B. Walczak

Rough sets theory

Abstract The basic concepts of the rough set theory are introduced and adequately illustrated. An example of the rough set theory application to the QSAR classification problem is presented. Numerous earlier applications of rough set theory to the various scientific domains suggest that it also can be a useful tool for the analysis of inexact, uncertain, or vague chemical data.

Noise suppression and signal compression using the wavelet packet transform

Abstract The basic concepts of the discrete wavelet transform (DWT) and the wavelet packet transform (WPT) are presented and illustrated. WPT is then applied to real and simulated signals. Different approaches to the WPT coefficients selection aiming at signal compression and denoising are described. Uniform compression of the set of signals is discussed as well.

A comparison of two algorithms for warping of analytical signals

The alignment of analytical signals is an important preprocessing step when further analysis (e.g. PCA) requires the same lengths of all of them. Two techniques for alignment of profiles, namely dynamic time warping (DTW) and correlation optimized warping (COW) were tested and compared. The attention was focused on chromatographic and spectroscopic profiles. Simulated and two sets of real data were studied in this study.

Looking for natural patterns in data: Part 1. Density-based approach

Abstract A density-based unsupervised clustering approach for detecting natural patterns in data (further denoted as NP) is presented, and its performance is illustrated for data sets with different types of clusters. NP works for arbitrary clusters, is a single-scan technique, requires no presumptions regarding data distribution and requires only one input parameter, which describes the minimal number of objects, considered as cluster. Moreover, a comparison of NP with partitioning approaches is demonstrated. NP can be applied not only for data clustering, but also for the identification of outliers.

The Radial Basis Functions — Partial Least Squares approach as a flexible non-linear regression technique

A new approach founded on Radial Basis Functions (RBF) and Partial Least Squares (PLS) is proposed to model non-linear chemical systems. Its performance is demonstrated for two simulated examples and compared with those of Multilayer Feedforward Network (MLP), Radial Basis Function Network (RBFN), and Spline-PLS. Good performance and a guaranteed learning algorithm of the RBF-PLS approach makes it an attractive alternative for the earlier established methods.

Representative subset selection

Fast development of analytical techniques enable to acquire huge amount of data. Large data sets are difficult to handle and therefore, there is a big interest in designing a subset of the original data set, which preserves the information of the original data set and facilitates the computations. There are many subset selection methods and their choice depends on the problem at hand. The two most popular groups of subset selection methods are uniform designs and cluster-based designs. Among the methods considered in this paper there are uniform designs, such as those proposed by Kennard and Stone, OptiSim, and cluster-based designs applying K-means technique and density based spatial clustering of applications with noise (DBSCAN). Additionally, a new concept of the subset selection with K-means is introduced.

Artificial neural networks in classification of NIR spectral data: Design of the training set

Abstract Artificial neural networks (NN) with back-error propagation were used for the classification with NIR spectra and applied to the classification of different strengths of drugs. Four training set selection methods were compared by applying each of them to three different data sets. The NN architecture was selected through a pruning method, and batching operation, adaptive learning rate and momentum were used to train the NN. The presented results demonstrate that selection methods based on Kennard-Stone and D-optimal designs are better than those based on the Kohonen self-organized mapping and on random selection methods and allow 100% correct classification for both recognition and prediction. The Kennard-Stone design is more practical than the D-optimal design. The Kohonen self-organized mapping method is better than the random selection method.

Comparison of regularized discriminant analysis linear discriminant analysis and quadratic discriminant analysis applied to NIR data

Three classifiers, namely linear discriminant analysis (LDA), quadratic discriminant analysis (QDA) and regularized discriminant analysis (RDA) are considered in this study for classification based on NIR data. Because NIR data sets are severely ill-conditioned, the three methods cannot be directly applied. A feature selection method was used to reduce the data dimensionality, and the selected features were used as the input of the classifiers. RDA can be considered as an intermediate method between LDA and QDA, and in several cases, RDA reduces to either LDA or QDA depending on which is better. In some other cases, RDA is somewhat better. However, optimization is time consuming. It is therefore concluded that in many cases, LDA or QDA should be recommended for practical use, depending on the characteristics of the data. However, in those cases where even small gains in classification quality are important, the application of RDA might be useful.

Dealing with missing data: Part II

Abstract The main concepts of the maximum likelihood (ML) approach in dealing with missing data are introduced and simple numerical examples of the application of ML are presented. Differences between ML and other techniques of treating missing data are illustrated. The idea of multiple imputation (MI) approach is presented and illustrated as well.

Projection methods in chemistry

Abstract Visualization of a data set structure is one of the most challenging goals in data mining. Often, chemical data sets are multidimensional, and therefore visualization of their structure is not directly possible. To overcome this problem, the original data is compressed to the few new features by using projection techniques, preserving the original data structure as good as possible, and allowing its visualization. In this paper, a survey of different projection techniques, linear and nonlinear, is given. Their performance is illustrated on chemical data sets, and the advantages and disadvantages are pointed out.