Incremental Concept Formation Algorithms Based on Galois (Concept) Lattices

Abstract

The Galois (or concept) lattice produced from a binary relation has proved useful for many applications. Building the Galois lattice can be considered a conceptual clustering method because it results in aconcept hierarchy. This article presents incremental algorithms for updating the Galois lattice and corresponding graph, resulting in an incremental concept formation method. Different strategies are considered based on a characterization of the modifications implied by such an update. Results of empirical tests are given in order to compare the performance of the incremental algorithms to three other batch algorithms. Surprisingly, when the total time for incremental generation is used, the simplest and less efficient variant of the incremental algorithms outperforms the batch algorithms in most cases. When only the incremental update time is used, the incremental algorithm outperforms all the batch algorithms. Empirical evidence shows that, on the average. the incremental update is done in time proportional to the number of instances previously treated. Although the worst case is exponential, when there is a fixed upper bound on the number of features related to an instance, which is usually the case in practical applications. the worst-case analysis of the algorithm also shows linear growth with respect to the number of instances.

An Incremental Learning Method to Support the Annotation of Workflows with Data-to-Data Relations

“…Formal Concept Analysis (FCA) [21] found a large variety of applications [19], and the literature reports several approaches to incremental lattice construction [15], including the Godin [12] algorithm, used in the present work. FCA found application in knowledge discovery as a valuable approach to association rule mining (ARM) [19].…”

“…In the present work, a datanode is any data object that can be the input or output of a workflow processor. Instead on characterizing the activities of a workflow (like in [10]), Datanode can be applied to describe it in terms of relations between the input and the output of processors 12 . The resulting network of data objects can be used to reason upon the propagation of policies, for example in the context of a Smart City data hub [6,4].…”

“…In a FCA lattice, concepts are ordered from the top concept (supremum), including all items and (usually) no shared features, to the bottom concept (infimum), including all the available features and a (possibly) empty set of items. The lattice is built incrementally using the Godin algorithm [12]. The algorithm (re)constructs the lattice integrating at each iteration a new item -the IO port pair, with its set of attributes (the features and annotations altogether).…”

ECCLAT: a New Approach of Clusters Discovery in Categorical Data

“…A transaction t supports an itemset X iff X ⊆ t. Given D, there is a unique ordered set which describes the inherent lattice structure defining natural groupings and relationships among the transactions and their items. This structure is known as a concepts lattice or Galois lattice [11] [25]. Each element of the lattice is a couple (T, I) composed of a set of transactions and an itemset.…”

“…They do not produce directly a clustering. Indeed, these methods create a hierarchy of concepts, generally represented by a lattice [11]. Every concept can be seen as a cluster with its properties (i.e.…”