70 | 63.19 | 74.51 |
duw03 | 89.79 ± 2.30 | 83.68 | 92.78 | 87.51 ± 01.89 | 83.68 | 89.93 | 76.87 ± 2.02 | 72.43 | 80.14 | 73.81 ± 2.81 | 68.82 | 77.29 |
duw04 | 90.61 ± 1.20 | 88.54 | 92.22 | 86.81 ± 01.81 | 83.26 | 90.97 | 77.90 ± 2.09 | 74.10 | 81.32 | 76.50 ± 2.45 | 71.11 | 79.86 |
duw05 | 89.83 ± 2.27 | 85.49 | 92.22 | 85.07 ± 02.45 | 80.42 | 89.93 | 76.84 ± 2.00 | 74.79 | 80.69 | 74.96 ± 1.37 | 72.78 | 77.43 |
duw06 | 89.03 ± 1.19 | 86.25 | 89.79 | 86.12 ± 01.34 | 85.00 | 89.93 | 74.68 ± 1.75 | 72.50 | 76.88 | 74.05 ± 1.71 | 71.60 | 76.39 |
duw07 | 89.98 ± 1.55 | 85.90 | 92.15 | 89.46 ± 00.49 | 88.06 | 89.65 | 76.87 ± 1.65 | 74.58 | 79.10 | 74.44 ± 1.67 | 70.00 | 76.04 |
duw08 | 89.44 ± 1.86 | 84.51 | 90.42 | 90.81 ± 01.73 | 86.94 | 92.22 | 76.69 ± 3.66 | 68.13 | 79.51 | 75.43 ± 1.64 | 72.50 | 79.44 |
duw09 | 89.20 ± 1.56 | 85.00 | 90.42 | 91.16 ± 01.45 | 90.35 | 94.51 | 77.15 ± 1.56 | 75.35 | 79.58 | 74.48 ± 2.18 | 71.18 | 77.43 |
duw10 | 89.82 ± 1.79 | 85.14 | 92.85 | 87.56 ± 01.44 | 87.01 | 91.74 | 76.86 ± 1.63 | 74.93 | 78.96 | 76.98 ± 1.26 | 74.03 | 78.61 |
OneR ranking | ||||||||||||
dsF | 89.46 ± 6.83 | 69.17 | 92.78 | 63.62 ± 18.74 | 50.00 | 90.28 | 77.77 ± 1.71 | 74.38 | 79.51 | 78.52 ± 2.04 | 74.10 | 80.76 |
dsK | 90.65 ± 3.01 | 82.29 | 92.78 | 91.98 ± 03.22 | 82.78 | 93.40 | 77.04 ± 1.52 | 74.24 | 79.51 | 78.52 ± 2.04 | 74.10 | 80.76 |
duf | 89.91 ± 1.27 | 82.64 | 93.33 | 87.66 ± 01.01 | 82.85 | 92.22 | 76.57 ± 0.91 | 71.88 | 82.08 | 74.32 ± 0.60 | 66.67 | 81.46 |
duf02 | 90.99 ± 0.85 | 89.79 | 92.78 | 89.00 ± 02.61 | 84.79 | 91.81 | 74.72 ± 2.14 | 71.88 | 78.40 | 71.71 ± 4.34 | 66.74 | 79.10 |
duf03 | 90.13 ± 1.77 | 85.63 | 93.33 | 85.81 ± 00.58 | 85.28 | 87.43 | 77.47 ± 2.25 | 74.79 | 82.08 | 77.23 ± 1.73 | 74.51 | 81.46 |
duf04 | 90.16 ± 1.68 | 85.63 | 91.53 | 89.36 ± 02.33 | 86.46 | 91.81 | 78.33 ± 1.90 | 76.60 | 81.94 | 71.95 ± 3.34 | 66.67 | 77.71 |
duf05 | 89.89 ± 1.55 | 86.94 | 92.78 | 85.01 ± 02.18 | 83.75 | 90.97 | 78.02 ± 1.09 | 76.67 | 80.14 | 72.22 ± 2.02 | 70.00 | 76.18 |
duf06 | 89.07 ± 2.61 | 82.64 | 90.42 | 89.73 ± 01.85 | 86.25 | 91.88 | 75.62 ± 1.54 | 73.54 | 77.92 | 74.20 ± 1.45 | 72.22 | 76.53 |
