Knowledge unit discovery for programming tutoring based on Formal Concept Analysis

Formal concept analysis (FCA) is an important theory on the study of hierarchical structures caused by a binary relation between objects and attributes. And it is well known that a soft set always induces a binary relationship between objects and attributes for a formal context. Based on these facts, we study a new system called a soft context, which is induced using a soft set instead of a binary relation in the formal context, and investigate its theoretical foundations. First, we introduce the notions of soft context and soft concept for objects and study some basic properties. In particular, for the purpose of studying soft concepts, we introduce and study the notions of independent and dependent soft concepts. And we obtain the important things: (1) the set of all soft concepts can be decomposed into the set of independent soft concepts and the set of dependent soft concepts; (2) every dependent soft concept is generated by some independent soft concepts. Second, we obtain important properties about the relationship between formal context and soft contexts as the following: (1) each formal context always induces an associated soft context; (2) for a given formal context, there exists a bijection between the set of all formal concepts and the set of all soft concepts of the associated soft context induced by the given formal context. And we apply the above-mentioned properties to get the set of all formal concepts of a given formal context and explain that this method is more effective than the traditional way of computing all formal concepts in formal contexts using the example. Finally, we introduce the notion of soft concept lattice. Also, for a given formal context, we show that the formal concept lattice is order-isomorphic to the soft concept lattice of the associated soft context.

A key ability of human reasoning is analogical reasoning. In this context, an important notion is that of analogical proportions that have been formalized and analyzed in the last decade. A bridging to Formal Concept Analysis (FCA) has been brought by introducing analogical complexes, i.e. formal concepts that share a maximal analogical relation enabling by this analogies between (formal) concepts. Electronic Health Record (EHR) systems are nowadays widespread and used in different scenarios. In this paper we consider the problem of improving EHR systems by using analogical complexes in an FCA based setting. Moreover, we present a study case of analogical complexes in a medical field. We analyze analogical proportions in Electronic Health Record Systems and prove that EHRs can be improved with an FCA grounded analogical reasoning component. This component offers methods for knowledge discovery and knowledge acquisition for medical experts based on patterns revealed by analogies. We also show that combining analogical reasoning with FCA brings a new perspective on the analyzed data that can improve the understanding of the subsequent knowledge structures and offering a valuable support for decision making.

The paper first offers a parallel between two approaches to conceptual clustering, namely formal concept analysis (augmented with the introduction of new operators) and bipartite graph analysis. It is shown that a formal concept (as defined in formal concept analysis) corresponds to the idea of a maximal bi-clique, while sub-contexts, which correspond to independent “conceptual worlds” that can be characterized by means of the new operators introduced, are disconnected sub-graphs in a bipartite graph. The parallel between formal concept analysis and bipartite graph analysis is further exploited by considering “approximation” methods on both sides. It leads to suggest new ideas for providing simplified views of datasets, taking also inspiration from the search for approximate itemsets in data mining (with relaxed requirements), and the detection of communities in hierarchical small worlds.

Knowledge discovery process from databases has gained importance recently. Finding and using the valuable and meaningful data which is hidden in large databases can have strategic importance for the organizations to gain competitive advantage. In this context, data mining methods are used to analyze customer purchasing data which is called “market basket analysis”. This analysis provides insight into the combination of products within a customer’s ‘basket’. In this study, a market basket analysis is conducted to identify a customer purchasing behaviour with Formal Concept Analysis (FCA). The FCA technique is one of the data mining methods using formal contexts and concept lattices. So, this method provides to create association rules based on lattices reflecting the relationships among the attributes in a database.

