Agglomerative Hierarchical Clustering (AHC)Agglomerative Hierarchical Clustering (AHC) is part of:
Easy and user-friendly
Easy and user-friendly XLSTAT is flawlessly integrated with Microsoft Excel which is the most popular spreadsheet worldwide. This integration makes it one of the simplest available tools to work with as it utilizes the same philosophy as Microsoft Excel. The program is accessible in a dedicated XLSTAT tab. The analyses are grouped into functional menus. The dialog boxes are user-friendly and setting up an analysis is straightforward.
Data and results shared seamlessly
Data and results shared seamlessly One of the greatest advantages of XLSTAT is the way you can share data and results seamlessly. As the results are stored in Microsoft Excel, anyone can access them. There is no need for the receiver to have an XLSTAT license or any additional viewer which makes your team-work easier and more affordable. In addition, results are easily integrable into other Microsoft Office software such as PowerPoint, so that you can create striking presentation in minutes.
Modular XLSTAT is a modular product. XLSTAT-Pro is a core statistical module of XLSTAT which includes all the mainstream functionalities in statistics and multivariate analysis. More advanced features contained in add-on modules can be added for specific applications. This way you can adapt the software to your needs making the software more cost-efficient.
Didactic The results of XLSTAT are organized by analysis and are easy to navigate. Moreover useful information is provided along with the results to assist you in your interpretation.
Affordable XLSTAT is a complete and modular analytical solution that can suit any analytical business needs. It is very reasonably priced so that the return of your investment is almost immediate. Any XLSTAT license comes with top level support and assistance.
Accessible - Available in many languages
Accessible - Available in many languages We have ensured XLSTAT is accessible to everyone by making the program available in many languages, including Chinese, English, French, German, Italian, Japanese, Polish, Portuguese and Spanish.
Automatable and customizable
Automatable and customizable Most of the statistical functions available in XLSTAT can be called directly from the Visual Basic window of Microsoft Excel. They can be modified and integrated to more code to fit to the specificity of your domain. Adding tables and plots as well as modifying existing outputs becomes easy. Furthermore, XLSTAT includes some special tools on the dialog boxes to generate automatically the VBA code in order to reproduce your analysis using the VBA editor or to simply load pre-set settings. This effortless automation of routine analysis will be a huge time saver on your part.
Advantages of Agglomerative Hierarchical Clustering
Agglomerative Hierarchical Clustering (AHC) is a classification method which has the following advantages:
- It works from the dissimilarities between the objects to be grouped together. A type of dissimilarity can be suited to the subject studied and the nature of the data.
- One of the results is the dendrogram which shows the progressive grouping of the data. It is then possible to gain an idea of a suitable number of classes into which the data can be grouped.
Principle of Agglomerative Hierarchical Clustering
Agglomerative Hierarchical Clustering (AHC) is an iterative classification method whose principle is simple.
- The process starts by calculating the dissimilarity between the N objects.
- Then two objects which when clustered together minimize a given agglomeration criterion, are clustered together thus creating a class comprising these two objects.
- Then the dissimilarity between this class and the N-2 other objects is calculated using the agglomeration criterion. The two objects or classes of objects whose clustering together minimizes the agglomeration criterion are then clustered together.
This process continues until all the objects have been clustered.
These successive clustering operations produce a binary clustering tree (dendrogram), whose root is the class that contains all the observations. This dendrogram represents a hierarchy of partitions. It is then possible to choose a partition by truncating the tree at a given level, the level depending upon either user-defined constraints (the user knows how many classes are to be obtained) or more objective criteria.
Agglomerative Hierarchical Clustering aggregation methods
XLSTAT proposes several aggregation methods:
- Ward's method (iniertia)
- Ward's method (variance)
- Complete linkage
- Simple linkage
- Strong linkage
- Flexible linkage
- Unweighted pair-group average
- Weighted pair-group average
Proximities used in Agglomerative Hierarchical Clustering
The proximity between two objects is measured by measuring at what point they are similar (similarity) or dissimilar (dissimilarity). If the user chooses a similarity, XLSTAT converts it into a dissimilarity as the AHC algorithm uses dissimilarities. The conversion for each object pair consists in taking the maximum similarity for all pairs and subtracting from this the similarity of the pair in question.
XLSTAT proposes several similarities/dissimilarities that are suitable for a particular type of data:
|Quantitative data||Pearson's coefficient of correlation Spearman's coefficient of rank correlation Kendall's coefficient of rank correlation Inertia Covariance (n) Covariance (n-1) Percent agreement||Euclidean distance Chi-square distance Manhattan distance Pearson's dissimilarity Spearman's dissimilarity Kendall's dissimilarity Percent disagreement|
|Binary data (0/1)||Jaccards coefficient Dice coefficient Sokal & Sneath coefficient (2) Rogers & Tanimoto coefficient Simple matching coefficient Indice de Sokal & Sneath coefficient (1) Phi coefficient Ochiais coefficient Kulczinskis coefficient Percent agreement||Jaccards coefficient Dice coefficient Sokal & Sneath coefficient (2) Rogers & Tanimoto coefficient Simple matching coefficient Indice de Sokal & Sneath coefficient (1) Phi coefficient Ochiais coefficient Kulczinskis coefficient Percent agreement|
Note: For non-binary categorical variables, it is preferable to first perform a Multiple Correspondence Analysis (MCA) and to consider the coordinates of the observations on the factorial axes as new variables.
Results provided by XLSTAT for Agglomerative Hierarchical Clustering
- Node statistics: This node statistics table shows the data for the successive nodes in the dendrogram. The first node has an index which is the number of objects increased by 1. Hence it is easy to see at any time if an object or group of objects is clustered with another object or group of objects at the level of a new node in the dendrogram.
- Levels bar chart: The level bar chart table displays the statistics for dendrogram nodes.
- Dendrograms: The full dendrogram displays the progressive clustering of objects. If truncation has been requested, a broken line marks the level the truncation has been carried out. The truncated dendrogram shows the classes after truncation.
- Class centroids: This class centroids table shows the class centroids for the various descriptors.
- Distance between the class centroids: The distance between the class centroids table shows the Euclidean distances between the class centroids for the various descriptors.
- Central objects: The central objects table shows the coordinates of the nearest object to the centroid for each class.
- Distance between the central objects: This distance between the central objects table shows the Euclidean distances between the class central objects for the various descriptors.
- Results by class: The descriptive statistics for the classes (number of objects, sum of weights, within-class variance, minimum distance to the centroid, maximum distance to the centroid, mean distance to the centroid) are displayed in the first part of the table. The second part shows the objects.
- Results by object: The results by object table shows the assignment class for each object in the initial object order.
- Running an Agglomerative Hierarchical Clustering (AHC) with XLSTAT
- Clustering big datasets with XLSTAT - Using k-means clustering followed by an AHC
- Choosing an appropriate clustering method in XLSTAT