Dynamics and topographic organization of recursive self-organizing maps

Recently there has been an outburst of interest in extending topographic maps of vectorial data to more general data structures, such as sequences or trees. However, there is no general consensus as to how best to process sequences using topographicmaps, and this topic remains an active focus of neurocomputational research. The representational capabilities and internal representations of the models are not well understood. Here, we rigorously analyze a generalization of the self-organizingmap (SOM) for processing sequential data, recursive SOM (RecSOM) (Voegtlin, 2002), as a nonautonomous dynamical system consisting of a set of fixed input maps. We argue that contractive fixed-input maps are likely to produce Markovian organizations of receptive fields on the RecSOM map. We derive bounds on parameter β (weighting the importance of importing past information when processing sequences) under which contractiveness of the fixed-input maps is guaranteed. Some generalizations of SOM contain a dynamic module responsible for processing temporal contexts as an integral part of the model. We show that Markovian topographic maps of sequential data can be produced using a simple fixed (nonadaptable) dynamic module externally feeding a standard topographic model designed to process static vectorial data of fixed dimensionality (e.g., SOM). However, by allowing trainable feedback connections, one can obtain Markovian maps with superior memory depth and topography preservation. We elaborate on the importance of non-Markovian organizations in topographic maps of sequential data. © 2006 Massachusetts Institute of Technology.

A low-cost remote sensing system for agricultural applications

This research develops a low cost remote sensing system for use in agricultural applications. The important features of the system are that it monitors the near infrared and it incorporates position and attitude measuring equipment allowing for geo-rectified images to be produced without the use of ground control points. The equipment is designed to be hand held and hence requires no structural modification to the aircraft. The portable remote sensing system consists of an inertia measurement unit (IMU), which is accelerometer based, a low-cost GPS device and a small format false colour composite digital camera. The total cost of producing such a system is below GBP 3000, which is far cheaper than equivalent existing systems. The design of the portable remote sensing device has eliminated bore sight misalignment errors from the direct geo-referencing process. A new processing technique has been introduced for the data obtained from these low-cost devices, and it is found that using this technique the image can be matched (overlaid) onto Ordnance Survey Master Maps at an accuracy compatible with precision agriculture requirements. The direct geo-referencing has also been improved by introducing an algorithm capable of correcting oblique images directly. This algorithm alters the pixels value, hence it is advised that image analysis is performed before image georectification. The drawback of this research is that the low-cost GPS device experienced bad checksum errors, which resulted in missing data. The Wide Area Augmented System (WAAS) correction could not be employed because the satellites could not be locked onto whilst flying. The best GPS data were obtained from the Garmin eTrex (15 m kinematic and 2 m static) instruments which have a highsensitivity receiver with good lock on capability. The limitation of this GPS device is the inability to effectively receive the P-Code wavelength, which is needed to gain the best accuracy when undertaking differential GPS processing. Pairing the carrier phase L1 with the pseudorange C/A-Code received, in order to determine the image coordinates by the differential technique, is still under investigation. To improve the position accuracy, it is recommended that a GPS base station should be established near the survey area, instead of using a permanent GPS base station established by the Ordnance Survey.