Ordinal Factor Analysis

Ganter, Bernhard; Glodeanu, Cynthia Vera

doi:10.1007/978-3-642-29892-9_15

Cited by 13 publications

(4 citation statements)

References 4 publications

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“…In 5-18, the yet unused intervals I C,D are searched in a greedy manner as follows. We start by the attribute concepts γ(j) ∈ I C,D and try to extend them greedily by adding attributes (loop [8][9][10][11][12]. Due to Lemma 3, restricting to J and using ↑ J and ↓ J guarantees that we do not leave I C,D .…”

Section: It Remains To Verify Ementioning

confidence: 99%

From-below approximations in Boolean matrix factorization: Geometry and new algorithm

Bělohlávek

Trnečka

2015

Journal of Computer and System Sciences

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We present new results on Boolean matrix factorization and a new algorithm based on these results. The results emphasize the significance of factorizations that provide from-below approximations of the input matrix. While the previously proposed algorithms do not consider the possibly different significance of different matrix entries, our results help measure such significance and suggest where to focus when computing factors. An experimental evaluation of the new algorithm on both synthetic and real data demonstrates its good performance in terms of good coverage by the first k factors as well as a small number of factors needed for exact decomposition and indicates that the algorithm outperforms the available ones in these terms. We also propose future research topics.

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Section: It Remains To Verify Ementioning

confidence: 99%

From-below approximations in Boolean matrix factorization: Geometry and new algorithm

Bělohlávek

Trnečka

2015

Journal of Computer and System Sciences

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“…2 of our paper, we use ordinal formal contexts for illustrative purposes, but we do not directly refer to the formal concepts analysis. The use of LOS values for describing similarity relationships differentiates our approach form such models as ordinal HICLASS [37] and ordinal FA [38]. In the latter proposal, ordinal scales are employed only for defining searched factors, whereas the matrix being factorized still contains binary values.…”

Section: Relation To Other Methodsmentioning

confidence: 99%

“…A similar approach was presented by Ganter and Glodeau [38]. The authors showed the way of searching ordinal factors for an initial binary matrix.…”

Section: Background and Related Workmentioning

confidence: 96%

Modeling human thinking about similarities by neuromatrices in the perspective of fuzzy logic

Grobelny

Michalski

Weber

2020

Neural Comput & Applic

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In this work, we propose a new method for modeling human reasoning about objects’ similarities. We assume that similarity depends on perceived intensities of objects’ attributes expressed by natural language expressions such as low, medium, and high. We show how to find the underlying structure of the matrix with intensities of objects’ similarities in the factor-analysis-like manner. The demonstrated approach is based on fuzzy logic and set theory principles, and it uses only maximum and minimum operators. Similarly to classic eigenvector decomposition, we aim at representing the initial linguistic ordinal-scale (LOS) matrix as a max–min product of other LOS matrix and its transpose. We call this reconstructing matrix a neuromatrix because we assume that such a process takes place at the neural level in our brain. We show and discuss on simple, illustrative examples, how the presented way of modeling grasps natural way of reasoning about similarities. The unique characteristics of our approach are treating smaller attribute intensities as less important in making decisions about similarities. This feature is consistent with how the human brain is functioning at a biological level. A neuron fires and passes information further only if input signals are strong enough. The proposal of the heuristic algorithm for finding the decomposition in practice is also introduced and applied to exemplary data from classic psychological studies on perceived similarities between colors and between nations. Finally, we perform a series of simulation experiments showing the effectiveness of the proposed heuristic.

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“…In this section, data analysis using factor concepts is described (Belohlavek, 2012;Ganter and Glodeanu, 2012;Glodeanu and Ganter, 2012;Glodeanu, 2011).…”

Section: Factor Conceptsmentioning

confidence: 99%

A comprehensive survey on formal concept analysis, its research trends and applications

Singh

Cherukuri

Gani

2016

International Journal of Applied Mathematics and Computer Science

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In recent years, FCA has received significant attention from research communities of various fields. Further, the theory of FCA is being extended into different frontiers and augmented with other knowledge representation frameworks. In this backdrop, this paper aims to provide an understanding of the necessary mathematical background for each extension of FCA like FCA with granular computing, a fuzzy setting, interval-valued, possibility theory, triadic, factor concepts and handling incomplete data. Subsequently, the paper illustrates emerging trends for each extension with applications. To this end, we summarize more than 350 recent (published after 2011) research papers indexed in Google Scholar, IEEE Xplore, ScienceDirect, Scopus, SpringerLink, and a few authoritative fundamental papers.

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Ordinal Factor Analysis

Cited by 13 publications

References 4 publications

From-below approximations in Boolean matrix factorization: Geometry and new algorithm

From-below approximations in Boolean matrix factorization: Geometry and new algorithm

Modeling human thinking about similarities by neuromatrices in the perspective of fuzzy logic

A comprehensive survey on formal concept analysis, its research trends and applications

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