EXPERT KNOWLEDGE AT A GLANCE

Tag: artificial intelligence

What does HCA stand for?

What does HCA stand for? What is the difference between Agglomerative and Divisive? When do I use the algorithm and what are its strengths? In this article we will clarify all these questions.

If you don’t know what clustering means, check out this article. Here we also explain four other clustering methods that you as a data scientist must know.

What is an HCA?

Hierarchical Cluster Analysis, or HCA, is a technique for optimal and compact connection of objects based on empirical similarity measures. The two most similar objects are assigned one after another until all objects are finally in one cluster. This then results in a tree-like structure.

What does HCA mean - This figure shows the basic principle of an applied HCA to raw data.
What does HCA stand for? Basic principle of an applied HCA to raw data.

So how does a hierarchical cluster procedure work?

Agglomerative vs Divisive Calculation

The basic clustering can be done in two opposite ways, Agglomerative and Divisive calculation.

Agglomerative clustering:

Agglomerative Nesting, abbreviated AGNES, is also known as the bottom-up method. This method first creates a cluster between two objects with high similarity, and then adds more clusters until all the data has been enclosed.

The divisive cluster calculation follows an opposite concept.

Divisive hierarchical clustering:

Divise Analysis, also known as DIANA, is a top-down method. All objects are directly framed into a cluster and then reduced in size.

In the following figure, the agglomerative process is compared with the divisive process.

What does HCA stand for?  The figure compares the agglomerative and divisive calculation.
What does HCA stand for? Agglomerative vs Divisive Calculation

Thus, the goal is to represent the common properties in low dimension in multidimensional raw data. A strength of this machine learning method is the inclusion of cluster relationships. With K-means, only all objects within a collection are similar to each other, while they are dissimilar to objects in other clusters. If you want to know more about this other popular clustering method, read this article.

How to calculate the cluster distances?

As mentioned earlier, not only are similarities between data points in a cluster weighted, but also similarities between groups. These similarities are represented by distances between the clusters. These distances can be determined in different ways. The distance between the centroids of two clusters can be calculated. A single linkage is the shortest distance between two clusters, a complete linkage is the largest distance between two clusters and an average linkage is the average distance between two clusters.

The figure below contrasts each cluster distance calculation method.

The figure contrasts each cluster distance calculation method. A single linkage is the shortest distance between two clusters, a complete linkage is the largest distance between two clusters and an average linkage is the average distance between two clusters
Cluster distance calculation methods

In addition to the planar representation, the HCA can also be represented in a dendrogram.

HCA represented in a Dendrogram

Since an HCA describes a tree structure, it can be well represented in a dendrogram. Here the connections between the individual data elements and the connections between the clusters become well visible. This diagram can help to choose the optimal number of clusters in the data depending on where you intersect the tree.

In the following figure, for example, such a dendrogram is shown in dependence on Agglomerative and Divisive Calculation.

The figure shows a HCA represented as a dendrogram in dependence to Agglomerative and Divisive Calculation.
HCA presented as dendrogram in dependence to Agglomerative and Divisive Calculation.

That is why Liquid State Machines (LSM) are great

– Recently developed computational model

– does not require information to be stored in some stable state of the system

→ the inherent dynamics of the system are used by a memory less readout function to compute the output

→ can be used for complex Tasks (pattern classification, function approximation, object tracking, …)

LSMs take the temporal aspect of the input into account

Concept

The figure shows a typical structure of a liquid State Machine.
Liquid State Machine

Reservoir/ Liquid

– large accumulation of recurrent interacting nodes
→ is stimulated by the input layer
– Liquid itself is not trained, but randomly constructed with the help of heuristics
– Loops cause a short-term memory effect
– preferably a Spiking Neural Network (SNNs)
→ are closer to biological neural networks than the multilayer Perceptron
→ can be any type of network that has sufficient internal dynamics

Running State

→ will be extracted by the readout function

– depend on the input streams they’ve been presented

Readout Function

– converts the high-dimensional state into the output

– since the readout function is separated from the liquid, several readout functions can be used with the same liquid

→ so different tasks can be performed with the same input

lsm readout fcts
different types of readout functions