Syntactic pattern recognition or structural pattern recognition is a form of pattern recognition, in which each object can be represented by a variable-cardinality set of symbolic, nominal features. This allows for representing pattern structures, taking into account more complex interrelationships between attributes than is possible in the case of flat, numerical feature vectors of fixed dimensionality, that are used in statistical classification.
Pattern recognition is the automated recognition of patterns and regularities in data. Pattern recognition is closely related to artificial intelligence and machine learning, together with applications such as data mining and knowledge discovery in databases (KDD), and is often used interchangeably with these terms. However, these are distinguished: machine learning is one approach to pattern recognition, while other approaches include hand-crafted rules or heuristics; and pattern recognition is one approach to artificial intelligence, while other approaches include symbolic artificial intelligence. A modern definition of pattern recognition is:
The field of pattern recognition is concerned with the automatic discovery of regularities in data through the use of computer algorithms and with the use of these regularities to take actions such as classifying the data into different categories.
In mathematics, the cardinality of a set is a measure of the "number of elements of the set". For example, the set contains 3 elements, and therefore has a cardinality of 3. There are two approaches to cardinality – one which compares sets directly using bijections and injections, and another which uses cardinal numbers. The cardinality of a set is also called its size, when no confusion with other notions of size is possible.
In machine learning and statistics, classification is the problem of identifying to which of a set of categories (sub-populations) a new observation belongs, on the basis of a training set of data containing observations whose category membership is known. Examples are assigning a given email to the "spam" or "non-spam" class, and assigning a diagnosis to a given patient based on observed characteristics of the patient. Classification is an example of pattern recognition.
Syntactic pattern recognition can be used instead of statistical pattern recognition if there is clear structure in the patterns. One way to present such structure is by means of a strings of symbols from a formal language. In this case the differences in the structures of the classes are encoded as different grammars.
In computer programming, a string is traditionally a sequence of characters, either as a literal constant or as some kind of variable. The latter may allow its elements to be mutated and the length changed, or it may be fixed. A string is generally considered a data type and is often implemented as an array data structure of bytes that stores a sequence of elements, typically characters, using some character encoding. String may also denote more general arrays or other sequence data types and structures.
In mathematics, computer science, and linguistics, a formal language consists of words whose letters are taken from an alphabet and are well-formed according to a specific set of rules.
In formal language theory, a grammar is a set of production rules for strings in a formal language. The rules describe how to form strings from the language's alphabet that are valid according to the language's syntax. A grammar does not describe the meaning of the strings or what can be done with them in whatever context—only their form.
An example of this would be diagnosis of the heart with ECG measurements. ECG waveforms can be approximated with diagonal and vertical line segments. If normal and unhealthy waveforms can be described as formal grammars, measured ECG signal can be classified as healthy or unhealthy by first describing it in term of the basic line segments and then trying to parse the descriptions according to the grammars. Another example is tessellation of tiling patterns.
The heart is a muscular organ in most animals, which pumps blood through the blood vessels of the circulatory system. Blood provides the body with oxygen and nutrients, as well as assisting in the removal of metabolic wastes. In humans, the heart is located between the lungs, in the middle compartment of the chest.
In electronics, acoustics, and related fields, the waveform of a signal is the shape of its graph as a function of time, independent of its time and magnitude scales and of any displacement in time.
A tessellation of a flat surface is the tiling of a plane using one or more geometric shapes, called tiles, with no overlaps and no gaps. In mathematics, tessellations can be generalized to higher dimensions and a variety of geometries.
A second way to represent relations are graphs, where nodes are connected if corresponding subpatterns are related. An item can be labeled as belonging to a class if its graph representation is isomorphic with prototype graphs of the class.
In 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 and each of the related pairs of vertices is called an edge. 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. Graphs are one of the objects of study in discrete mathematics.
Typically, patterns are constructed from simpler sub patterns in a hierarchical fashion. This helps in dividing the recognition task into easier subtask of first identifying sub patterns and only then the actual patterns.
Structural methods provide descriptions of items, which may be useful in their own right. For example, syntactic pattern recognition can be used to find out what objects are present in an image. Furthermore, structural methods are strong in finding a correspondence mapping between two images of an object. Under natural conditions, corresponding features will be in different positions and/or may be occluded in the two images, due to camera-attitude and perspective, as in face recognition. A graph matching algorithm will yield the optimal correspondence.
Graph matching is the problem of finding a similarity between graphs.
