S-TREE: Self-Organizing Trees for Data Clustering and Online Vector Quantization

This paper introduces S-TREE (Self-Organizing Tree), a family of models that use unsupervised learning to construct hierarchical representations of data and online tree-structured vector quantizers. The S-TREE1 model, which features a new tree-building algorithm, can be implemented with various cost functions. An alternative implementation, S-TREE2, which uses a new double-path search procedure, is also developed. S-TREE2 implements an online procedure that approximates an optimal (unstructured) clustering solution while imposing a tree-structure constraint. The performance of the S-TREE algorithms is illustrated with data clustering and vector quantization examples, including a Gauss-Markov source benchmark and an image compression application. S-TREE performance on these tasks is compared with the standard tree-structured vector quantizer (TSVQ) and the generalized Lloyd algorithm (GLA). The image reconstruction quality with S-TREE2 approaches that of GLA while taking less than 10% of computer time. S-TREE1 and S-TREE2 also compare favorably with the standard TSVQ in both the time needed to create the codebook and the quality of image reconstruction.Office of Naval Research (N00014-95-10409, N00014-95-0G57

Hierarchical growing cell structures: TreeGCS

We propose a hierarchical clustering algorithm (TreeGCS) based upon the Growing Cell Structure (GCS) neural network of Fritzke. Our algorithm refines and builds upon the GCS base, overcoming an inconsistency in the original GCS algorithm, where the network topology is susceptible to the ordering of the input vectors. Our algorithm is unsupervised, flexible, and dynamic and we have imposed no additional parameters on the underlying GCS algorithm. Our ultimate aim is a hierarchical clustering neural network that is both consistent and stable and identifies the innate hierarchical structure present in vector-based data. We demonstrate improved stability of the GCS foundation and evaluate our algorithm against the hierarchy generated by an ascendant hierarchical clustering dendogram. Our approach emulates the hierarchical clustering of the dendogram. It demonstrates the importance of the parameter settings for GCS and how they affect the stability of the clustering

Wide Field Imaging. I. Applications of Neural Networks to object detection and star/galaxy classification

[Abriged] Astronomical Wide Field Imaging performed with new large format CCD detectors poses data reduction problems of unprecedented scale which are difficult to deal with traditional interactive tools. We present here NExt (Neural Extractor): a new Neural Network (NN) based package capable to detect objects and to perform both deblending and star/galaxy classification in an automatic way. Traditionally, in astronomical images, objects are first discriminated from the noisy background by searching for sets of connected pixels having brightnesses above a given threshold and then they are classified as stars or as galaxies through diagnostic diagrams having variables choosen accordingly to the astronomer's taste and experience. In the extraction step, assuming that images are well sampled, NExt requires only the simplest a priori definition of "what an object is" (id est, it keeps all structures composed by more than one pixels) and performs the detection via an unsupervised NN approaching detection as a clustering problem which has been thoroughly studied in the artificial intelligence literature. In order to obtain an objective and reliable classification, instead of using an arbitrarily defined set of features, we use a NN to select the most significant features among the large number of measured ones, and then we use their selected features to perform the classification task. In order to optimise the performances of the system we implemented and tested several different models of NN. The comparison of the NExt performances with those of the best detection and classification package known to the authors (SExtractor) shows that NExt is at least as effective as the best traditional packages.Comment: MNRAS, in press. Paper with higher resolution images is available at http://www.na.astro.it/~andreon/listapub.htm

Evolutionary Neural Gas (ENG): A Model of Self Organizing Network from Input Categorization

Despite their claimed biological plausibility, most self organizing networks have strict topological constraints and consequently they cannot take into account a wide range of external stimuli. Furthermore their evolution is conditioned by deterministic laws which often are not correlated with the structural parameters and the global status of the network, as it should happen in a real biological system. In nature the environmental inputs are noise affected and fuzzy. Which thing sets the problem to investigate the possibility of emergent behaviour in a not strictly constrained net and subjected to different inputs. It is here presented a new model of Evolutionary Neural Gas (ENG) with any topological constraints, trained by probabilistic laws depending on the local distortion errors and the network dimension. The network is considered as a population of nodes that coexist in an ecosystem sharing local and global resources. Those particular features allow the network to quickly adapt to the environment, according to its dimensions. The ENG model analysis shows that the net evolves as a scale-free graph, and justifies in a deeply physical sense- the term gas here used.Comment: 16 pages, 8 figure

Self-Organizing Time Map: An Abstraction of Temporal Multivariate Patterns

This paper adopts and adapts Kohonen's standard Self-Organizing Map (SOM) for exploratory temporal structure analysis. The Self-Organizing Time Map (SOTM) implements SOM-type learning to one-dimensional arrays for individual time units, preserves the orientation with short-term memory and arranges the arrays in an ascending order of time. The two-dimensional representation of the SOTM attempts thus twofold topology preservation, where the horizontal direction preserves time topology and the vertical direction data topology. This enables discovering the occurrence and exploring the properties of temporal structural changes in data. For representing qualities and properties of SOTMs, we adapt measures and visualizations from the standard SOM paradigm, as well as introduce a measure of temporal structural changes. The functioning of the SOTM, and its visualizations and quality and property measures, are illustrated on artificial toy data. The usefulness of the SOTM in a real-world setting is shown on poverty, welfare and development indicators