Distributed Formal Concept Analysis Algorithms Based on an Iterative MapReduce Framework

Abstract

While many existing formal concept analysis algorithms are efficient, they are typically unsuitable for distributed implementation. Taking the MapReduce (MR) framework as our inspiration we introduce a distributed approach for performing formal concept mining. Our method has its novelty in that we use a light-weight MapReduce runtime called Twister which is better suited to iterative algorithms than recent distributed approaches. First, we describe the theoretical foundations underpinning our distributed formal concept analysis approach. Second, we provide a representative exemplar of how a classic centralized algorithm can be implemented in a distributed fashion using our methodology: we modify Ganter's classic algorithm by introducing a family of MR ⋆ algorithms, namely MRGanter and MRGanter+ where the prefix denotes the algorithm's lineage. To evaluate the factors that impact distributed algorithm performance, we compare our MR * algorithms with the state-of-the-art. Experiments conducted on real datasets demonstrate that MRGanter+ is efficient, scalable and an appealing algorithm for distributed problems.

Ghostbusters: A Parts-based NMF algorithm

“…Traditionally, the practitioner has little control over the quality of the NMF approximation save for running the NMF routine (sometimes) exhaustively until the approximation quality criteria is met. Ghostbusters is slow, admittedly; However, we point to a related paper which indicates how the underpinning routine may be significantly sped-up by parallelizing the decomposition without communication between the different computational resources [4] -a common failing of MapReduce implementations of NMF [21,2].…”

“…We appeal to a procedure called NextClosure, a well-known application of lattice and order theory [20], to build the Galois lattice of X, using an algorithm proposed in [20,6] and made more efficient by distribution in [21] and again by parallelization [4]. We then convert the lattice D into an ordered ensemble-tuned dictionary H. This lattice has the property that it is unique and complete.…”

Learning convolutive features for storage and transmission between networked sensors

“…Processing time vs Bandwidth: In practice modern computers are fast and frameworks such as MapReduce [25] improve computation speeds; however many IoT sensing devices may have orders of magnitude less processing power and may require that processing is performed on a local gateway or dedicated learning server. We consider the case where sensing is performed using a 1-channel microphone on a (standard) laptop computer.…”

Formal Concept Analysis via Atomic Priming

“…Lectic ordering recommends itself on account of its thoroughness [10]. Mining times are typically long: this is demonstrated in [26], where the Twister Map-Reduce framework [8] is used to parallelize computational effort. However, in many cases some notion of Formal Concept (FC) importance might yield a better ordering, for example in knowledge discovery [17], information retrieval [21], and social networking analysis [22] applications.…”

“…Alternatively, the input S may denote some partition of the entire dataset by extending the distributed FCA method proposed in [26]. Algorithm 1 initializes ≈ R + 1 NextClosure-like processes, described in Algorithms 2, 3, to mine all of the FCs in a given range F i -F j which allows for time-savings in FCA due to distribution.…”