Latent Space
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A latent space, also known as a latent feature space or embedding space, is an
embedding In mathematics, an embedding (or imbedding) is one instance of some mathematical structure contained within another instance, such as a group (mathematics), group that is a subgroup. When some object X is said to be embedded in another object Y ...
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. Position within the latent space can be viewed as being defined by a set of
latent variable In statistics, latent variables (from Latin: present participle of ) are variables that can only be inferred indirectly through a mathematical model from other observable variables that can be directly observed or measured. Such '' latent va ...
s 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 Feature may refer to: Computing * Feature recognition, could be a hole, pocket, or notch * Feature (computer vision), could be an edge, corner or blob * Feature (machine learning), in statistics: individual measurable properties of the phenom ...
from which the data points are drawn, making the construction of a latent space an example of
dimensionality reduction Dimensionality reduction, or dimension reduction, is the transformation of data from a high-dimensional space into a low-dimensional space so that the low-dimensional representation retains some meaningful properties of the original data, ideally ...
, which can also be viewed as a form of
data compression In information theory, data compression, source coding, or bit-rate reduction is the process of encoding information using fewer bits than the original representation. Any particular compression is either lossy or lossless. Lossless compressi ...
. Latent spaces are usually fit via
machine learning Machine learning (ML) is a field of study in artificial intelligence concerned with the development and study of Computational statistics, statistical algorithms that can learn from data and generalise to unseen data, and thus perform Task ( ...
, 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-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.


Embedding models

Several embedding models have been developed to perform this transformation to create latent space embeddings given a set of data items and a similarity function. These models learn the embeddings by leveraging statistical techniques and machine learning algorithms. Here are some commonly used embedding models: #
Word2Vec Word2vec is a technique in natural language processing (NLP) for obtaining vector representations of words. These vectors capture information about the meaning of the word based on the surrounding words. The word2vec algorithm estimates these rep ...
: Word2Vec is a popular embedding model used in
natural language processing Natural language processing (NLP) is a subfield of computer science and especially artificial intelligence. It is primarily concerned with providing computers with the ability to process data encoded in natural language and is thus closely related ...
(NLP). It learns word embeddings by training a neural network on a large corpus of text. Word2Vec captures semantic and syntactic relationships between words, allowing for meaningful computations like word analogies. #
GloVe A glove is a garment covering the hand, with separate sheaths or openings for each finger including the thumb. Gloves protect and comfort hands against cold or heat, damage by friction, abrasion or chemicals, and disease; or in turn to provide a ...
: GloVe (Global Vectors for Word Representation) is another widely used embedding model for NLP. It combines global statistical information from a corpus with local context information to learn word embeddings. GloVe embeddings are known for capturing both semantic and relational similarities between words. # Siamese Networks: Siamese networks are a type of neural
network architecture Network architecture is the design of a computer network. It is a framework for the specification of a network's physical components and their functional organization and configuration, its operational principles and procedures, as well as commun ...
commonly used for similarity-based embedding. They consist of two identical subnetworks that process two input samples and produce their respective embeddings. Siamese networks are often used for tasks like image similarity, recommendation systems, and face recognition. # Variational Autoencoders (VAEs): VAEs are generative models that simultaneously learn to encode and decode data. The latent space in VAEs acts as an embedding space. By training VAEs on high-dimensional data, such as images or audio, the model learns to encode the data into a compact latent representation. VAEs are known for their ability to generate new data samples from the learned latent space.


Multimodality

Multimodality refers to the integration and analysis of multiple modes or types of data within a single model or framework. Embedding multimodal data involves capturing relationships and interactions between different data types, such as images, text, audio, and structured data. Multimodal embedding models aim to learn joint representations that fuse information from multiple modalities, allowing for cross-modal analysis and tasks. These models enable applications like image captioning, visual
question answering Question answering (QA) is a computer science discipline within the fields of information retrieval and natural language processing (NLP) that is concerned with building systems that automatically answer questions that are posed by humans in a n ...
, and multimodal sentiment analysis. To embed multimodal data, specialized architectures such as deep multimodal networks or multimodal transformers are employed. These architectures combine different types of neural network modules to process and integrate information from various modalities. The resulting embeddings capture the complex relationships between different data types, facilitating multimodal analysis and understanding.


Applications

Embedding latent space and multimodal embedding models have found numerous applications across various domains: * Information retrieval: Embedding techniques enable efficient similarity search and recommendation systems by representing data points in a compact space. * Natural language processing: Word embeddings have revolutionized NLP tasks like sentiment analysis, machine translation, and document classification. * Computer vision: Image and video embeddings enable tasks like object recognition, image retrieval, and video summarization. * Recommendation systems: Embeddings help capture user preferences and item characteristics, enabling personalized recommendations. * Healthcare: Embedding techniques have been applied to electronic health records, medical imaging, and genomic data for disease prediction, diagnosis, and treatment. * Social systems: Embedding techniques can be used to learn latent representations of social systems such as internal migration systems, academic citation networks, and world trade networks.


See also

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Induced topology In topology and related areas of mathematics, a subspace of a topological space (''X'', ''𝜏'') is a subset ''S'' of ''X'' which is equipped with a topology induced from that of ''𝜏'' called the subspace topology (or the relative topology, o ...
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Clustering algorithm Cluster analysis or clustering is the data analyzing technique in which 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 specific sense defined by the analyst) to each o ...
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Intrinsic dimension The intrinsic dimension for a data set can be thought of as the minimal number of variables needed to represent the data set. Similarly, in signal processing of multidimensional signals, the intrinsic dimension of the signal describes how many vari ...
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Latent semantic analysis Latent semantic analysis (LSA) is a technique in natural language processing, in particular distributional semantics, of analyzing relationships between a set of documents and the terms they contain by producing a set of concepts related to the d ...
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Latent variable model A latent variable model is a statistical model that relates a set of observable variables (also called ''manifest variables'' or ''indicators'') to a set of latent variables. Latent variable models are applied across a wide range of fields such ...
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Ordination (statistics) Ordination or gradient analysis, in multivariate analysis, is a method complementary to data clustering, and used mainly in exploratory data analysis (rather than in hypothesis testing). In contrast to cluster analysis, ordination orders quantities ...
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Manifold hypothesis The manifold hypothesis posits that many high-dimensional data sets that occur in the real world actually lie along low-dimensional latent manifolds inside that high-dimensional space. As a consequence of the manifold hypothesis, many data sets t ...
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Nonlinear dimensionality reduction Nonlinear dimensionality reduction, also known as manifold learning, is any of various related techniques that aim to project high-dimensional data, potentially existing across non-linear manifolds which cannot be adequately captured by linear de ...
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Self-organizing map A self-organizing map (SOM) or self-organizing feature map (SOFM) is an unsupervised machine learning technique used to produce a low-dimensional (typically two-dimensional) representation of a higher-dimensional data set while preserving the t ...


References

{{reflist Data mining Cluster analysis