A lattice conceptual clustering system and its application to browsing retrieval

Carpineto, Claudio; Romano, Giovanni

doi:10.1007/bf00058654

Cited by 163 publications

(144 citation statements)

References 29 publications

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“…(6) Ex. 4 We demonstrate Property 3: the closure F 6 = {4, 5}, {d, e} is written as the outer product of two vectors, F 6 = xy T , the vectors associated with the objects and attributes of the closure, a rank-1 approximation of S. This product is a special case of the Kronecker product of matrices. …”

Section: Propertymentioning

confidence: 99%

Formal Concept Analysis via Atomic Priming

Fréin

2013

Formal Concept Analysis

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Formal Concept Analysis (FCA) looks to decompose a matrix of objectsattributes into a set of sparse matrices capturing the underlying structure of a formal context. We propose a Rank Reduction (RR) method to prime approximate FCAs, namely RRFCA. While many existing FCA algorithms are complete, lectic ordering of the lattice may not minimize search/decomposition time. Initially, RRFCA decompositions are not unique or complete; however, a set of good closures with high support is learned quickly, and then, made complete. RRFCA has its novelty in that we propose a new multiplicative two-stage method. First, we describe the theoretical foundations underpinning our RR approach. Second, we provide a representative exemplar, showing how RRFCA can be implemented. Further experiments demonstrate that RRFCA methods are efficient, scalable and yield time-savings. We demonstrate the resulting methods lend themselves to parallelization.Key words: Formal Concept Analysis, Rank Reduction, Factorization. IntroductionFormal Concept Analysis (FCA) leverages the notion of a concept, an objectattribute building block of a binary relational dataset, and its ranking in a concept hierarchy to mine data-sets [25]. One short-coming is that concepts are mined according to lectic ordering and not concept importance or support in the formal context. Lectic ordering recommends itself on account of its thoroughness [10] [24,13]. The theoretical and empirical complexity of various approaches is compared by Kuznetsov in [16]. Computational complexity is the main measure for comparing algorithms: Kuznetsov and Obiedkov focus on the properties of the data ensemble, namely sparsity, the primary complexity inducing characteristic of the decomposition. Aside from sparsity, the main bottlenecks are memory and processing constraints. Ganter's algorithm computes concepts iteratively based on the previous concept, without incurring exponential memory requirements, by exploiting lectic ordering. CloseByOne produces many concepts in each iteration. Bordat's algorithm, described in [3], introduces a data structure to store previously found concepts, which results in considerable timesavings. This approach is made more efficient in [2] by removing the need for a structure of exponential size.A significant short-coming of batch approaches is that the entire lattice must be reconstructed if the database changes. Here, we look to the memory and computation challenge by using rank reduction method and disjointness to select good starting-intents for FCA.The justification goes as follows: all concepts are not equal in a binary relational dataset. FC support (the extent to which it overlaps with the formal context) and its expressiveness (FC disjointness given a set of FCs), may be different for FCs. NextClosure's lectic ordering does not consider these concerns. To address this, we prime NextClosure with multiple starting-intents by taking reduced rank approximations of the binary relation using Nonnegative Matrix Factorization (NMF) [18]. Lectic order...

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Section: Propertymentioning

confidence: 99%

Formal Concept Analysis via Atomic Priming

Fréin

2013

Formal Concept Analysis

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“…The structuring of information that FCA supports has inspired work on browsing [13,3], clustering [4], and ranking [6,15]. A basic drawback of these approaches is that they require the computation of the whole concept lattice, whose size may be exponential in that of the context, as it will be argued below.…”

Section: Related Workmentioning

confidence: 99%

Preference-Based Query Tuning Through Refinement/Enlargement in a Formal Context

Spyratos

Meghini

2006

Lecture Notes in Computer Science

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Abstract. The user of an information system rarely knows exactly what he is looking for, but once shown a piece of information he can quickly tell whether it is what he needs. Query tuning is the process of searching for the query that best approximates the information need of the user. Typically, navigation and querying are two completely separate processes, and the user usually has to switch often from one to the other-a painstaking process producing a frustrating experience. In this paper, we propose an approach to query tuning that integrates navigation and querying into a single process, thus leading to a more flexible and more user friendly method of query tuning. The proposed approach is based on formal concept analysis, and models the directory of an information source as a formal context in which the underlying concept lattice serves for navigation and the attributes of the formal context serve for query formulation. In order to support the user in coping with a possibly overwhelming number of alternative query tunings, preferences are introduced.

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“…We also studied the space complexity of Galois lattices, and found empirical and theoretical evidence that, when the number of index terms per document is bounded, the size of the lattice grows linearly with respect to the number of documents. A detailed explanation of Galois lattices, of their complexity and of the construction algorithm is contained in (Carpineto & Romano, 1996a); in the same paper we describe also a generalization of Galois lattices that can take into account semantic information over the terms describing the documents. 1 A Galois lattice presents many useful properties for supporting information retrieval.…”

Section: Lattice Conceptual Clustering Of Indexed Textsmentioning

confidence: 99%

Information retrieval through hybrid navigation of lattice representations

Carpineto¹,

Romano²

1996

International Journal of Human-Computer Studies

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Summary. In this paper we present a comprehensive approach to automatic organization and hybrid navigation of text databases. An organizing stage first builds a particular lattice representation of the data, through text indexing followed by lattice clustering of the indexed texts. The lattice representation, then, supports the navigation stage of the system, a visual retrieval interface that combines three main retrieval strategies: browsing, querying, and bounding. Browsing and querying are used to search the retrieval space, bounding is used to restrict it based on the information that users have, or get during their interaction with the system. We show that such a hybrid paradigm permits high flexibility in trading off information exploration and retrieval and, in addition, has good retrieval performance. We compared information retrieval using lattice-based hybrid navigation with conventional Boolean querying. The results of an experiment conducted on two medium-sized bibliographic databases showed that the performance of lattice retrieval was comparable to or better than Boolean retrieval.

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A lattice conceptual clustering system and its application to browsing retrieval

Cited by 163 publications

References 29 publications

Formal Concept Analysis via Atomic Priming

Formal Concept Analysis via Atomic Priming

Preference-Based Query Tuning Through Refinement/Enlargement in a Formal Context

Information retrieval through hybrid navigation of lattice representations

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