## Self-Organising Maps

The Self-Organising Map is a popular unsupervised neural network model which has successfully been used for analysing various
kinds of data. The SOM performs both a vector quantisation, i.e. finding of prototypical representatives of the data, such as in
k-means clustering, as well as a vector projection, that performs topology-preserving mapping from a high-dimensional input space
to a normally two-dimensional output space, the map.

Our group has extensive knowledge on SOMs; some of our work is
illustrated below. We also release the open-source Java SOMToolbox

The Java SOMToolbox is an open-source toolkit implemented in Java, that allows you to easily train self-organising maps, and
analyse them with an advanced viewer application, which implements a large range of different visualisations and quality measures
of the SOM. These allow in-depth analysis and evaluation of the trained maps and the characteristics of the data, resulting in a
powerful tool for data mining.

[SOMToolbox website]
### Visualisations for Matlab Toolbox

As an add-on to the

Matlab SOMToolbox, we provide a set of
visualisations, along with a graphical interface. We add Neighbourhood Graphs, Gradient Fields, P-Matrix and U*-Matrix, and the
Metro Map. Moreover, our software package includes several map quality measures, as well as clustering techniques such as k-means
and Ward's linkage that can be applied on the SOM lattice.

[SOMVIS
website]

### Smoothed Data Histograms

Smoothed Data Histograms are a visualization method for Self-Organizing Maps that show the data distribution of the data samples
by counting a number of most likely positions for each sample. The results can be visualized in a very intuitive landscape-like
way, with islands and mountains in densely occupied regions and oceans in between.

### Gradient Field & Borderline

The Gradient Field method is a visualization technique that aims at providing insight into the clustering structure of a
Self-Organizing Map by a vector field representation. The arrows are pointing towards cluster centres and away from dissimilar
regions on the map. This method has been extended for discriminative plotting of groups of variables, and by rotating the
vectors by 90 degrees such that the boundaries are depicted directly.

### Graphical Methods

Graphical methods for the visualization of Self-Organizing Maps provide a unique view of the adjacency of the clusters. Data
points are connected visually on the map if they are within a certain range in the original input space. Thus, dense regions can
be identified as well as outliers. Further, it can be observed which regions on the map are related to each other although not
necessarily next to each other, an effect that frequently occurs with high-dimensional data.

### Metro Map

The Metro Map is a novel visualisation, helping to uncover the influence of single variables (components) on the SOM clustering.
It is based on the discretisation of the components and makes use of the well-known metro map metaphor. Component Lines are drawn
for each component of the data, allowing the combination of numerous Component Planes into one plot It thus depicts consistent
values and their ordering across the map, as well as component correlations. It is also possible to further aggregate the display,
by grouping highly correlated variables, i.e. similar lines on the map.

### Sky Metaphor Visualisation

Although various visualisations have been proposed for Self-Organising Maps, these techniques lack in distinguishing between the
items mapped to the same unit. The Sky Metaphor Visualisation is a novel technique that displays inputs not in the centre of the
map units, but shifts them towards the closest neighbours, the degree of the movement depending on the similarity to the
neighbours. The night-sky visualisation facilitates better understanding of the underlying data.

### Analytical Comparison of SOMs

There are very few visualisations for directly comparing two or more SOMs with each other. Thus we developed three visualisations
to compare SOMs, trained on the same dataset but with different parameters, to visualise where the data gets projected on each map
and to assess the stability and quality of the mappings. The analysis of shifts in position can be for single data vector or on a
cluster level, while the Multi-SOM Comparison Analysis assesses the stability of the SOM's data projection in multiple maps.
### Mnemonic SOM

The mnemonic SOM is an adaption of the original SOM algorithm that utilisizes non-rectangular shapes. The idea is to present to
the user shapes, such as country or continent maps, or geometrical shapes such as icons, he is familiar with. This will allow an
easier description of the location of certain data items, and provides an additional mnemonic clue for remembering the locations
and relationships between clusters.

[Details]
### Growing Hierarchical SOM

The Growing Hierarchical Self-Organizing Map (GHSOM) is an extension of the original SOM algorithm that modifies the network
topology such that it can grow both in map size and in depth. The training algorithm automatically selects the most fitting
hierarchical structure for a given data set. The GHSOM provides a structural representation that is rough on the first layer and
can be zoomed into if the fine details are of interest. It has been applied to various document databases, where the most similar
articles are grouped together.

[Details]