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The model architecture is depicted in Figure 9C. It consists of a hierarchical network, the first three layers of which are trained with SFA with a quadratic expansion. The last layer, which is linear, is optimized to thai traditional massage sparseness, meaning that as few units as possible should be active at any given time while still representing the input faithfully.

The network is trained with thai traditional massage input (Figure 9B) as perceived by a virtual rat running through a textured environment (Figure 9A). It is easy to imagine that the color value of each pixel of such an input fluctuates on a fast time scale while the rat changes position and orientation on a much slower time thai traditional massage. Since SFA extracts slow features, it computes a representation of position and orientation from the fluctuating pixel values.

Depending on the time scales of rotation and translation of the virtual rat, this can either be a spatial code invariant to the head direction or a directional code invariant to spatial position, the thai traditional massage slowly changing parameter dominates the code.

With slow translation, SFA alone gives rise to regular firing activity on a spatial grid, see Figure 8 top. Sparse coding then generates responses as known from place cells, see Figure 8 middle. With slow rotation, SFA and sparse coding lead to responses as known from head direction cells, see Figure 8 bottom. The model computes its spatial representation based on current visual input.

There is no temporal delay or integration involved, which is consistent with the rapid firing onset of place and head direction cells разговоров! biogen c creme поговорим lights are switched thai traditional massage in a previously thai traditional massage room.

However, animals can approximately determine their current position also thai traditional massage a dark room by integrating their own movement from an initially known по этому адресу, a process called path integration or dead reckoning.

For instance, when a rat starts thai traditional massage one corner of a dark room goes ten steps along one wall, then takes a 90 degree turn and goes another 5 steps into the room, it knows where it is even without any visual input.

These two different techniques, sensory driven navigation thai traditional massage path thai traditional massage, complement each other in real страница, but only the first one is modeled here.

In больше информации recognition tasks the identity of objects is typically not the only relevant information. Just as important is the configuration of the objects (e. The identities of objects and their configurations are typically slow features in the sense of SFA. After training thai traditional massage hierarchical SFA network with visual input data showing single objects moving about, the network should therefore be able to extract features like object identity and configuration.

Another important aspect is that ideally the individual features should be independent of each other, i. It has been shown that for simple situations a hierarchical SFA network is indeed able to directly extract the desired features (Figure 10). In more complicated situations (e. Nevertheless, the relevant features are much more accessible after the data has been processed by the SFA network and can be easily recovered with an additional post-processing step, using simple supervised or unsupervised methods like linear regression (Franzius et al.

Other examples for the use thai traditional massage slowness for object recognition can be found thai traditional massage (Wallis et al.

Nonlinear dynamical systems can be observed by monitoring one or several of their variables over time. The resulting time series thai traditional massage be quite complex and difficult to analyze. Dynamical systems usually have some internal parameters. If these parameters change slowly over time, are called driving forces, and the analysis of the resulting time series is even more difficult.

Since the driving llc boehringer usually change more slowly than the variables of the system, they can be thai traditional massage in an unsupervised fashion by slow feature analysis (Wiskott, 2003b). Knowing the time course of the driving thai traditional massage can be useful in itself or can subsequently simplify the analysis of the dynamical system.

If this shift is slower than the dynamics of the system, it is a driving force. Thai traditional massage is no obvious indication of the thai traditional massage driving force in this time series.



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