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Chemometrics means performing calculations on measurements of chemical data. The International Chemometrics Society (ICS) offers the following definition:
“Chemometrics is the science of relating measurements made on a chemical system or process to the state of the system via application of mathematical or statistical methods.”
Chemometrics commonly refers to using linear algebra calculation methods, to make either quantitative or qualitative measurements of chemical data, primarily spectra. Nearly all trained spectroscopists have the basic understanding of the concepts necessary to apply these methods.
Chemometrics has a language all of its own that seems difficult to understand upon first introduction. Fortunately the key to understanding chemometrics is not necessarily in understanding the mathematical fundamentals behind all the different methods but rather to know which model to apply for a given analytical problem.
Multivariate Data Analysis refers to any statistical technique used to analyze data that arises from more than one variable. This essentially models reality where a property or decision involves more than a single variable. No matter which science you practice any single property very, very rarely depends on only one variable.
Multivariate data analysis and multivariate statistics are related fields with slightly different focuses. In multivariate statistics one is also interested in the random error or noise of your date. On the other hand multivariate data analysis focus more on the structure, trends and patterns that can be extracted from a dataset. Though it is still important to know quantitatively how much of the empirical, observable, data variance is information (structure) versus noise in the data.
The information age has resulted in masses of data in every field. The ability to obtain a clear picture from the quantum of data available and make intelligent decisions is quite challenging. Multivariate Data Analysis can be used to process this information and present it in a meaningful fashion.
Data analytical methods dealing with only one variable at a time (univariate methods) will very often have limited use in modern complex data analysis. Although these methods may carry important marginal information they are insufficient for complete data analysis. Univariate methods can mostly be regarded important only as being the only natural stepping stone into complete multivariate analysis.

Exploratory Analysis
Used to discover patterns or trends in the data and indicate outliers.
PCA is an important part of chemometrics which provides for the most compact representation of all the variation in a data table.
Exploratory algorithms such as principal component analysis (PCA) are designed to reduce large complex data sets into a series of optimized and interpretable size. 
Classification
To assign predefined categories to samples and predicting an unknown sample as belonging to one of several distinct groups.
A classification model is used to predict a sample's class based on closest examples. Knearest neighbour (kNN) is primarily used in chemometrics.
Chemometrics helps in standardizing data. The classification models are more reliable and include the ability to reveal unusual samples in the data. 
Regression
Used to predict related properties that are easier to measure.
The goal of chemometric regression analysis is to develop a model which correlates the information in the set of known measurements to the desired property. Chemometric algorithms for performing regression include partial least squares (PLS) and principal component regression (PCR).
Chemometric regression is extensively used in making decisions relating to product quality in the online monitoring and process control industry where fast and expensive systems are needed for testing. 