Clustering: A neural network approach

The SOM algorithm is very astonishing. On the one hand, it is very simple to write down and to simulate, its practical properties are clear and easy to observe. But, on the other hand, its theoretical properties still remain without proof in the general case, despite the great efforts of several authors. In this paper, we pass in review the last results and provide some conjectures for the future work.

Theoretical Aspects of the SOM Algorithm

https://hal.archives-ouvertes.fr/hal-00141470/document

Theoretical aspects of the SOM algorithm

The surface micromachining process of Robert Bosch GmbH has been used to fabricate a novel type of magnetic-field sensor. The Lorentz force, caused by the interaction of a current and an external magnetic field in a suspended surface micromachined conducting beam, laterally displaces the suspended structure. The displacement of the structure is converted into a capacitance change by comb-electrodes, which form a differential capacitor. An appropriate electronic circuitry measures the magnetic field by quantifying the displacement of the conducting beam. In order to increase sensitivity to magnetic fields, the magnitude of the deflection is increased by resonant operation in a vacuum ambient. The sensor obtains its vacuum environment by encapsulation with a new wafer bonding process. Prototype sensors with resonant frequencies in the range around 1300 Hz show Q-factors above 30. With these samples, relative magnetic sensitivities of 900 000 (V/A/spl middot/T) with a detection limit in the sub /spl mu/T-range are reported.

Magnetic field measurements with a novel surface micromachined magnetic-field sensor

This paper presents a new micro-fluxgate magnetic sensor based on micromachined 3-dimensional toroidal type planar coils used as excitation and sensing elements. A rectangular-ring shaped magnetic core and the `second harmonic' operation principle are adopted in this fluxgate sensor. With the use of a newly developed UV-LIGA thick photoresist process and electroplating techniques, excitation and sensing coils as well as permalloy magnetic cores were fabricated to realize a planar three-dimensional magnetic fluxgate sensor on silicon wafers. Excellent linear response over the range of −500 μT to +500 μT, with a system sensitivity of 8360 V T−1 and a resolution of 60 nT was achieved from the sensor realized in this work. The total response range of the sensor is −1.3 to +1.3 mT. The electroplated thick, Cu coil windings result in low coil resistance and a low power consumption of ∼100 mW for an operational frequency range of 1–100 kHz. The small size, the high sensitivity and resolution, and lower power consumption, make this integratable magnetic fluxgate sensor suitable for various applications such as: portable navigation systems, space research, and proximity sensors and detectors.

A micro-fluxgate magnetic sensor using micromachined planar solenoid coils

The operation of magnetic-field sensors is based on many different physical principles ranging from induction to magneto-optical effects. This in turn leads to a vast range of possible magnetic sensor types. What will finally decide the commercial viability of a particular magnetic sensor is its performance as well as its compatibility with miniaturization and microelectronic circuits. The magnetic sensors with the most potential for future applications include: Hall devices, magnetoresistors, inductive coils and fluxgates. The Hall device, while very compatible with microelectronics, suffers from a limited sensitivity in silicon, a high level oof 1 F noise and a relatively large offset. Ferromagnetic magnetoresistors generally have a high sensitivity at a low field; associated problems are the flipping effect and hysteresis. Inductive coils find many applications in proximity and distance sensors, but the miniaturization of coils is difficult. The fluxgate is a highly sensitive magnetic sensor. In principle, it could be integrated, but the main challenges are the three-dimensional structure of the coils and the low magnetic permeability of integrated ferromagnetic cores. The performance of sensors can be considerably improved by incorporating them into a system and using synergistic relationships such as feedback and compensation. The future of magnetic sensor microsystems looks bright with many promising application areas.

The future of magnetic sensors

Self-organisation in Kohonen's SOM

A method for measuring a weak magnetic field with a Hall sensor is described. This method consists of chopping the magnetic field to be measured with a magnetic shield surrounding the Hall sensor. The magnetic shield is periodically driven into saturation by means of an excitation coil. Thus, the Hall device is alternately exposed to/shielded from the d.c. or slowly varying external field to be measured. During the time intervals when the magnetic shield is saturated, the external field passes and is detected by the Hall sensor. When it is not saturated the Hall sensor is shielded from the external field. This chopping method yields a magnetic measurement unaffected by 1/ƒ noise and offset errors of the Hall sensor, therefore improving its detectivity.

Chopping of a weak magnetic field by a saturable magnetic shield

Analysing a self-organising algorithm

Self-organisation is displayed during the unsupervised learning of the Kohonen Neural Network (KNN) algorithm. Classical Markov techniques, the ordinary differential equation (ODE) method being included among these, have so far not yielded a complete general analysis of self-organisation in the KNN. In order to obtain a more general understanding of self-organising behaviour which could then be applied to the analysis of self-organisation in the KNN two simpler self-organising algorithms are described. The first algorithm is based on a simple intuitive understanding of self-organisation. The second is based on a simplification of the KNN algorithm. Using the ODE method general results on the self-organising abilities of the two algorithms are given.

John A. Flanagan

Papers

The future of magnetic sensors

Self-organisation in Kohonen's SOM

Chopping of a weak magnetic field by a saturable magnetic shield

Analysing a self-organising algorithm

Self-Organising Artificial Neural Networks