duf07 | 89.88 ± 2.40 | 82.92 | 92.15 | 84.63 ± 02.82 | 82.85 | 92.22 | 75.60 ± 0.88 | 74.58 | 76.88 | 77.30 ± 2.67 | 73.26 | 80.42 |
duf08 | 89.97 ± 1.12 | 87.08 | 91.53 | 88.83 ± 01.26 | 88.19 | 92.15 | 76.46 ± 1.55 | 73.89 | 78.54 | 76.58 ± 2.11 | 72.64 | 79.10 |
duf09 | 89.85 ± 1.06 | 86.88 | 90.97 | 88.34 ± 00.87 | 86.53 | 90.42 | 77.66 ± 0.94 | 76.11 | 78.47 | 73.54 ± 2.57 | 69.65 | 77.50 |
duf10 | 89.20 ± 1.34 | 86.25 | 90.35 | 88.22 ± 01.50 | 87.15 | 91.81 | 75.28 ± 1.21 | 72.92 | 77.36 | 74.14 ± 3.75 | 69.38 | 79.31 |
duw | 90.09 ± 0.88 | 82.22 | 92.85 | 87.63 ± 01.31 | 80.35 | 94.51 | 77.18 ± 1.35 | 68.13 | 81.32 | 74.37 ± 0.65 | 63.89 | 79.79 |
duw02 | 90.59 ± 1.72 | 87.01 | 92.22 | 84.68 ± 03.50 | 80.35 | 90.35 | 76.63 ± 3.25 | 70.69 | 79.72 | 68.74 ± 2.48 | 63.89 | 72.22 |
duw03 | 90.73 ± 1.13 | 89.24 | 92.78 | 86.73 ± 02.35 | 83.06 | 89.17 | 78.39 ± 1.63 | 76.25 | 80.83 | 74.57 ± 2.52 | 68.82 | 77.36 |
duw04 | 90.20 ± 2.26 | 84.58 | 92.22 | 87.45 ± 01.68 | 85.14 | 90.97 | 77.58 ± 2.41 | 73.26 | 81.32 | 76.20 ± 2.66 | 71.11 | 79.79 |
duw05 | 90.64 ± 2.04 | 85.49 | 92.22 | 84.57 ± 03.80 | 80.42 | 92.22 | 78.11 ± 1.96 | 74.24 | 80.69 | 74.72 ± 1.56 | 72.78 | 77.99 |
duw06 | 89.24 ± 0.78 | 87.92 | 90.35 | 85.84 ± 01.66 | 84.51 | 90.35 | 75.20 ± 1.79 | 72.01 | 77.85 | 74.59 ± 0.82 | 73.40 | 76.25 |
duw07 | 90.39 ± 0.89 | 88.54 | 92.15 | 89.67 ± 00.30 | 89.10 | 90.42 | 76.13 ± 2.19 | 73.61 | 79.10 | 73.56 ± 2.33 | 70.28 | 76.04 |
duw08 | 88.80 ± 2.75 | 82.22 | 90.42 | 91.07 ± 01.24 | 88.06 | 92.22 | 77.67 ± 3.27 | 68.13 | 79.51 | 75.66 ± 1.93 | 72.85 | 79.44 |
duw09 | 89.75 ± 0.82 | 88.06 | 90.42 | 91.05 ± 01.55 | 89.79 | 94.51 | 77.36 ± 1.88 | 74.79 | 79.58 | 75.39 ± 1.97 | 73.06 | 78.26 |
duw10 | 90.47 ± 1.08 | 89.79 | 92.85 | 87.59 ± 01.46 | 87.01 | 91.74 | 77.56 ± 1.39 | 74.93 | 79.51 | 75.94 ± 1.64 | 73.06 | 78.61 |
F-Writers | M-Writers | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
Ascending | Descending | Ascending | Descending | |||||||||
Avg. ± St.dev. | Min | Max | Avg. ± St.dev. | Min | Max | Avg. ± St.dev. | Min | Max | Avg. ± St.dev. | Min | Max | |
Domain | Relief ranking | |||||||||||
