Principal Coordinate AnalysisPrincipal Coordinate Analysis is part of:
ADA Advanced Data Analysis on Multiple tables software
- Versions: 9x/Me/NT/2000/XP/Vista/Win 7/Win 8
- Excel: 97 and later
- Processor: 32 or 64 bits
- Hard disk: 150 Mb
- Mac OS X:
- OS: OS X
- Excel: X, 2004 and 2011
- Hard disk: 150Mb.
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.
Principles of Principal Coordinate Analysis
Principal Coordinate Analysis (often referred to as PCoA) is aimed at graphically representing a resemblance matrix between p elements (individuals, variables, objects, among others).
The algorithm can be divided into three steps:
- Computation of a distance matrix for the p elements
- Centering of the matrix by rows and columns
- Eigen-decomposition of the centered distance matrix
The rescaled eigenvectors correspond to the principal coordinates that can be used to display the p objects in a space with 1, 2, p-1 dimensions.
As with PCA (Principal Component Analysis) eigenvalues can be interpreted in terms of percentage of total variability that is being represented in a reduced space.
Results of Principal Coordinate Analysis in XLSTAT
- Delta1 matrix: This matrix corresponds to the D1 matrix of Gower, used to compute the eigen-decomposition.
- Eigenvalues and percentage of inertia: this table displays the eigenvalues and the corresponding percentage of inertia.
- Principal coordinates: This table displays of the principal coordinates of the objects that are used to create the chart where the proximities between the charts can be interpreted.
- Contributions: This table displays the contributions that help evaluate how much an object contributes to a given axis.
- Squared cosines: This table displays the contributions that help evaluate how close an object is to a given axis.
Principal Coordinate Analysis and Principal Component Analysis
PCA and Principal Coordinate Analysis are quite similar in that the PCA can also represent observations in a space with less dimensions, the later being optimal in terms of variability carried. A Principal Coordinate Analysis applied to matrix of Euclidean distances between observations (calculated after standardization of the columns using the unbiased standard deviation) leads to the same results as a PCA based on the correlation matrix. The eigenvalues obtained with the Principal Coordinate Analysis are equal to (p-1) times those obtained with the PCA.
Principal Coordinate Analysis and Multidimensional Scaling
Principal Coordinate Analysis and MDS (Multidimensional Scaling) share the same goal of representing objects for which we have a proximity matrix.
MDS has two drawbacks when compared with Principal Coordinate Analysis:
- The algorithm is much more complex and performs slower.
- Axes obtained with MDS cannot be interpreted in terms of variability.
MDS has two advantages compared with Principal Coordinate Analysis:
- The algorithm allows having missing data in the proximity matrix.
- The non-metric version of MDS provides a simpler and clear way to handle matrices where only the ranking of the distances is important.