Ranking in the context of Total order

College and university rankings order higher education institutions based on various criteria, with factors differing depending on the specific ranking system. These rankings can be conducted at the national or international level, assessing institutions within a single country, within a specific geographical region, or worldwide. Rankings are typically conducted by magazines, newspapers, websites, governments, or academics.

In addition to ranking entire institutions, specific programs, departments, and schools can be ranked. Some rankings consider measures of wealth, excellence in research, selective admissions, and alumni success. Rankings may also consider various combinations of measures of specialization expertise, student options, award numbers, internationalization, graduate employment, industrial linkage, historical reputation and other criteria.

Niche.com, formerly known as College Prowler, is an American company headquartered in Pittsburgh, Pennsylvania, that runs a ranking and review site. The company was founded by Luke Skurman in 2002 as a publisher of print guidebooks on U.S. colleges, but is now an online resource providing information on K–12 schools, colleges, cities, neighborhoods, and companies across the United States.

A hierarchy of evidence, comprising levels of evidence (LOEs), that is, evidence levels (ELs), is a heuristic used to rank the relative strength of results obtained from experimental research, especially medical research. There is broad agreement on the relative strength of large-scale, epidemiological studies. More than 80 different hierarchies have been proposed for assessing medical evidence. The design of the study (such as a case report for an individual patient or a blinded randomized controlled trial) and the endpoints measured (such as survival or quality of life) affect the strength of the evidence. In clinical research, the best evidence for treatment efficacy is mainly from meta-analyses of randomized controlled trials (RCTs) and the least relevant evidence is expert opinion, including consensus of such. Systematic reviews of completed, high-quality randomized controlled trials – such as those published by the Cochrane Collaboration – rank the same as systematic review of completed high-quality observational studies in regard to the study of side effects. Evidence hierarchies are often applied in evidence-based practices and are integral to evidence-based medicine (EBM).

Ordinal data is a categorical, statistical data type where the variables have natural, ordered categories and the distances between the categories are not known. These data exist on an ordinal scale, one of four levels of measurement described by S. S. Stevens in 1946. The ordinal scale is distinguished from the nominal scale by having a ranking. It also differs from the interval scale and ratio scale by not having category widths that represent equal increments of the underlying attribute.

The World Rugby Rankings is a ranking system for national teams in rugby union, managed by World Rugby, the sport's governing body. There are separate men's and women's rankings. The teams of World Rugby's member nations are ranked based on their game results, with the most successful teams being ranked highest. A point system is used, with points being awarded on the basis of the results of World Rugby-recognized international matches. Rankings are based on the team's performance, with more recent results and more significant matches being more heavily weighted to help reflect the current competitive state of a team. The men's ranking system was introduced the month before the 2003 Rugby World Cup, with the first new rankings issued on 8 September 2003, when they were called the "IRB Rankings".

In poker, players form sets of five playing cards, called hands, according to the rules of the game. Each hand has a rank, which is compared against the ranks of other hands participating in the showdown to decide who wins the pot. In high games, like Texas hold 'em and seven-card stud, the highest-ranking hands win. In low games, like razz, the lowest-ranking hands win. In high-low split games, both the highest-ranking and lowest-ranking hands win, though different rules are used to rank the high and low hands.

Each hand belongs to a category determined by the patterns formed by its cards. A hand in a higher-ranking category always ranks higher than a hand in a lower-ranking category. A hand is ranked within its category using the ranks of its cards. Individual cards are ranked, from highest to lowest: A, K, Q, J, 10, 9, 8, 7, 6, 5, 4, 3 and 2. However, aces have the lowest rank under ace-to-five low or ace-to-six low rules, or under high rules as part of a five-high straight or straight flush. Suits are not ranked, so hands that differ by suit alone are of equal rank.

A record chart, in the music industry, also called a music chart, is a ranking of recorded music according to certain criteria during a given period. Many different criteria are used in worldwide charts, often in combination. These include record sales, the amount of radio airplay, the number of downloads, and the amount of streaming activity.

Some charts are specific to a particular musical genre and most to a particular geographical location. The most common period covered by a chart is one week with the chart being printed or broadcast at the end of this time. Summary charts for years and decades are then calculated from their component weekly charts. Component charts have become an increasingly important way to measure the commercial success of individual songs.

Citation impact or citation rate is a measure of how many times an academic journal article or book or author is cited by other articles, books or authors.Citation counts are interpreted as measures of the impact or influence of academic work and have given rise to the field of bibliometrics or scientometrics, specializing in the study of patterns of academic impact through citation analysis. The importance of journals can be measured by the average citation rate,the ratio of number of citations to number articles published within a given time period and in a given index, such as the journal impact factor or the citescore. It is used by academic institutions in decisions about academic tenure, promotion and hiring, and hence also used by authors in deciding which journal to publish in. Citation-like measures are also used in other fields that do ranking, such as Google's PageRank algorithm, software metrics, college and university rankings, and business performance indicators.

In mathematics, especially order theory, a weak ordering is a mathematical formalization of the intuitive notion of a ranking of a set, some of whose members may be tied with each other. Weak orders are a generalization of totally ordered sets (rankings without ties) and are in turn generalized by (strictly) partially ordered sets and preorders.

There are several common ways of formalizing weak orderings, that are different from each other but cryptomorphic (interconvertable with no loss of information): they may be axiomatized as strict weak orderings (strictly partially ordered sets in which incomparability is a transitive relation), as total preorders (transitive binary relations in which at least one of the two possible relations exists between every pair of elements), or as ordered partitions (partitions of the elements into disjoint subsets, together with a total order on the subsets). In many cases another representation called a preferential arrangement based on a utility function is also possible.

PageRank (PR) is an algorithm used by Google Search to rank web pages in their search engine results. It is named after both the term "web page" and co-founder Larry Page. PageRank is a way of measuring the importance of website pages. According to Google:

Currently, PageRank is not the only algorithm used by Google to order search results, but it is the first algorithm that was used by the company, and it is the best known. As of September 24, 2019, all patents associated with PageRank have expired.

In machine learning, kernel machines are a class of algorithms for pattern analysis, whose best known member is the support-vector machine (SVM). These methods involve using linear classifiers to solve nonlinear problems. The general task of pattern analysis is to find and study general types of relations (for example clusters, rankings, principal components, correlations, classifications) in datasets. For many algorithms that solve these tasks, the data in raw representation have to be explicitly transformed into feature vector representations via a user-specified feature map: in contrast, kernel methods require only a user-specified kernel, i.e., a similarity function over all pairs of data points computed using inner products. The feature map in kernel machines is infinite dimensional but only requires a finite dimensional matrix from user-input according to the representer theorem. Kernel machines are slow to compute for datasets larger than a couple of thousand examples without parallel processing.

Kernel methods owe their name to the use of kernel functions, which enable them to operate in a high-dimensional, implicit feature space without ever computing the coordinates of the data in that space, but rather by simply computing the inner products between the images of all pairs of data in the feature space. This operation is often computationally cheaper than the explicit computation of the coordinates. This approach is called the "kernel trick". Kernel functions have been introduced for sequence data, graphs, text, images, as well as vectors.