dsF | 72.85 ± 11.39 | 57.78 | 91.04 | 64.47 ± 09.61 | 55.56 | 85.83 | 77.32 ± 4.10 | 70.69 | 85.76 | 75.26 ± 2.86 | 70.14 | 78.61 |
dsK | 74.06 ± 10.11 | 66.67 | 91.04 | 71.43 ± 09.23 | 57.22 | 85.83 | 77.83 ± 4.04 | 69.58 | 85.21 | 75.41 ± 3.04 | 70.14 | 79.17 |
duf | 83.80 ± 02.53 | 73.89 | 88.75 | 88.79 ± 01.11 | 81.94 | 93.47 | 72.24 ± 1.74 | 61.81 | 78.68 | 74.12 ± 0.94 | 64.72 | 80.00 |
duf02 | 81.48 ± 05.85 | 73.89 | 88.68 | 86.36 ± 02.20 | 81.94 | 89.72 | 67.80 ± 5.48 | 61.94 | 76.04 | 71.70 ± 1.69 | 69.31 | 74.58 |
duf03 | 81.24 ± 02.80 | 76.32 | 86.88 | 89.49 ± 01.76 | 86.88 | 93.47 | 67.69 ± 4.17 | 61.81 | 73.61 | 73.24 ± 3.14 | 68.96 | 80.00 |
duf04 | 83.74 ± 02.73 | 79.17 | 87.36 | 90.08 ± 01.20 | 88.68 | 92.78 | 73.28 ± 2.64 | 69.79 | 78.68 | 74.65 ± 1.80 | 70.90 | 76.46 |
duf05 | 84.68 ± 02.96 | 79.72 | 88.61 | 87.84 ± 02.35 | 84.65 | 92.01 | 72.30 ± 2.85 | 69.24 | 77.71 | 71.45 ± 3.84 | 64.72 | 77.08 |
duf06 | 85.14 ± 01.25 | 82.57 | 86.88 | 90.43 ± 00.84 | 88.75 | 91.60 | 74.13 ± 2.46 | 70.49 | 77.22 | 74.76 ± 2.31 | 70.35 | 77.64 |
duf07 | 82.95 ± 03.16 | 78.68 | 86.88 | 87.90 ± 01.57 | 85.83 | 90.97 | 73.48 ± 2.37 | 70.14 | 77.78 | 76.75 ± 1.63 | 74.58 | 79.51 |
duf08 | 85.28 ± 02.92 | 80.35 | 88.75 | 88.76 ± 01.38 | 87.36 | 91.39 | 73.28 ± 1.92 | 70.14 | 75.49 | 73.52 ± 1.73 | 70.97 | 76.32 |
duf09 | 84.96 ± 02.28 | 80.90 | 87.43 | 89.04 ± 01.47 | 86.81 | 90.90 | 74.73 ± 1.35 | 73.68 | 78.40 | 75.74 ± 1.48 | 73.68 | 78.19 |
duf10 | 84.75 ± 02.38 | 80.90 | 87.50 | 89.20 ± 01.56 | 86.39 | 91.53 | 73.45 ± 1.65 | 71.04 | 75.83 | 75.29 ± 2.09 | 71.74 | 79.31 |
duw | 86.09 ± 01.75 | 73.82 | 90.97 | 86.47 ± 01.20 | 80.35 | 90.83 | 72.80 ± 1.06 | 65.90 | 80.07 | 75.25 ± 1.81 | 63.06 | 82.50 |
duw02 | 85.94 ± 03.10 | 79.79 | 89.93 | 83.06 ± 01.45 | 80.35 | 85.07 | 73.40 ± 4.38 | 66.67 | 80.07 | 70.16 ± 4.49 | 63.06 | 77.08 |
duw03 | 82.17 ± 03.79 | 73.82 | 86.94 | 86.86 ± 02.93 | 82.64 | 90.83 | 71.00 ± 1.72 | 68.19 | 74.72 | 74.07 ± 2.57 | 70.49 | 78.47 |
duw04 | 86.45 ± 02.19 | 82.78 | 89.10 | 85.46 ± 02.49 | 82.71 | 89.79 | 73.62 ± 2.69 | 68.47 | 76.53 | 76.00 ± 2.19 | 71.67 | 78.33 |
