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

Fundamentals of Recurrent Neural Network (RNN) and Long Short-Term Memory (LSTM) Network

Because of their effectiveness in broad practical applications, LSTM networks have received a wealth of coverage in scientific journals, technical blogs, and implementation guides. However, in most articles, the inference formulas for the LSTM network and its parent, RNN, are stated axiomatically, while the training formulas are omitted altogether. In addition, the technique of "unrolling" an RNN is routinely presented without justification throughout the literature. The goal of this paper is to explain the essential RNN and LSTM fundamentals in a single document. Drawing from concepts in signal processing, we formally derive the canonical RNN formulation from differential equations. We then propose and prove a precise statement, which yields the RNN unrolling technique. We also review the difficulties with training the standard RNN and address them by transforming the RNN into the "Vanilla LSTM" network through a series of logical arguments. We provide all equations pertaining to the LSTM system together with detailed descriptions of its constituent entities. Albeit unconventional, our choice of notation and the method for presenting the LSTM system emphasizes ease of understanding. As part of the analysis, we identify new opportunities to enrich the LSTM system and incorporate these extensions into the Vanilla LSTM network, producing the most general LSTM variant to date. The target reader has already been exposed to RNNs and LSTM networks through numerous available resources and is open to an alternative pedagogical approach. A Machine Learning practitioner seeking guidance for implementing our new augmented LSTM model in software for experimentation and research will find the insights and derivations in this tutorial valuable as well.Comment: 43 pages, 10 figures, 78 reference

Software verification plan for GCS

This verification plan is written as part of an experiment designed to study the fundamental characteristics of the software failure process. The experiment will be conducted using several implementations of software that were produced according to industry-standard guidelines, namely the Radio Technical Commission for Aeronautics RTCA/DO-178A guidelines, Software Consideration in Airborne Systems and Equipment Certification, for the development of flight software. This plan fulfills the DO-178A requirements for providing instructions on the testing of each implementation of software. The plan details the verification activities to be performed at each phase in the development process, contains a step by step description of the testing procedures, and discusses all of the tools used throughout the verification process

Interfaces between statistical analysis packages and the ESRI geographic information system

Interfaces between ESRI's geographic information system (GIS) data files and real valued data files written to facilitate statistical analysis and display of spatially referenced multivariable data are described. An example of data analysis which utilized the GIS and the statistical analysis system is presented to illustrate the utility of combining the analytic capability of a statistical package with the data management and display features of the GIS

The Geneva-Copenhagen Survey of the Solar neighbourhood II. New uvby calibrations and rediscussion of stellar ages, the G dwarf problem, age-metallicity diagram, and heating mechanisms of the disk

Ages, metallicities, space velocities, and Galactic orbits of stars in the Solar neighbourhood are fundamental observational constraints on models of galactic disk evolution. We aim to consolidate the calibrations of uvby photometry into Te, [Fe/H], distance, and age for F and G stars and rediscuss the results of the Geneva-Copenhagen Survey (Nordstrom et al. 2004; GCS) in terms of the evolution of the disk. We substantially improve the Te and [Fe/H] calibrations for early F stars, where spectroscopic temperatures have large systematic errors. Our recomputed ages are in excellent agreement with the independent determinations by Takeda et al. (2007), indicating that isochrone ages can now be reliably determined. The revised G-dwarf metallicity distribution remains incompatible with closed-box models, and the age-metallicity relation for the thin disk remains almost flat, with large and real scatter at all ages (sigma intrinsic = 0.20 dex). Dynamical heating of the thin disk continues throughout its life; specific in-plane dynamical effects dominate the evolution of the U and V velocities, while the W velocities remain random at all ages. When assigning thick and thin-disk membership for stars from kinematic criteria, parameters for the oldest stars should be used to characterise the thin disk.Comment: Accepted for publication in A&A on June 20, 200