The theory introduced, presented and developed in this paper, is concerned with Rough Concept Analysis. This theory is a synthesis of the theory of Rough Sets pioneered by Zdzislaw Pawlak [10] with the theory of Formal Concept Analysis pioneered by Rudolf Wille [11]. The central notion in this paper of a rough formal concept combines in a natural fashion the two notions of rough set and formal concept — to use a slogan: “rough set + formal concept = rough formal concept”. This paper is an extension of the paper [5] presented at the international workshop on Rough Sets and Knowledge Discovery (RSKD'93). A related paper [8] using distributed constraints provides a synthesis of the two important data modeling techniques: conceptual scaling of Formal Concept Analysis, and Entity-Relationship database modeling. A follow-up paper [9] will extend rough concept analysis from formal contexts to distributed constraints.

In traditional formal concept analysis, the attributes in the formal context are considered fixed. However, in the real world data set, attributes always have different levels of granularity, correspondingly, the derived concept lattice may reveal different information and patterns. Therefore, the capability to change the level of granularity of an attribute in formal concept analysis to capture relevant patterns in data is a natural requirement. In this paper, a theoretical study has been undertaken in multi-scale formal contexts, where attributes with different levels of granularity possess different attribute values. Two types of formal concepts, i.e., object-oriented and property-oriented multi-scale concepts, are introduced and studied in detail. The collection of object-oriented concept lattices and property-oriented concept lattices can be obtained at different granularity levels of attributes. It has been shown that the set of extents in the derived concept lattices increases when we choose to use a finer level of granularity. Moreover, a corresponding bidirectional approach to concept construction(i.e., from coarser to finer and from finer to coarser, respectively) is exhibited, and some characterization theorems have been obtained.

Text knowledge analysis plays a very important role in knowledge processing. In order to find interesting patters, we introduce text analysis into the Formal Concept Analysis(FCA) field. FCA is a valid tool for data ming and knowledge processing. In the paper, we present a method for exacting the conceptual patterns and concept lattice from multiple knowledge sources. The method consists of two steps: the first is to insert some related many-valued contexts(MVCs)(which represent text knowledge) into some corresponding column or cell of other MVC in accordance with certain rules, and then extract formal concepts and concept lattice. Our insertion method not only is semanticpreserving, but adds the dimension of attributes for describing objects. Hence, the discovered concepts have the more richer intents and are more denser in the concept lattice. The paper mainly applied the method to column insertion operation and cell insertion operation, and obtained some propositions, which can be used by knowledge engineers to represent and analyze text knowledge(especially,text objects) and to extract new semantics information or associate rules from concept lattices.

Galois (concept) lattices and formal concept analysis have been proved useful in the resolution of many problems of theoretical and practical interest. Recent studies have put the emphasis on the need for both efficient and flexible algorithms to construct the lattice. In this paper, some equivalent conditions for an attributes subset to be a reduction of a formal concept are presented. Further more, the structure of concept lattice was analyzed and it is proved that each concept is the meet of some single attribute generalized concepts. Based on the above research, reduction-based approaches towards constructing concept lattice was presented.

This paper presents results of the finding of the author’s profiles using formal concepts generated from DBLP database. Our main aim was to evaluate the use of formal concept analysis as a method for extracting the author’s profiles. There are several commonly used methods for clustering and for finding experts in a large database. These methods are mainly based on different kinds of clustering and metrics which are sometimes difficult to understand. Finding experts for particular and mainly special areas of research is not an easy task. Formal concept analysis (FCA) is a method with a very strong mathematical background, which makes it easy to understand. Properties of FCA can give us a very strong tool for finding author’s profiles.

Concept lattices constructed by formal concept analysis have been successfully applied in structuring stored information to facilitate its retrieval. However, the models used in retrieval determine the results, and we propose an improved retrieval model to rank query results. The proposed concept similarity enables concept approximation, using both attribute extent and object intent, as well as occurrence frequencies in formal concepts. This approach avoids the computation of a Hasse diagram, only using the concepts of a formal context in query-based retrieval.

