Foundation of Pattern Recognition

(Harvard University - Harvard Taiwan ROC Student Club)

Pattern recognition (PR) is the automatic identification of patterns and regularities in data. It has applications in statistical data analysis, signal processing, image analysis, information retrieval, bioinformatics, data compression, computer graphics, and machine learning (ML). 

PR has its roots in statistics and engineering; due to the increased availability of big data and the abundance of new processing power, some modern methods of PR include the use of ML. These activities can be viewed as two sides of the same application area and have undergone substantial development over the past few decades. 

PR systems are typically trained from labeled "training" data. When no labeled data is available, other algorithms can be used to discover previously unknown patterns. KDD and data mining are more focused on unsupervised methods and stronger connections to business usage. 

In ML, PR is the assignment of labels to given input values. In statistics, discriminant analysis was introduced in 1936 for the same purpose. An example of PR is classification, which attempts to assign each input value to one of a given set of categories (eg, to determine whether a given email is "spam" or "not spam"). 

PR is a more general problem, and it encompasses other types of output as well. Other examples are regression, which assigns a real-valued output to each input; sequence tokens, which assign a class to each member of a sequence of values ​​(e.g., part-of-speech tokens, which assign a part of the speech of each word in the input sentence); and parsing, which assigns a parse tree to the input sentence, describing the syntactic structure of the sentence. 

PR algorithms generally aim to provide reasonable answers for all possible inputs, and perform a "most likely" match of the inputs taking into account their statistical variation. This is in contrast to pattern-matching algorithms, which look for matches in the input that exactly match pre-existing patterns. 

A common example of a pattern matching algorithm is regular expression matching, which finds patterns of a given type in text data and is included in the search capabilities of many text editors and word processors.  

In math, a number pattern is a sequence of numbers that follow a specific rule. Recognizing a mathematical pattern involves observing patterns within given data.

Solving a mathematical pattern involves making predictions or extending the pattern based on the pattern recognized. 

Here are some types of number patterns: 

• Geometric pattern: A sequence of numbers based on multiplication and division operations.
• Arithmetic number pattern: A sequence where the same amount is either being added or subtracted every time. For example, in the sequence 9, 18, 27, 36, 45, 54, the common difference is 9.
• Triangular numbers: A sequence of numbers that can be represented as a triangle of dots. The term to term rule for the triangle numbers is to add one more each time.

[More to come ...]