Self-Organizing Hierarchical Neural Network
with Correlation Based Sparse Connections
Janusz A. Starzyk, James Graham
Ohio University, Athens, OH
NETWORK DESIGN
INTRODUCTION
•This work attempts to build a self-organized hierarchical structure with correlation
based sparse connectivity.
•Self-organizing networks, hierarchical or otherwise, have been researched for many
years, and have applications in such areas as: surveillance, traffic monitoring, flight
control, rescue mission, etc.
•The sparsity of connections greatly reduces computational overhead and facilitates
eventual hardware implementation of a network based on the proposed algorithm.
•Sparse connection are provided only to those neurons on a lower level of hierarchy
that are most correlated to each other.
•This yields a structured self-organization of feature selection, providing an
effective tool to associate different regions of memory.
•Correlation over the time and space produces wiring to build sequential memories
that store spatio-temporal patterns of sensory representations and motor skills.
•The neural network representations are built using spatio-temporal associations
observed locally in the input space and extended upwards through the hierarchy
towards associations in the feature space.
•“Higher” layers form increasingly abstract feature representations, eventually
representing entire objects, scenes, concepts, and skills.
BACKGROUND
The design for our network was based
on Fritzke’s GNG [1]. It was modified to
not rely on parameters for adjusting the
error or weights of nodes.
We refer to it as a hybrid network.
Some relevant features of the Hybrid
Network are:
•The hybrid method starts with a random
pre-generated network of a fixed size.
•Connections get “stiffer” with age,
making their weights harder to change.
•Error is calculated after the node position
updates rather than before as in Fritzke’s.
•Weight adjustment and error distribution
are based on “Force” calculations rather
than constants.
•Neighborhood connections are removed
only under the following conditions
(instead of all the time).
• When a connection is added and
there is another connection of
length 2x greater than the node’s
average connection length.
• When a node is moved it looses
its existing connections
This work took the Hybrid algorithm and
expanded upon it. Our self-organizing
hierarchical network is designed to allow
for invariant object recognition.
In a typical NN all of the input pixels
would be connected to all of the neurons.
This is an inefficient use of resources.
Instead, we implemented:
•Correlation based sparse input
connections.
•Hierarchical expanding layers for
building invariance.

Algorithm Operation Overview
•Once data is input, correlation is performed on the provided images.
•This tells how each pixel is correlated to all other pixels in the input space.
•Feedback correlation is also determined by offsetting the data 1 time step.
•Next, the first layer’s input and feedback connectivity structures are determined
from the correlation data.
•Then training is performed using the Hybrid algorithm with some changes
needed to account for the sparse connectivity.
•Once training is complete, the entire set of images is presented to the network
and the output is determined.
•Output is used to determine correlation data needed to construct the next layer.
•The process is repeated in all layers.

•The simple 1D nature of the pixel value input does not lend itself to useful
correlation, therefore, we perform a multi-dimentional correlations.
•Fig. 2 presents a 3D correlation vs. a 10D correlation.
•For our work 10D was deemed sufficient, even though at higher dimensionality
even the slight curves visible in the 10D images disappear.

Fig.5 Five Layers of Network Activity
Performing the correlation:
Fig.6 Growth of Neighborhood Connections
Fig.2 Multi-Dimentional Correlation
(3D vs. 10D)
Determining the connections:
•Now that pixel correlations are known, the input connections can be determined.
•The concept is similar to Fig. 4, but in a 3D sense.
•For the first layer each pixel has a neuron “positioned” directly above. This is
not necessarily the case in higher layers and a composite correlation of the
surrounding neurons is used. To determine input connections, positive portions
of the correlation are treated as a probability distribution function (PDF).
•The PDF is translated into a CDF function and used to randomly select a
number of points in the correlated region.
•The actual number of points is determined randomly about a mean based upon
the size of each layer - a predefined constant.
•Fig. 3 shows an example of the correlation about pixel 132 in a simple 18x14
pixel image set.
•Ideally, this will result in an overlapping connectivity structure that will end
with the type of forward connectivity shown in Fig. 4.
Training
Fig.1 2-D Network Example of the
standard SOM[2], Fritzke’s GNG,
and the Hybrid network
NETWORK OUTPUT
the Network:
•To train a layer, images are presented in sequential order.
•Next, winning neurons are determined based on how close their weights are to
their input values (as in the Hybrid and GNG networks).
•Neighbors are chosen in a similar manner to the GNG network, in that their next
nearest neighbor becomes a neighbor. However, to be a neighbor a node must
share at least some percentage of the same input connections (usually 50%).
•The winning neurons are then evaluated to see if they are strong enough to fire
(taking feedback into account as well).
•Feedback may be able to activate a neuron with insufficient input activation.
•At the end of training the network is evaluated to determine the output for the
known images.
•The output data is then correlated and presented to the layer building subroutine
to construct the next layer.
•In this way the feed-forward and feedback connections are created leading
toward invariant representations for a sequence of images.
Fig.7 Network Activity in the Layers
Wiring area
Above, Figures 5, 6, and 7 depict the results of training a 5 layer network on a small set of 252
pixel images. Figure 5 shows the actual layer outputs. Figure 6 shows the growth in
neighborhood connectivity within the individual layers. And figure 7 shows actual neuron
activity within the layers.
CONCLUSIONS
Fig.3 Correlation/PDF Example
We have successfully implemented a method for determining sparse input connectivity.
And combined it with the hybrid self-organizing structure described in the background section.
The networks was then expanded and adjusted to work as a hierarchical network.
We have shown from the results in Figure 6 and 7 that this work lends itself to forming invariant
representations.
The next step will be implementing feedback to form the invariances and ensuring that the
algorithm is able to handle larger images than those already in use.
Some early testing of larger image sets consisting of higher resolution images has shown that there
are some bottlenecks in the program due to the conflict between sparse matrices (needed to conserve
memory for large matrices) and the slowdown they cause when being accessed.
Also, there is the possibility of implementing lateral input connections to improve the selection of
winning neurons.
REFERENCES
Fig.4 Network Connectivity Example
[1] B. Fritzke, “A Growing Neural Gas Network Learns Topologies,” Advances in Neural
Information Processing Systems 7, G. Tesauro, D.S. Toretzky, and T.K. Leen, (eds.), MIT Press,
Cambridge MA, 1995.
[2] T. Kohonen, "The Self-Organizing map", Proc. of IEEE, 78:1464-1480, 1990.