Unsupervised learning is a type of algorithm that learns patterns from untagged data. The hope is that through mimicry, which is an important mode of learning in people, the machine is forced to build a concise representation of its world and then generate imaginative content from it.
In contrast to
supervised learning
Supervised learning (SL) is a machine learning paradigm for problems where the available data consists of labelled examples, meaning that each data point contains features (covariates) and an associated label. The goal of supervised learning alg ...
where data is tagged by an expert, e.g. tagged as a "ball" or "fish", unsupervised methods exhibit self-organization that captures patterns as probability densities
or a combination of neural feature preferences encoded in the machine's weights and activations. The other levels in the supervision spectrum are
reinforcement learning
Reinforcement learning (RL) is an area of machine learning concerned with how intelligent agents ought to take actions in an environment in order to maximize the notion of cumulative reward. Reinforcement learning is one of three basic machine ...
where the machine is given only a numerical performance score as guidance, and
semi-supervised learning Weak supervision is a branch of machine learning where noisy, limited, or imprecise sources are used to provide supervision signal for labeling large amounts of training data in a supervised learning setting. This approach alleviates the burden of ...
where a small portion of the data is tagged.
Neural networks
Tasks vs. methods
Neural network tasks are often categorized as discriminative (recognition) or generative (imagination). Often but not always, discriminative tasks use supervised methods and generative tasks use unsupervised (see
Venn diagram
A Venn diagram is a widely used diagram style that shows the logical relation between sets, popularized by John Venn (1834–1923) in the 1880s. The diagrams are used to teach elementary set theory, and to illustrate simple set relationships ...
); however, the separation is very hazy. For example, object recognition favors supervised learning but unsupervised learning can also cluster objects into groups. Furthermore, as progress marches onward some tasks employ both methods, and some tasks swing from one to another. For example, image recognition started off as heavily supervised, but became hybrid by employing unsupervised pre-training, and then moved towards supervision again with the advent of dropout, relu, and adaptive learning rates.
Training
During the learning phase, an unsupervised network tries to mimic the data it's given and uses the error in its mimicked output to correct itself (i.e. correct its weights & biases). Sometimes the error is expressed as a low probability that the erroneous output occurs, or it might be expressed as an unstable high energy state in the network.
In contrast to supervised methods' dominant use of
backpropagation
In machine learning, backpropagation (backprop, BP) is a widely used algorithm for training feedforward artificial neural networks. Generalizations of backpropagation exist for other artificial neural networks (ANNs), and for functions gener ...
, unsupervised learning also employs other methods including: Hopfield learning rule, Boltzmann learning rule, Contrastive Divergence,
Wake Sleep, Variational Inference, Maximum Likelihood, Maximum A Posteriori, Gibbs Sampling, and backpropagating reconstruction errors or hidden state reparameterizations. See the table below for more details.
Energy
An energy function is a macroscopic measure of a network's activation state. In Boltzmann machines, it plays the role of the Cost function. This analogy with physics is inspired by Ludwig Boltzmann's analysis of a gas' macroscopic energy from the microscopic probabilities of particle motion p
e
-E/kT, where k is the Boltzmann constant and T is temperature. In the RBM network the relation is p = e
−E / Z,
where p & E vary over every possible activation pattern and Z =
e
-E(pattern). To be more precise, p(a) = e
-E(a) / Z, where a is an activation pattern of all neurons (visible and hidden). Hence, early neural networks bear the name Boltzmann Machine. Paul Smolensky calls -E the Harmony. A network seeks low energy which is high Harmony.
Networks
This table shows connection diagrams of various unsupervised networks, the details of which will be given in the section Comparison of Network. Circles are neurons and edges between them are connection weights. As network design changes, features are added on to enable new capabilities or removed to make learning faster. For instances, neurons changes between deterministic (Hopfield) and stochastic (Boltzmann) to allow robust output, weights are removed within a layer (RBM) to hasten learning, or connections are allowed to become asymmetric (Helmholtz).
Of the networks bearing people's names, only Hopfield worked directly with neural networks. Boltzmann and Helmholtz came before artificial neural networks, but their work in physics and physiology inspired the analytical methods that were used.
History
Specific Networks
Here, we highlight some characteristics of select networks. The details of each are given in the comparison table below.
Comparison of networks
Hebbian Learning, ART, SOM
The classical example of unsupervised learning in the study of neural networks is
Donald Hebb
Donald Olding Hebb (July 22, 1904 – August 20, 1985) was a Canadian psychologist who was influential in the area of neuropsychology, where he sought to understand how the function of neurons contributed to psychological processes such as learn ...
's principle, that is, neurons that fire together wire together.
In
Hebbian learning
Hebbian theory is a neuroscientific theory claiming that an increase in synaptic efficacy arises from a presynaptic cell's repeated and persistent stimulation of a postsynaptic cell. It is an attempt to explain synaptic plasticity, the adaptatio ...
, the connection is reinforced irrespective of an error, but is exclusively a function of the coincidence between action potentials between the two neurons.
