On the size of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll" id="d1e521" altimg="si326.gif"><mml:mo>∃</mml:mo></mml:math>-generalized concept lattices

Kwuida, Léonard; Kuitché, Rostand S.; Temgoua, Romuald

doi:10.1016/j.dam.2019.02.035

Cited by 3 publications

(6 citation statements)

References 9 publications

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“…For the Zoo dataset we obtain 357 concepts in total. The top-3 most stable are c 1 , c 2 , c 3 with extent stability indices: σ e (G, ∅) = 1, σ e (∅, M) = 0.997, σ e (A, A ) = 0.625, respectively, where A = {f eathers, eggs, backbone, breathes, legs 2 , tail} and A = {11, 16,20,21,23,33,37,41,43,56,57,58,59, 71, 78, 79, 83, 87, 95, 100}. The most important attributes are six legs, eight legs, five legs, feathers, and four legs for c 2 (Fig.…”

Section: Theorem 2 ([21]mentioning

confidence: 99%

“…For ∀-generalisations, the number of concepts does not increase [42]. But for ∃generalisations, the size can actually increase [40][41][42][43][44].…”

Section: Generalisation and Extracted Patternsmentioning

confidence: 99%

“…In [41] a more succinct analysis of ∃-generalisations presents a family of contexts where generalising two attributes results in an exponential increase in the number of concepts. An example of such context is given in the Table 4 (left).…”

Section: Generalisation and Extracted Patternsmentioning

confidence: 99%

“…[41]). Let (G, M, I) be an attribute reduced context and a, b be two attributes such that their generalisation s = a∪b increases the size of the concept lattice.…”

mentioning

confidence: 99%

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On Interpretability and Similarity in Concept-Based Machine Learning

Kwuida

Ignatov

2021

Lecture Notes in Computer Science

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Machine Learning (ML) provides important techniques for classification and predictions. Most of these are black-box models for users and do not provide decision-makers with an explanation. For the sake of transparency or more validity of decisions, the need to develop explainable/interpretable ML-methods is gaining more and more importance. Certain questions need to be addressed:-How does an ML procedure derive the class for a particular entity? -Why does a particular clustering emerge from a particular unsupervised ML procedure? -What can we do if the number of attributes is very large? -What are the possible reasons for the mistakes for concrete cases and models? For binary attributes, Formal Concept Analysis (FCA) offers techniques in terms of intents of formal concepts, and thus provides plausible reasons for model prediction. However, from the interpretable machine learning viewpoint, we still need to provide decision-makers with the importance of individual attributes to the classification of a particular object, which may facilitate explanations by experts in various domains with high-cost errors like medicine or finance.We discuss how notions from cooperative game theory can be used to assess the contribution of individual attributes in classification and clustering processes in concept-based machine learning. To address the 3rd question, we present some ideas on how to reduce the number of attributes using similarities in large contexts.

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Section: Theorem 2 ([21]mentioning

confidence: 99%

“…For ∀-generalisations, the number of concepts does not increase [42]. But for ∃generalisations, the size can actually increase [40][41][42][43][44].…”

Section: Generalisation and Extracted Patternsmentioning

confidence: 99%

Section: Generalisation and Extracted Patternsmentioning

confidence: 99%

“…[41]). Let (G, M, I) be an attribute reduced context and a, b be two attributes such that their generalisation s = a∪b increases the size of the concept lattice.…”

mentioning

confidence: 99%

See 2 more Smart Citations

On Interpretability and Similarity in Concept-Based Machine Learning

Kwuida

Ignatov

2021

Lecture Notes in Computer Science

Self Cite

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show abstract

“…For ∀-generalisations, the number of concepts does not increase [42]. But for ∃-generalisations, the size can actually increase [43,44,42,40,41].…”

Section: Generalisation and Extracted Patternsmentioning

confidence: 99%

On Interpretability and Similarity in Concept-Based Machine Learning

Kwuida¹,

Ignatov²

2021

Preprint

Self Cite

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Machine Learning (ML) provides important techniques for classification and predictions. Most of these are black-box models for users and do not provide decision-makers with an explanation. For the sake of transparency or more validity of decisions, the need to develop explainable/interpretable ML-methods is gaining more and more importance. Certain questions need to be addressed:-How does an ML procedure derive the class for a particular entity? -Why does a particular clustering emerge from a particular unsupervised ML procedure? -What can we do if the number of attributes is very large? -What are the possible reasons for the mistakes for concrete cases and models? For binary attributes, Formal Concept Analysis (FCA) offers techniques in terms of intents of formal concepts, and thus provides plausible reasons for model prediction. However, from the interpretable machine learning viewpoint, we still need to provide decision-makers with the importance of individual attributes to the classification of a particular object, which may facilitate explanations by experts in various domains with high-cost errors like medicine or finance. We discuss how notions from cooperative game theory can be used to assess the contribution of individual attributes in classification and clustering processes in concept-based machine learning. To address the 3rd question, we present some ideas on how to reduce the number of attributes using similarities in large contexts.

show abstract