A latent space, also known as a latent feature space or embedding space, is an
embedding of a set of items within a
manifold
In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point. More precisely, an n-dimensional manifold, or ''n-manifold'' for short, is a topological space with the property that each point has a n ...
in which items resembling each other are positioned closer to one another in the latent space. Position within the latent space can be viewed as being defined by a set of
latent variables that emerge from the resemblances from the objects.
In most cases, the
dimensionality of the latent space is chosen to be lower than the dimensionality of the
feature space from which the data points are drawn, making the construction of a latent space an example of
dimensionality reduction, which can also be viewed as a form of
data compression. Latent spaces are usually fit via
machine learning
Machine learning (ML) is a field of inquiry devoted to understanding and building methods that 'learn', that is, methods that leverage data to improve performance on some set of tasks. It is seen as a part of artificial intelligence.
Machine ...
, and they can then be used as feature spaces in machine learning models, including classifiers and other supervised predictors.
The interpretation of the latent spaces of machine learning models is an active field of study, but latent space interpretation is difficult to achieve. Due to the black-box nature of machine learning models, the latent space may be completely unintuitive. Additionally, the latent space may be high-dimensional, complex, and nonlinear, which may add to the difficulty of interpretation. Some visualization techniques have been developed to connect the latent space to the visual world, but there is often not a direct connection between the latent space interpretation and the model itself. Such techniques include
t-distributed stochastic neighbor embedding
t-distributed stochastic neighbor embedding (t-SNE) is a statistical method for visualizing high-dimensional data by giving each datapoint a location in a two or three-dimensional map. It is based on Stochastic Neighbor Embedding originally de ...
(t-SNE), where the latent space is mapped to two dimensions for visualization. Latent space distances lack physical units, so the interpretation of these distances may depend on the application.
A number of algorithms exist to create latent space embeddings given a set of data items and a
similarity function
In statistics and related fields, a similarity measure or similarity function or similarity metric is a real-valued function that quantifies the similarity between two objects. Although no single definition of a similarity exists, usually such meas ...
.
See also
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Induced topology
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Clustering algorithm
Cluster analysis or clustering is the task of grouping a set of objects in such a way that objects in the same group (called a cluster) are more similar (in some sense) to each other than to those in other groups (clusters). It is a main task of ...
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Intrinsic dimension
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Latent semantic analysis
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Manifold hypothesis
In theoretical computer science and the study of machine learning
Machine learning (ML) is a field of inquiry devoted to understanding and building methods that 'learn', that is, methods that leverage data to improve performance on some set ...
*
Nonlinear dimensionality reduction
Nonlinear dimensionality reduction, also known as manifold learning, refers to various related techniques that aim to project high-dimensional data onto lower-dimensional latent manifolds, with the goal of either visualizing the data in the low-d ...
*
Self-organizing map
References
Data mining
Cluster analysis
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