cluster analysis
-
What is cluster analysis in statistics?
Cluster analysis is a statistical method used to classify objects into groups, maximizing similarity within the same group and minimizing it between different groups. It's an exploratory technique that uncovers structures without explaining why they exist, making it useful for generating hypotheses rather than testing them.
Cluster analysis methods can be hierarchical or nonhierarchical. Hierarchical methods build nested clusters, either by dividing a single cluster or by agglomerating individual objects. Nonhierarchical methods create a unique data partition. Key to these methods are distance and similarity measures, often based on a distance matrix. Euclidean distance is common, calculating the square root of the sum of squared differences between object coordinates. Cluster analysis is a data mining technique that identifies anomaly detection and natural groupings within data.
2 Britannica SourcesCreated from Britannica articles using AI. AI can make mistakes, so verify using Britannica articles. -
Why do people use cluster analysis?
People use cluster analysis, a statistical technique, to classify a population into different groups by quantitatively comparing multiple characteristics. This method groups objects so that similarity within the same group is maximized, and similarity between different groups is minimized.
Cluster analysis is useful for classifying large amounts of information into meaningful categories. It is applied in various fields such as biology for taxonomy, clinical medicine for identifying patient groups, and epidemiology for finding regions with similar profiles. As an inductive exploratory technique, it uncovers structures without explaining their existence and generates hypotheses rather than testing them.
3 Britannica SourcesCreated from Britannica articles using AI. AI can make mistakes, so verify using Britannica articles. -
How does cluster analysis group data or objects?
Cluster analysis is a statistical method for classifying objects into groups such that objects in the same group are similar, and objects in different groups are dissimilar.
Cluster analysis techniques can be hierarchical or nonhierarchical. Hierarchical methods create nested clusters, while nonhierarchical methods produce a single partition of the data. Hierarchical algorithms can be divisive (splitting a large cluster) or agglomerative (merging single-member clusters). Many algorithms rely on a distance or similarity matrix, with Euclidean distance being common for interval scale variables. Other distance measures include Manhattan, Chebyshev, and power distance, each suited to different data characteristics and cluster shapes.
2 Britannica SourcesCreated from Britannica articles using AI. AI can make mistakes, so verify using Britannica articles. -
What is a cluster in data analysis?
In statistics, cluster analysis is a tool to classify objects into groups, ensuring similarity within the same group and dissimilarity between different groups. It is an inductive exploratory technique that uncovers structures without explaining their existence, and it can generate hypotheses rather than test them. Cluster analysis is useful for classifying large amounts of information into a smaller number of meaningful categories. The algorithms can be hierarchical, with nested classes, or nonhierarchical, with a unique partition of objects.
3 Britannica SourcesCreated from Britannica articles using AI. AI can make mistakes, so verify using Britannica articles. -
What are some common methods used in cluster analysis, like k-means or hierarchical clustering?
Cluster analysis involves classifying objects into groups where similarity within a group is maximized and similarity between groups is minimized. Methods are either hierarchical or nonhierarchical.
Hierarchical methods are either divisive, starting with one cluster and dividing it, or agglomerative, starting with single-member clusters that are successively fused. Key to these methods are distance and similarity matrices, often using Euclidean distance, which can yield spherical clusters. Other distances include Manhattan, Chebyshev, and power distances.
The k-means algorithm is a frequently used nonhierarchical technique that starts with (k) random clusters and moves objects between them to minimize variability within clusters and maximize variability between clusters.
1 Britannica SourceCreated from Britannica articles using AI. AI can make mistakes, so verify using Britannica articles. -
How do scientists decide if the results of cluster analysis are useful or meaningful?
Cluster analysis is a statistical method used to classify objects into groups, ensuring similarity within the same group and dissimilarity between different groups. It's useful in various fields like biology, medicine, and epidemiology, where classifying large amounts of information into meaningful categories is essential.
As an exploratory technique, cluster analysis uncovers structures without explaining their reasons, making it a hypothesis-generating tool rather than a hypothesis-testing one. It identifies groupings or discovers hidden structures within data, differing from discriminant analysis, where objects are assigned to predefined groups based on statistical rules.
