4727 Words19 Pages

High-dimensional data

Data that requires more than two or three dimensions to represent can be difficult to interpret. One approach to simplification is to assume that the data of interest lie on an embedded non-linear manifold within the higher-dimensional space. If the manifold is of low enough dimension, the data can be visualised in the low-dimensional space.

Abstract— Dimensionality Reduction is a key issue in many scientific problems, in which data is originally given by high dimensional vectors, all of which lie however over a fewer dimensional manifold. Therefore, they can be represented by a reduced number of values that parameterize their position over the mentioned non-linear manifold. This dimensionality reduction is essential not only for representing and managing data, but also for its understanding at a high interpretation level, similar to the way it is performed by the mammal cortex. This paper presents an algorithm for representing the data that lie on a non-linear manifold .

Need to reduce the data:

Scientists working with large volumes of high-dimensional data, such as global climate patterns, stellar spectra, or human gene distributions, regularly con- front the problem of dimensionality reduction: finding meaningful low-dimensional structures hidden in their high-dimensional observations. The human brain confronts the same problem in everyday perception, extracting from its high-dimensional sensory inputs-30,000 auditory nerve fibers or 10^6 optic

Data that requires more than two or three dimensions to represent can be difficult to interpret. One approach to simplification is to assume that the data of interest lie on an embedded non-linear manifold within the higher-dimensional space. If the manifold is of low enough dimension, the data can be visualised in the low-dimensional space.

Abstract— Dimensionality Reduction is a key issue in many scientific problems, in which data is originally given by high dimensional vectors, all of which lie however over a fewer dimensional manifold. Therefore, they can be represented by a reduced number of values that parameterize their position over the mentioned non-linear manifold. This dimensionality reduction is essential not only for representing and managing data, but also for its understanding at a high interpretation level, similar to the way it is performed by the mammal cortex. This paper presents an algorithm for representing the data that lie on a non-linear manifold .

Need to reduce the data:

Scientists working with large volumes of high-dimensional data, such as global climate patterns, stellar spectra, or human gene distributions, regularly con- front the problem of dimensionality reduction: finding meaningful low-dimensional structures hidden in their high-dimensional observations. The human brain confronts the same problem in everyday perception, extracting from its high-dimensional sensory inputs-30,000 auditory nerve fibers or 10^6 optic

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