Possibilistic fuzzy c-means with partial supervision

Antoine, Violaine; Guerrero, José Atilio; Romero, Gerardo

doi:10.1016/j.fss.2022.08.003

Cited by 12 publications

(4 citation statements)

References 47 publications

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“…The scaling factor α weighs the impact of partial supervision in semi-supervised fuzzy clustering and thus has a substantial effect on the estimated memberships and clusters' prototypes. All the models building on the additive combination technique introduced in [3], ranging from semi-supervised adaptations of Possibilistic Fuzzy C-Means [28] to complex workflows that wrap the SSFCMeans model [23], share the same mechanism of regulating the impact of partial supervision by means of the scaling factor α.…”

Section: Discussionmentioning

confidence: 99%

“…EXPLANATIONS OF THE SCALING FACTOR α Despite a wealth of literature spanning over 30 years on the topic of SSFC, surprisingly little attention was paid to the sound understanding of the scaling factor α. One of the main contributions of this article is that we systematically reviewed existing descriptions of the scaling factor [5]- [23], [27], [28] and concluded that these are highly alike and do not challenge the core meaning of the interpretation of the scaling factor α provided by Pedrycz and Waletzky in [3]. Therefore, we treat the interpretation from [3] as canonical and formulate Interpretation 1: The role of the scaling factor α is to maintain a balance between the supervised and unsupervised components within the optimization mechanism.…”

Section: Semi-supervised Possibilistic C-meansmentioning

confidence: 99%

“…For instance, Bouchachia and Pedrycz [8] tried grid B = ⟨0.3, 0.5, 0.7, 0.9, 1⟩, whereas Antoine et al [28] tried grid A = ⟨0.01, 0.05, 0.1, 0.5, 1⟩. These CV grids cover the space of α values, since they implicitly follow Interpretation 1 and the associated proportionality assumption that was expressed as IPS P97 (α) = α.…”

Section: A Constructing Cross-validation Gridsmentioning

confidence: 99%

“…PCM, just like FCM, was studied and modified by many researchers, including [26] who proposed Repulsive PCM. A semi-supervised version of Repulsive PCM was proposed in [27], and a semi-supervised adaptation of PFCM was described in [28].…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Explainable Impact of Partial Supervision in Semi-Supervised Fuzzy Clustering

Kmita,

Kaczmarek-Majer,

Hryniewicz

2024

IEEE Trans. Fuzzy Syst.

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Controlling the impact of partial supervision on the outcomes of modeling is of uttermost importance in semisupervised fuzzy clustering. Semi-Supervised Fuzzy C-Means (SSFCMeans), a specific model we consider, uses a single hyperparameter called a scaling factor α to weigh the impact of partially labeled data. This concept became widespread and was reused directly in many works building on SSFCMeans, or even applied to other fuzzy clustering algorithms such as Possibilistic C-Means. However, none of the works challenged the original interpretation of α which suggests that the impact of partial supervision is directly proportional to the scaling factor. We fill the above research gap and thoroughly analyze this relationship. We provide novel explanations of the scaling factor α in terms of the key element of fuzzy clustering -the membership values. We prove that the impact of partial supervision is a non-linear function of α. Our approach is rooted in the explainability framework, which distinguishes interpretation from an explanation and treats the latter as superior. Explaining the scaling factor leads to an explainable impact of partial supervision and enables greater control of it. Finally, built on the novel explanations, we propose a unified, analytically justified framework for selecting the value of the hyperparameter α that is based on the crossvalidation approach. We illustrate that the proposed framework enables an extensive analysis of the impact of partial supervision in SSFCMeans with a simulation experiment.

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Section: Discussionmentioning

confidence: 99%