1 Britannica SourceCreated from Britannica articles using AI. AI can make mistakes, so verify using Britannica articles.
cluster analysis, in statistics, set of tools and algorithms that is used to classify different objects into groups in such a way that the similarity between two objects is maximal if they belong to the same group and minimal otherwise. In biology, cluster analysis is an essential tool for taxonomy (the classification of living and extinct organisms). In clinical medicine, it can be used to identify patients who have diseases with a common cause, patients who should receive the same treatment, or patients who should have the same level of response to treatment. In epidemiology, cluster analysis has many uses, such as finding meaningful conglomerates of regions, communities, or neighbourhoods with similar epidemiological profiles when many variables are involved and natural groupings do not exist. In general, whenever one needs to classify large amounts of information into a small number of meaningful categories, cluster analysis may be useful.
Researchers are often confronted with the task of sorting observed data into meaningful structures. Cluster analysis is an inductive exploratory technique in the sense that it uncovers structures without explaining the reasons for their existence. It is a hypothesis-generating, rather than a hypothesis-testing, technique. Unlike discriminant analysis, where objects are assigned to preexisting groups on the basis of statistical rules of allocation, cluster analysis generates the groups or discovers a hidden structure of groups within the data.
Classification of methods
In a first broad approach, cluster analysis techniques may be classified as hierarchical, if the resultant grouping has an increasing number of nested classes that resemble a phylogenetic classification, or nonhierarchical, if the results are expressed as a unique partition of the whole set of objects.
" height="20" alt="HEW Logo">
Hierarchical algorithms can be divisive or agglomerative. A divisive method begins with all cases in one cluster. That cluster is gradually broken down into smaller and smaller clusters. Agglomerative techniques usually start with single-member clusters that are successively fused until one large cluster is formed. In the initial step, the two objects with the lowest distance (or highest similarity) are combined into a cluster. In the next step, the object with the lowest distance to either of the first two is identified and studied. If it is closer to a fourth object than to either of the first two, the third and fourth objects become the second two-case cluster; otherwise, the third object is included in the first cluster. The process is repeated, adding cases to existing clusters, creating new clusters, or combining those that have emerged until each object has been examined and allocated to one cluster or stands as one separate cluster by itself. At each step of the process, a different partition is formed that is nested in the partition generated in the following step. Usually, the researcher chooses the partition that turns out to be the most meaningful for a particular application.
Distance and similarity are key concepts in the context of cluster analysis. Most algorithms, particularly those yielding hierarchical partitions, start with a distance-or-similarity matrix. The cell entries of this matrix are distances or similarities between pairs of objects. There are many types of distances, of which the most common is the Euclidean distance. The Euclidean distance between any two objects is the square root of the sum of the squares of the differences between all the coordinates of the vectors that define each object. It can be used for variables measured at an interval scale. When two or more variables are used to calculate the distance, the variable with the larger magnitude will dominate. To avoid that, it is common practice to first standardize all variables.
The choice of a distance type is crucial for all hierarchical clustering algorithms and depends on the nature of the variables and the expected form of the clusters. For example, the Euclidean distance tends to yield spherical clusters. Other commonly used distances include the Manhattan distance, the Chebyshev distance, the power distance, and the percent disagreement. The Manhattan distance is defined as the average distance across variables. In most cases, it yields results similar to the simple Euclidean distance. However, the effect of single large differences (outliers) is dampened (since they are not squared). The Chebyshev distance may be appropriate when objects that differ in just one variable should be considered different. The power distance is used when it is important to increase or decrease the progressive weight that is assigned to variables on which the respective objects are very different. The power distance is controlled by two user-defined parameters, r and p. Parameter p controls the progressive weight that is placed on differences on individual variables, while parameter r controls the progressive weight that is placed on larger differences between objects. If r and p are equal to 2, then that distance is equal to the Euclidean distance. The percent disagreement may be used when the data consist of categorical variables.
Linkage rules
When clusters are composed of a single object, the distance between them can be calculated with any of the aforementioned distances. However, when clusters are formed by two or more objects, rules have to be defined to calculate those distances.
The trusted destination for professionals, college students, and lifelong learners.
SUBSCRIBE
The distance between two clusters may be defined as the distance between the two closest objects in the two clusters. Known as the nearest neighbour rule, this approach will string objects together and tends to form chainlike clusters.
Other popular linkage rules are the pair-group average and the pair-group centroid. The first of those rules is defined as the average distance between all pairs of objects in the two different clusters. That method tends to form natural distinct clumps of objects. The pair-group centroid is the distance between the centroids, or centres of gravity, of the clusters.
The most frequently used nonhierarchical clustering technique is the k-means algorithm, which is inspired by the principles of analysis of variance. In fact, it may be thought of as an analysis of variance in reverse. If the number of clusters is fixed as k, the algorithm will start with k random clusters and then move objects between them with the goals of minimizing variability within clusters and maximizing variability between clusters.