Graph (discrete mathematics)In discrete mathematics, and more specifically in graph theory, a graph is a structure amounting to a set of objects in which some pairs of the objects are in some sense "related". The objects correspond to mathematical abstractions called vertices (also called nodes or points) and each of the related pairs of vertices is called an edge (also called link or line). Typically, a graph is depicted in diagrammatic form as a set of dots or circles for the vertices, joined by lines or curves for the edges.
Lattice graphIn graph theory, a lattice graph, mesh graph, or grid graph is a graph whose drawing, embedded in some Euclidean space \mathbb{R}^n, forms a regular tiling. This implies that the group of bijective transformations that send the graph to itself is a lattice in the group-theoretical sense. Typically, no clear distinction is made between such a graph in the more abstract sense of graph theory, and its drawing in space (often the plane or 3D space). This type of graph may more shortly be called just a lattice, mesh, or grid.
Knowledge extractionKnowledge extraction is the creation of knowledge from structured (relational databases, XML) and unstructured (text, documents, s) sources. The resulting knowledge needs to be in a machine-readable and machine-interpretable format and must represent knowledge in a manner that facilitates inferencing. Although it is methodically similar to information extraction (NLP) and ETL (data warehouse), the main criterion is that the extraction result goes beyond the creation of structured information or the transformation into a relational schema.
Directed graphIn mathematics, and more specifically in graph theory, a directed graph (or digraph) is a graph that is made up of a set of vertices connected by directed edges, often called arcs. In formal terms, a directed graph is an ordered pair where V is a set whose elements are called vertices, nodes, or points; A is a set of ordered pairs of vertices, called arcs, directed edges (sometimes simply edges with the corresponding set named E instead of A), arrows, or directed lines.
Chordal graphIn the mathematical area of graph theory, a chordal graph is one in which all cycles of four or more vertices have a chord, which is an edge that is not part of the cycle but connects two vertices of the cycle. Equivalently, every induced cycle in the graph should have exactly three vertices. The chordal graphs may also be characterized as the graphs that have perfect elimination orderings, as the graphs in which each minimal separator is a clique, and as the intersection graphs of subtrees of a tree.
Sentiment analysisSentiment analysis (also known as opinion mining or emotion AI) is the use of natural language processing, text analysis, computational linguistics, and biometrics to systematically identify, extract, quantify, and study affective states and subjective information. Sentiment analysis is widely applied to voice of the customer materials such as reviews and survey responses, online and social media, and healthcare materials for applications that range from marketing to customer service to clinical medicine.
Text miningText mining, text data mining (TDM) or text analytics is the process of deriving high-quality information from text. It involves "the discovery by computer of new, previously unknown information, by automatically extracting information from different written resources." Written resources may include websites, books, emails, reviews, and articles. High-quality information is typically obtained by devising patterns and trends by means such as statistical pattern learning. According to Hotho et al.
Word-sense disambiguationWord-sense disambiguation (WSD) is the process of identifying which sense of a word is meant in a sentence or other segment of context. In human language processing and cognition, it is usually subconscious/automatic but can often come to conscious attention when ambiguity impairs clarity of communication, given the pervasive polysemy in natural language. In computational linguistics, it is an open problem that affects other computer-related writing, such as discourse, improving relevance of search engines, anaphora resolution, coherence, and inference.
Euler methodIn mathematics and computational science, the Euler method (also called the forward Euler method) is a first-order numerical procedure for solving ordinary differential equations (ODEs) with a given initial value. It is the most basic explicit method for numerical integration of ordinary differential equations and is the simplest Runge–Kutta method. The Euler method is named after Leonhard Euler, who first proposed it in his book Institutionum calculi integralis (published 1768–1870).
Edge coloringIn graph theory, a proper edge coloring of a graph is an assignment of "colors" to the edges of the graph so that no two incident edges have the same color. For example, the figure to the right shows an edge coloring of a graph by the colors red, blue, and green. Edge colorings are one of several different types of graph coloring. The edge-coloring problem asks whether it is possible to color the edges of a given graph using at most k different colors, for a given value of k, or with the fewest possible colors.