Pattern extraction is one of the major topics in Knowledge Discovery. Out of numerous data mining techniques we propose to use a new approach: Formal Concept Analysis (FCA) together with Graph Databases with the implementation Neo4j. FCA is a prominent field of applied mathematics using maximal clusters of object-attribute relationships to discover and represent knowledge structures. The use of FCA gained much importance in many research domains in recent years. Despite the similarity of the graph representation between FCA and Neo4j, the structure and relations among the elements are represented differently and can offer a different perspective on the analysis. This paper gives more insight into how patterns can be extracted from medical data and interpreted by means of FCA and Neo4j in order to help medical staff improve the accuracy of diagnoses. We examine the factors related to patients' symptoms and diagnostics and then compare the results with the ones provided by a medical care center. We apply knowledge discovery techniques and conceptual landscapes paradigm in order to obtain an in-depth and high qualitative knowledge representation of medical data. By making use of the effectiveness and the graphical representation of conceptual hierarchies we extract valuable knowledge from medical data sets through which we solve the knowledge discovery, processing and representation task in Electronic Health Record systems.

In recent times Formal Concept Analysis (FCA), in which the data is represented as a formal context, has gained popularity for Association Rules Mining (ARM). Application of ARM in health care datasets is challenging and a highly rewarding problem. However, datasets in the medical domain are of high dimension. As the dimensionality of dataset increases, size of the formal context as well as complexity of FCA based ARM also increases. To handle the problem of high dimensionality and mine the associations, we propose to apply Singular Value Decomposition (SVD) on the dataset to reduce the dimensionality and apply FCA on the reduced dataset for ARM. To demonstrate the proposed method, experiments are conducted on Tuberculosis (TB) and Hypertension (HP) datasets. Results indicate that with fewer concepts, SVD based FCA has achieved the performance of FCA on TB data and performed better than FCA on HP data.

Because they provide patient-specific guideline-based recommendations, clinical decision support systems (CDSSs) are expected to promote the implementation of clinical practice guidelines (CPGs). OncoDoc2 is a CDSS applied to the management of breast cancer. However, despite it was routinely used during weekly multidisciplinary staff meetings (MSMs) at the Tenon Hospital (Paris, France), the compliance rate of MSMs' decisions with CPGs did not reach 100%. Formal Concept Analysis (FCA) has been applied to elicit formal concepts related to non-compliance. A statistical pre-treatment of attributes has been proposed to leverage FCA and discriminate between compliant and non-compliant decisions. Among the 1,889 decisions made over a 3 year-period, 199 decisions of recommended re-excisions have been considered for analysis. In this sample, non-compliance was explained by uncommon clinical profiles and specific patient-centred clinical criteria.

Basic level of concepts represents a significant, thoroughly explored psychological phenomenon in the psychology of concepts. We argue that formal concept analysis provides a convenient formal framework for considerations regarding the basic level. In this first part of our study, we present a direct formalization of a rudimentary view of basic level due to Rosch. We also demonstrate by experiments that among all formal concepts the basic level concepts represent natural and interesting ones and are therefore of interest from the data analysis viewpoint. In the second part, we shall utilize the present approach to examine existing psychological views of basic level and explore relationships among them.

Formal concept analysis (FCA) is now widely recognized as a useful approach for extracting, representing, and analyzing knowledge in various domains. The high computational cost of knowledge processing and the difficulty of visualizing the lattice are two key challenges in practical FCA implementations. Moreover, assessing the finalized built-up lattice may be problematic due to the enormous number of formal concepts and the complexity of their connections. The challenge of constructing concept lattices of adequate size and structure to convey high-importance context features remains a significant FCA aim. In the literature, various strategies for concept lattice reduction have been presented. In this work, we suggest a categorization of reduction methods for concept lattice based on three main categories: context pre-processing, non-essential distinctions elimination, and concept filtration, whereby using FCA-based analysis, the most important methods in the literature are analyzed and compared based on six pillars: the preliminary step of the reduction process, domain expert, changing the original data structure, final concept lattice, quality of reduction, and category of reduction method.