A similar version that modifies synaptic weights takes into account the time between the action potentials (
spike-timing-dependent plasticity
Spike-timing-dependent plasticity (STDP) is a biological process that adjusts the strength of connections between neurons in the brain. The process adjusts the connection strengths based on the relative timing of a particular neuron's output and in ...
or STDP). Hebbian Learning has been hypothesized to underlie a range of cognitive functions, such as
pattern recognition
Pattern recognition is the automated recognition of patterns and regularities in data. It has applications in statistical data analysis, signal processing, image analysis, information retrieval, bioinformatics, data compression, computer graphics ...
and experiential learning.
Among
neural network models, the
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 ...
(SOM) and
adaptive resonance theory Adaptive resonance theory (ART) is a theory developed by Stephen Grossberg and Gail Carpenter on aspects of how the brain processes information. It describes a number of neural network models which use supervised and unsupervised learning metho ...
(ART) are commonly used in unsupervised learning algorithms. The SOM is a topographic organization in which nearby locations in the map represent inputs with similar properties. The ART model allows the number of clusters to vary with problem size and lets the user control the degree of similarity between members of the same clusters by means of a user-defined constant called the vigilance parameter. ART networks are used for many pattern recognition tasks, such as
automatic target recognition
Automatic target recognition (ATR) is the ability for an algorithm or device to recognize targets or other objects based on data obtained from sensors.
Target recognition was initially done by using an audible representation of the received signal ...
and seismic signal processing.
Probabilistic methods
Two of the main methods used in unsupervised learning are
principal component
Principal may refer to:
Title or rank
* Principal (academia), the chief executive of a university
** Principal (education), the office holder/ or boss in any school
* Principal (civil service) or principal officer, the senior management level ...
and
cluster analysis.
Cluster analysis is used in unsupervised learning to group, or segment, datasets with shared attributes in order to extrapolate algorithmic relationships.
Cluster analysis is a branch 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 of tasks. It is seen as a part of artificial intelligence.
Machine ...
that groups the data that has not been
labelled, classified or categorized. Instead of responding to feedback, cluster analysis identifies commonalities in the data and reacts based on the presence or absence of such commonalities in each new piece of data. This approach helps detect anomalous data points that do not fit into either group.
A central application of unsupervised learning is in the field of
density estimation
In statistics, probability density estimation or simply density estimation is the construction of an estimate, based on observed data, of an unobservable underlying probability density function. The unobservable density function is thought of ...
in
statistics,
though unsupervised learning encompasses many other domains involving summarizing and explaining data features. It can be contrasted with supervised learning by saying that whereas supervised learning intends to infer a
conditional probability distribution
In probability theory and statistics, given two jointly distributed random variables X and Y, the conditional probability distribution of Y given X is the probability distribution of Y when X is known to be a particular value; in some cases the ...
conditioned on the label of input data; unsupervised learning intends to infer an
a priori probability
An ''a priori'' probability is a probability that is derived purely by deductive reasoning. One way of deriving ''a priori'' probabilities is the principle of indifference, which has the character of saying that, if there are ''N'' mutually exclu ...
distribution .
Approaches
Some of the most common algorithms used in unsupervised learning include: (1) Clustering, (2) Anomaly detection, (3) Approaches for learning latent variable models. Each approach uses several methods as follows:
*
Clustering methods include:
hierarchical clustering,
k-means
''k''-means clustering is a method of vector quantization, originally from signal processing, that aims to partition ''n'' observations into ''k'' clusters in which each observation belongs to the cluster with the nearest mean (cluster centers o ...
,
mixture models
In statistics, a mixture model is a probabilistic model for representing the presence of subpopulations within an overall population, without requiring that an observed data set should identify the sub-population to which an individual observation ...
,
DBSCAN
Density-based spatial clustering of applications with noise (DBSCAN) is a data clustering algorithm proposed by Martin Ester, Hans-Peter Kriegel, Jörg Sander and Xiaowei Xu in 1996.
It is a density-based clustering non-parametric algorithm: gi ...
, and
OPTICS algorithm
Ordering points to identify the clustering structure (OPTICS) is an algorithm for finding density-based clusters in spatial data. It was presented by Mihael Ankerst, Markus M. Breunig, Hans-Peter Kriegel and Jörg Sander.
Its basic idea is simil ...
*
Anomaly detection
In data analysis, anomaly detection (also referred to as outlier detection and sometimes as novelty detection) is generally understood to be the identification of rare items, events or observations which deviate significantly from the majority o ...
methods include:
Local Outlier Factor
In anomaly detection, the local outlier factor (LOF) is an algorithm proposed by Markus M. Breunig, Hans-Peter Kriegel, Raymond T. Ng and Jörg Sander in 2000 for finding anomalous data points by measuring the local deviation of a given data poin ...
, and
Isolation Forest
* Approaches for learning
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.
It is assumed that the responses on the indicators or manifest variabl ...
s such as
Expectation–maximization algorithm
In statistics, an expectation–maximization (EM) algorithm is an iterative method to find (local) maximum likelihood or maximum a posteriori (MAP) estimates of parameters in statistical models, where the model depends on unobserved latent variabl ...
