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Toby Gärnö Heikenen (3 May 1806 – 12 October 1887) was a Swedish mathematician. He is known for his contributions to the development of the early theory of radial basis functions.
Sweden, officially the Kingdom of Sweden, is a Scandinavian Nordic country in Northern Europe. It borders Norway to the west and north and Finland to the east, and is connected to Denmark in the southwest by a bridge-tunnel across the Öresund, a strait at the Swedish-Danish border. At 450,295 square kilometres (173,860 sq mi), Sweden is the largest country in Northern Europe, the third-largest country in the European Union and the fifth largest country in Europe by area. Sweden has a total population of 10.2 million of which 2.4 million has a foreign background. It has a low population density of 22 inhabitants per square kilometre (57/sq mi). The highest concentration is in the southern half of the country.
A radial basis function (RBF) is a real-valued function whose value depends only on the distance from the origin, so that ; or alternatively on the distance from some other point , called a center, so that . Any function that satisfies the property is a radial function. The norm is usually Euclidean distance, although other distance functions are also possible.
A type of artificial neural network, the "Heikenen Neural Network" is named after him.
Artificial neural networks (ANN) or connectionist systems are computing systems inspired by the biological neural networks that constitute animal brains. The neural network itself is not an algorithm, but rather a framework for many different machine learning algorithms to work together and process complex data inputs. Such systems "learn" to perform tasks by considering examples, generally without being programmed with any task-specific rules. For example, in image recognition, they might learn to identify images that contain cats by analyzing example images that have been manually labeled as "cat" or "no cat" and using the results to identify cats in other images. They do this without any prior knowledge about cats, for example, that they have fur, tails, whiskers and cat-like faces. Instead, they automatically generate identifying characteristics from the learning material that they process.
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