Unsupervised Learning

machine-learning

Definition

Unsupervised Learning

Unsupervised learning is a paradigm of machine learning where the objective is to infer the intrinsic structure, density, or latent representations of an unlabelled dataset. Formally, given an instance space $\mathcal{X}$ and a dataset $D=\{x_i{\}}_{i=1}^n\subset \mathcal{X}$ sampled i.i.d. from an unknown probability distribution $P(X)$, the learner seeks to identify patterns or structural properties of $P(X)$ without the supervision of target labels.

Methodological Approaches

The learner identifies patterns through structure discovery, such as clustering, where discrete groups are identified by maximising intra-cluster similarity. Alternatively, representation learning identifies lower-dimensional manifolds or latent spaces $\mathcal{Z}$ that preserve the essential information content of the original distribution. These methods are often complemented by density estimation to model the underlying probability density function $f(x)$ of the data.

Learning Algorithm

Definition

Unsupervised Learning Algorithm

An unsupervised learning algorithm is a learning algorithm that maps unlabelled training data to a specific hypothesis:

$$A:{\mathcal{X}}^m\to \mathcal{H}$$

where:

• $\mathcal{X}$ is the instance space.
• $\mathcal{H}$ is the hypothesis class.

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