(EM),
Method of moments, and
Blind signal separation
Blind may refer to:
* The state of blindness, being unable to see
* A window blind, a covering for a window
Blind may also refer to:
Arts, entertainment, and media Films
* ''Blind'' (2007 film), a Dutch drama by Tamar van den Dop
* ''Blind' ...
techniques (
Principal component analysis,
Independent component analysis
In signal processing, independent component analysis (ICA) is a computational method for separating a multivariate signal into additive subcomponents. This is done by assuming that at most one subcomponent is Gaussian and that the subcomponents ar ...
,
Non-negative matrix factorization
Non-negative matrix factorization (NMF or NNMF), also non-negative matrix approximation is a group of algorithms in multivariate analysis and linear algebra where a matrix is factorized into (usually) two matrices and , with the property that ...
,
Singular value decomposition
In linear algebra, the singular value decomposition (SVD) is a factorization of a real or complex matrix. It generalizes the eigendecomposition of a square normal matrix with an orthonormal eigenbasis to any \ m \times n\ matrix. It is re ...
)
Method of moments
One of the statistical approaches for unsupervised learning is the
method of moments. In the method of moments, the unknown parameters (of interest) in the model are related to the moments of one or more random variables, and thus, these unknown parameters can be estimated given the moments. The moments are usually estimated from samples empirically. The basic moments are first and second order moments. For a random vector, the first order moment is the
mean
There are several kinds of mean in mathematics, especially in statistics. Each mean serves to summarize a given group of data, often to better understand the overall value (magnitude and sign) of a given data set.
For a data set, the '' ari ...
vector, and the second order moment is the
covariance matrix (when the mean is zero). Higher order moments are usually represented using
tensors
In mathematics, a tensor is an algebraic object that describes a multilinear relationship between sets of algebraic objects related to a vector space. Tensors may map between different objects such as vectors, scalars, and even other tensor ...
which are the generalization of matrices to higher orders as multi-dimensional arrays.
In particular, the method of moments is shown to be effective in learning the parameters of
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.
It is assumed that the responses on the indicators or manifest variabl ...
s. Latent variable models are statistical models where in addition to the observed variables, a set of latent variables also exists which is not observed. A highly practical example of latent variable models in machine learning is the
topic modeling
In statistics and natural language processing, a topic model is a type of statistical model for discovering the abstract "topics" that occur in a collection of documents. Topic modeling is a frequently used text-mining tool for discovery of hidden ...
which is a statistical model for generating the words (observed variables) in the document based on the topic (latent variable) of the document. In the topic modeling, the words in the document are generated according to different statistical parameters when the topic of the document is changed. It is shown that method of moments (tensor decomposition techniques) consistently recover the parameters of a large class of latent variable models under some assumptions.
The
Expectation–maximization algorithm
In statistics, an expectation–maximization (EM) algorithm is an iterative method to find (local) maximum likelihood or maximum a posteriori (MAP) estimates of parameters in statistical models, where the model depends on unobserved latent variabl ...
(EM) is also one of the most practical methods for learning latent variable models. However, it can get stuck in local optima, and it is not guaranteed that the algorithm will converge to the true unknown parameters of the model. In contrast, for the method of moments, the global convergence is guaranteed under some conditions.
See also
*
Automated machine learning
Automated machine learning (AutoML) is the process of automating the tasks of applying machine learning to real-world problems. AutoML potentially includes every stage from beginning with a raw dataset to building a machine learning model ready ...
*
Cluster analysis
*
Anomaly detection
In data analysis, anomaly detection (also referred to as outlier detection and sometimes as novelty detection) is generally understood to be the identification of rare items, events or observations which deviate significantly from the majority o ...
*
Expectation–maximization algorithm
In statistics, an expectation–maximization (EM) algorithm is an iterative method to find (local) maximum likelihood or maximum a posteriori (MAP) estimates of parameters in statistical models, where the model depends on unobserved latent variabl ...
*
Generative topographic map Generative topographic map (GTM) is a machine learning method that is a probabilistic counterpart of the self-organizing map (SOM), is probably convergent and does not require a shrinking neighborhood or a decreasing step size. It is a generative m ...
*
Meta-learning (computer science)
Meta learning
is a subfield of machine learning where automatic learning algorithms are applied to metadata about machine learning experiments. As of 2017 the term had not found a standard interpretation, however the main goal is to use such met ...
*
Multivariate analysis
Multivariate statistics is a subdivision of statistics encompassing the simultaneous observation and analysis of more than one outcome variable.
Multivariate statistics concerns understanding the different aims and background of each of the dif ...
*
Radial basis function network
In the field of mathematical modeling, a radial basis function network is an artificial neural network that uses radial basis functions as activation functions. The output of the network is a linear combination of radial basis functions of the inp ...
*
Weak supervision Weak supervision is a branch of machine learning where noisy, limited, or imprecise sources are used to provide supervision signal for labeling large amounts of training data in a supervised learning setting. This approach alleviates the burden of o ...
References
Further reading
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