duw05 | 86.40 ± 02.36 | 82.36 | 89.17 | 85.93 ± 02.38 | 83.40 | 89.79 | 68.87 ± 1.75 | 65.90 | 71.46 | 74.21 ± 2.86 | 70.28 | 78.47 |
duw06 | 86.07 ± 01.70 | 82.36 | 88.06 | 86.75 ± 02.18 | 83.96 | 89.58 | 74.03 ± 1.67 | 70.63 | 76.04 | 77.47 ± 1.27 | 75.35 | 80.69 |
duw07 | 87.18 ± 01.99 | 85.07 | 90.97 | 87.51 ± 00.75 | 86.39 | 88.61 | 74.74 ± 2.43 | 70.56 | 77.71 | 74.29 ± 2.00 | 71.32 | 77.50 |
duw08 | 86.22 ± 01.87 | 82.22 | 88.54 | 87.02 ± 01.18 | 84.51 | 88.54 | 73.35 ± 2.05 | 69.58 | 76.74 | 78.02 ± 2.33 | 75.00 | 82.50 |
duw09 | 87.76 ± 01.30 | 85.14 | 89.79 | 89.06 ± 01.05 | 86.81 | 90.42 | 73.51 ± 1.50 | 71.53 | 76.46 | 74.63 ± 2.38 | 70.83 | 79.58 |
duw10 | 86.62 ± 02.11 | 83.47 | 89.17 | 86.55 ± 00.98 | 84.58 | 88.47 | 72.67 ± 1.30 | 70.76 | 74.38 | 78.36 ± 1.95 | 74.79 | 81.53 |
OneR ranking | ||||||||||||
dsF | 68.31 ± 07.42 | 57.78 | 88.13 | 66.05 ± 10.03 | 58.33 | 90.28 | 76.89 ± 3.17 | 74.03 | 85.76 | 75.76 ± 3.74 | 67.01 | 81.25 |
dsK | 69.48 ± 06.28 | 66.11 | 88.13 | 73.74 ± 07.95 | 60.56 | 90.28 | 77.92 ± 3.68 | 73.47 | 85.21 | 75.86 ± 3.80 | 67.01 | 81.25 |
duf | 83.98 ± 02.64 | 73.89 | 89.24 | 89.22 ± 00.83 | 83.26 | 93.47 | 72.57 ± 1.70 | 61.04 | 79.38 | 73.65 ± 0.90 | 64.72 | 78.82 |
duf02 | 80.65 ± 05.21 | 73.89 | 87.36 | 86.48 ± 02.08 | 83.26 | 90.28 | 68.53 ± 6.00 | 61.04 | 78.96 | 72.75 ± 3.46 | 66.18 | 77.50 |
duf03 | 82.22 ± 03.29 | 76.32 | 86.88 | 89.07 ± 02.15 | 86.39 | 93.47 | 68.63 ± 2.72 | 63.47 | 72.15 | 70.54 ± 2.52 | 65.56 | 75.07 |
duf04 | 84.60 ± 03.20 | 79.17 | 88.19 | 90.10 ± 01.26 | 87.99 | 92.01 | 73.51 ± 2.21 | 70.28 | 77.64 | 75.73 ± 1.24 | 72.78 | 77.01 |
duf05 | 84.63 ± 03.38 | 79.72 | 89.24 | 88.55 ± 01.72 | 85.14 | 92.01 | 71.45 ± 1.48 | 69.24 | 74.44 | 71.43 ± 3.50 | 64.72 | 75.90 |
duf06 | 85.93 ± 01.61 | 82.57 | 88.61 | 90.43 ± 00.87 | 88.54 | 91.60 | 74.37 ± 2.23 | 71.39 | 77.22 | 73.91 ± 2.00 | 70.97 | 77.15 |
duf07 | 82.75 ± 02.87 | 78.68 | 86.88 | 88.63 ± 01.45 | 86.18 | 90.97 | 74.27 ± 2.57 | 71.32 | 79.38 | 75.96 ± 2.22 | 71.18 | 78.82 |
duf08 | 85.25 ± 02.85 | 80.35 | 87.99 | 89.70 ± 01.17 | 87.36 | 91.39 | 73.74 ± 2.04 | 70.14 | 75.97 | 73.14 ± 1.65 | 70.69 | 75.76 |
