Select Other Tags

SOMs can be used as a means of learning principal manifolds.⇒

There is the hypothesis that complex motions are comprised of combinations of simple muscle synergies, which would reduce the dimensionality of the control signal.⇒

A low-dimensional representation of motion patterns in a high-dimensional space restricts the actual dimensionality of those motions.⇒

I'm not so sure that a low-dimensional representation of motion patterns in a high-dimensional space necessarily restricts the actual dimensionality of those motions:

$\mathbb{Q}^3$ is bijective to $\mathbb{Q}$ (right?).

It is probably the case for natural behavior, though.⇒

The concept of reduction of the dimensionality of motor space by using motor synergies has been used in robotics.⇒

Zhang et al. propose an unsupervised dimensionality reduction algorithm, which they call 'multi-modal'.

Their notion of multi-modality is a different notion from the one used in my work: it means that a latent, low-dimensional variable is expressed according to a multi-modal PDF.

This is can be difficult depending the transformation function mapping the high-dimensional data into low-dimensional space. Especially linear methods, like PCA will suffer from this.

The authors focus on (mostly binary) classification. In that context, multi-modality requires complex decision boundaries.⇒

The number of reservoir nodes in reservoir computing is typically much larger than the number of input or output neurons.

A reservoir network therefore first translates the low-dimensional input into a high-dimensional space and back into a low-dimensional space.⇒

The transfer functions of reservoir nodes in reservoir computing is usually non-linear. Therefore, the transfer from low-to high-dimensional space is non-linear, and linearly inseparable representations in the input layer can be transferred into linearly separable representations in the reservoir layer. Training of the linear, non-recurrent output layer is therefore enough even for problems which could not be solved with a single-layer perceptron on its own.⇒

A principal manifold can only be learned correctly using a SOM if

- the SOM's dimensionality is the same as that of the principal manifold
- the noise does not 'smear' the manifold too much, thus making it indistinguishable from a manifold with higher dimensionality.
- there are enough data points to infer the manifold behind the noise.⇒