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Big high dimensional data is becoming a challenging field of research. There exist a lot of techniques which infer information. However, because of the curse of dimensionality, a necessary step is the dimensionality reduction (DR) of the information. DR can be performed by linear and nonlinear algorithms. In general, linear algorithms are faster because of less computational burden. A related problem is dealing with time-varying high dimensional data, where the time dependence is due to nonstationary data distribution. Data stream algorithms are not able to project in lower dimensional spaces. Indeed, only linear projections, like principal component analysis (PCA), are used in real time while nonlinear techniques need the whole database (offline). The Growing Curvilinear Component Analysis (GCCA) neural network addresses this problem; it has a self-organized incremental architecture adapting to the changing data distribution and performs simultaneously the data quantization and projection by using CCA, a nonlinear distance-preserving reduction technique. This is achieved by introducing the idea of “seed”, pair of neurons which colonize the input domain, and “bridge”, a novel kind of edge in the manifold graph, which signals the data non-stationarity. Some artificial examples and a real application are given, with a comparison with other existing techniques. [ABSTRACT FROM AUTHOR]

Hierarchical clustering is an important tool for extracting information from data in a multi-resolution way. It is more meaningful if driven by data, as in the case of divisive algorithms, which split data until no more division is allowed. However, they have the drawback of the splitting threshold setting. The neural networks can address this problem, because they basically depend on data. The growing hierarchical GH-EXIN neural network builds a hierarchical tree in an incremental (data-driven architecture) and self-organized way. It is a top-down technique which defines the horizontal growth by means of an anisotropic region of influence, based on the novel idea of neighborhood convex hull. It also reallocates data and detects outliers by using a novel approach on all the leaves, simultaneously. Its complexity is estimated and an analysis of its user-dependent parameters is given. The advantages of the proposed approach, with regard to the best existing networks, are shown and analyzed, qualitatively and quantitatively, both in benchmark synthetic problems and in a real application (image recognition from video), in order to test the performance in building hierarchical trees. Furthermore, an important and very promising application of GH-EXIN in two-way hierarchical clustering, for the analysis of gene expression data in the study of the colorectal cancer is described. [ABSTRACT FROM AUTHOR]