duf09 | 85.32 ± 02.43 | 80.90 | 87.99 | 89.79 ± 01.37 | 87.22 | 91.46 | 75.13 ± 1.70 | 73.13 | 77.78 | 74.76 ± 2.30 | 70.56 | 77.71 |
duf10 | 84.50 ± 02.29 | 80.90 | 88.54 | 90.24 ± 00.98 | 88.61 | 91.60 | 73.50 ± 1.91 | 71.04 | 77.15 | 74.65 ± 2.07 | 71.74 | 78.19 |
duw | 85.73 ± 01.68 | 73.82 | 90.97 | 86.98 ± 01.00 | 80.35 | 90.21 | 72.53 ± 1.56 | 64.65 | 77.29 | 74.61 ± 1.92 | 66.74 | 80.35 |
duw02 | 85.12 ± 03.53 | 77.43 | 88.68 | 84.17 ± 01.91 | 80.35 | 87.92 | 72.60 ± 4.13 | 64.65 | 77.01 | 72.76 ± 3.76 | 67.71 | 77.22 |
duw03 | 81.81 ± 03.64 | 73.82 | 86.25 | 87.08 ± 02.31 | 82.64 | 90.21 | 72.52 ± 1.60 | 70.21 | 75.14 | 72.96 ± 2.51 | 67.78 | 76.88 |
duw04 | 86.07 ± 02.35 | 81.11 | 88.61 | 86.12 ± 02.19 | 82.85 | 89.79 | 73.04 ± 1.65 | 70.35 | 75.56 | 73.98 ± 2.52 | 69.17 | 77.78 |
duw05 | 85.42 ± 02.04 | 82.36 | 89.17 | 86.71 ± 02.23 | 84.10 | 89.79 | 69.29 ± 2.09 | 65.90 | 74.17 | 72.58 ± 3.12 | 66.74 | 77.92 |
duw06 | 86.19 ± 01.57 | 82.36 | 87.43 | 87.65 ± 01.50 | 85.28 | 89.58 | 74.10 ± 1.99 | 70.63 | 77.29 | 75.80 ± 2.56 | 69.51 | 77.64 |
duw07 | 87.34 ± 02.12 | 85.00 | 90.97 | 88.18 ± 00.79 | 87.01 | 89.93 | 73.36 ± 1.81 | 70.56 | 75.83 | 74.19 ± 2.17 | 71.04 | 78.33 |
duw08 | 86.22 ± 02.04 | 82.22 | 88.68 | 87.60 ± 00.82 | 86.25 | 88.54 | 72.92 ± 2.87 | 69.58 | 77.22 | 77.05 ± 1.74 | 74.38 | 79.72 |
duw09 | 87.62 ± 01.61 | 85.14 | 89.79 | 88.58 ± 00.91 | 86.88 | 89.72 | 72.78 ± 1.73 | 71.11 | 75.90 | 74.53 ± 3.14 | 68.61 | 79.58 |
duw10 | 85.74 ± 01.64 | 83.47 | 88.06 | 86.70 ± 01.15 | 84.58 | 88.47 | 72.16 ± 1.40 | 70.00 | 74.38 | 77.62 ± 1.98 | 73.54 | 80.35 |
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Stańczyk, U.; Zielosko, B.; Baron, G. Importance of Characteristic Features and Their Form for Data Exploration. Entropy 2024, 26, 404. https://doi.org/10.3390/e26050404
Stańczyk U, Zielosko B, Baron G. Importance of Characteristic Features and Their Form for Data Exploration. Entropy. 2024; 26(5):404. https://doi.org/10.3390/e26050404
Chicago/Turabian StyleStańczyk, Urszula, Beata Zielosko, and Grzegorz Baron. 2024. "Importance of Characteristic Features and Their Form for Data Exploration" Entropy 26, no. 5: 404. https://doi.org/10.3390/e26050404