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okay, let's dive deep into self-organizing maps (soms). this is going to be a comprehensive tutorial, starting from the fundamental concepts and gradually progressing to implementation with python code. this is part 1, focusing on the core mechanics and a basic implementation. part 2 will cover more advanced topics, practical considerations, and variations.

*what is a self-organizing map (som)?*

a self-organizing map (som), also known as a kohonen map, is a type of unsupervised learning algorithm primarily used for *dimensionality reduction* and *visualization**. it belongs to the family of artificial neural networks. however, unlike many other neural networks, soms use a **competitive learning* approach instead of error correction like backpropagation.

think of it as a way to project high-dimensional data onto a lower-dimensional (usually 2d) grid while preserving the topological relationships within the data. this means data points that are close to each other in the original high-dimensional space will tend to be mapped to neighboring neurons on the som grid.

*key concepts and components*

1. *input space (data space):* this is where your original data resides. each data point (or sample) is a vector with 'n' features (dimensions). for instance, if you're dealing with customer data, your features could be age, income, spending habits, etc.

2. *som grid (map):* the som is a typically a 2d grid of neurons. each neuron (or node) on the grid has a weight vector associated with it. the weight vector has the same dimensionality as the input data vectors.
the topology of the grid is crucial. common choices include rectangular and hexagonal grids.

3. *weight vectors:* each neuron in the som grid has a weight vector (also known as a model vector). the weight vector has the same dimensionality as the input data. the weight vectors represent the "position" of the neuron in the input data space. during training, these weight vectors wil ...

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self organizing maps
SOM
neural networks
unsupervised learning
clustering
dimensionality reduction
data visualization
training process
distance metrics
feature mapping
Kohonen network
topology preservation
application in AI
pattern recognition
machine learning techniques