Self-Organizing Maps (SOM)

Suppose you manage the indoor environment of a smart building. The building manager collects temperature, humidity, carbon dioxide concentration, noise level and power use for each space with sensors. But as the number of measurements grows, it becomes hard to see at a glance which spaces have similar conditions, or where ventilation and cooling problems are concentrated.

One method for this situation is the self-organizing map (SOM). A SOM is an unsupervised learning method that maps observations described by many variables onto a grid, usually two-dimensional. Because it learns to place similar observations near each other on the map, it helps you explore complex data and understand the characteristics of each type.

A SOM is a bit different from methods that just assign cluster numbers. Each grid node has a representative vector with the same dimension as the original data, and during training not only the most similar node but also its neighbors are adjusted. In the process, similar patterns in the data can end up arranged continuously across the map.

In this article we'll cover the basic structure of a SOM and how it learns, a worked example with sensor data, map size and training settings, the U-Matrix and component planes, clustering the map, evaluating performance and reporting results.

It usually uses a two-dimensional grid with nodes arranged in fixed rows and columns.

Each node has a weight vector (prototype) as long as the number of input variables. For example, with five variables (temperature, humidity, CO₂ concentration, noise and power use), each node is also represented by a vector of five values.

After training, each observation is mapped to the node whose prototype is closest to it. This shows which areas have similar conditions and where on the map particular environmental patterns gather. However, distance on the SOM grid is not exactly the same as actual distance in the original data space.

A SOM is similar in that it learns representative vectors, but it differs in that those vectors sit on a connected grid, so it also learns the relationships between neighboring nodes.

So the number of SOM nodes is not the final number of clusters. For example, a 6×6 grid has 36 nodes, but you can analyze the similarity of the nodes again and end up defining three operating types.

Each observation summarizes one day of sensor readings.

The goal of this example is not to pin down the cause of a particular equipment failure, but to group similar environmental states and find areas that need further inspection.

So when variables differ in units and magnitude, variables with large numbers can dominate the distance. For example, CO₂ is measured in hundreds of ppm and humidity in tens of percent, so using the raw data as is can distort the comparison. To reduce this, you can standardize each variable (z-scores).

You should also check for extreme values caused by sensor errors, missing observations and mismatched measurement periods. But simply removing extreme values that matter operationally, such as genuinely high CO₂, can erase the very patterns you need to find. It's best to train the SOM after unifying units, handling missing data, checking outliers and standardizing.

First, the distance between the input observation and every prototype on the grid is calculated, and the closest node is selected.

η(t) is the learning rate, and h_b,j(t) is the neighborhood weight based on grid distance from the BMU. A common approach is to move a wide area together early in training and then shrink the range of adjustment later to refine the detailed structure.

Each of the 960 observations is assigned to the closest of the 36 nodes. Not every node gets the same number of observations, and some nodes may be left empty.

These numbers are examples for explanation, not universally optimal values. In practice, you should train several times with different map sizes and starting values and compare stability and how interpretable the maps are.

Observations gathered in the same node on the map show measurement patterns similar to its prototype, and neighboring nodes are trained to have similar patterns too.

A heat map or hit count shows the number of observations assigned to each node. If many observations pile up in one node, it may be a frequently occurring environmental state. But a high count doesn't by itself mean that state is desirable or safe.

Also, even if values change smoothly between neighboring nodes, not every local neighborhood relationship is fully preserved. In building a low-dimensional map, a SOM can lose some of the distance information in the original data.

If neighboring nodes have similar prototypes, the value is small; if they differ, it is large.

Areas with a run of low distance values can be seen as zones where similar environmental patterns gather. Conversely, bands of high distance values may be boundaries between different patterns.

For example, if a high-distance zone appears between two separate areas of the U-Matrix, the observations assigned to those two areas may have different environmental characteristics. But a U-Matrix boundary should not be read as an automatically confirmed cluster boundary. Its shape can also change with the map size, the distance measure and the standardization method.

For example, areas with high values on the CO₂ component plane may also show high values on the power-use component plane. When two maps show similar patterns like this, it's a clue that those variables vary in similar ways across the trained map.

But visually similar patterns are not enough to conclude a causal relationship between the two variables. In this example, you can compare the component planes for temperature, humidity, CO₂, noise and power use one by one to see in which areas a high-CO₂ pattern, a high-temperature/high-power pattern and a relatively stable environmental pattern appear.

You can apply hierarchical clustering or K-means to the trained node prototypes to group them into larger types. For example, suppose the 36 nodes were grouped into three types and each observation was assigned to the type that its BMU belongs to.

The names of the operating types are not labels whose meaning the statistical model guarantees automatically. They should be assigned after reviewing each type's actual variable values and the facility's operating standards. In particular, types B and C are only a reference for prioritizing further inspection, not a confirmed diagnosis of failures in the ventilation or cooling equipment.

You need to check both how well it represents the raw data and how well it preserves the relationships between nearby observations. The standard measures are quantization error (QE) and topographic error (TE).

Quantization error is the mean distance between each observation and its BMU's prototype; the lower it is, the more closely the map nodes represent the data. Topographic error is commonly measured as the proportion of observations whose closest and second-closest nodes are not neighbors on the grid. A lower value can be evidence that local topological relationships were better preserved.

QE depends on the map size and variable scaling, and TE depends on the grid structure, so keep the same preprocessing and evaluation rules when comparing different settings. If you grouped the node prototypes into final clusters, you can also check silhouette coefficients and cluster stability as supporting evidence.

If sensor variables in different units go straight into the distance calculation, the results can be skewed toward some variables. Record the standardization method and apply the same rule in repeated analyses.

Don't assume that looking close on the map means being close in reality.

A SOM represents similarity on a low-dimensional grid, but it does not preserve every distance relationship in the original data space.

Results can be sensitive to map size and starting values.

Even with the same data, results can change with the number of nodes, the learning rate and the random initialization, so it's good to train repeatedly under several settings to check stability.

Don't carelessly assume that the observations are independent.

This example uses data from the same spaces measured on many days, so repetition over time and space-specific characteristics are both present. A SOM provides exploratory mapping, but it does not perform causal inference on repeated observations.

Don't interpret cluster names as actual causes.

Even if you find a high-CO₂ type, there may be many reasons, such as sensor errors or a temporary increase in occupancy. Check on-site information and further diagnostics before making operational decisions.

In actual research, presenting the SOM map together with the U-Matrix and the key component planes makes it easier to understand how each operating type is separated on the map. It's also good to report the stability across repeated training runs and the final clustering method.

Each node has a prototype with the same dimension as the input variables, and during training the best matching unit and its neighboring nodes are adjusted together.

In the results, you can use the hit count, U-Matrix and component planes to see how observations are distributed, where the boundaries between nodes lie and the pattern of each variable. If needed, you can cluster the node prototypes again to organize them into types that are easier to interpret.

But the visual structure of the map does not accurately preserve every relationship in the actual data. Review variable standardization, map size, initialization and training settings, quantization and topographic error, and the stability of the results together.