Related papers: Archetypal cases for questionnaires with nominal m…
Archetypal analysis is an exploratory tool that explains a set of observations as mixtures of pure (extreme) patterns. If the patterns are actual observations of the sample, we refer to them as archetypoids. For the first time, we propose…
Archetypal analysis represents a set of observations as convex combinations of pure patterns, or archetypes. The original geometric formulation of finding archetypes by approximating the convex hull of the observations assumes them to be…
Archetypal analysis approximates data by means of mixtures of actual extreme cases (archetypoids) or archetypes, which are a convex combination of cases in the data set. Archetypes lie on the boundary of the convex hull. This makes the…
Archetypal analysis represents each individual member of a set of data vectors as a mixture (a constrained linear combination) of the pure types or archetypes of the data set. The archetypes are themselves required to be mixtures of the…
Archetypal analysis is a data decomposition method that describes each observation in a dataset as a convex combination of "pure types" or archetypes. These archetypes represent extrema of a data space in which there is a trade-off between…
Archetypal analysis is an unsupervised learning method that uses a convex polytope to summarize multivariate data. For fixed $k$, the method finds a convex polytope with $k$ vertices, called archetype points, such that the polytope is…
Archetype and archetypoid analysis can be extended to functional data. Each function is represented as a mixture of actual observations (functional archetypoids) or functional archetypes, which are a mixture of observations in the data set.…
We introduce a novel exploratory technique, termed biarchetype analysis, which extends archetype analysis to simultaneously identify archetypes of both observations and features. This innovative unsupervised machine learning tool aims to…
Archetypes are typical population representatives in an extremal sense, where typicality is understood as the most extreme manifestation of a trait or feature. In linear feature space, archetypes approximate the data convex hull allowing…
"Deep Archetypal Analysis" generates latent representations of high-dimensional datasets in terms of fractions of intuitively understandable basic entities called archetypes. The proposed method is an extension of linear "Archetypal…
Prototypal analysis is introduced to overcome two shortcomings of archetypal analysis: its sensitivity to outliers and its non-locality, which reduces its applicability as a learning tool. Same as archetypal analysis, prototypal analysis…
Archetypal analysis (AA) is a matrix decomposition method that identifies distinct patterns using convex combinations of the data points denoted archetypes with each data point in turn reconstructed as convex combinations of the archetypes.…
Archetypal analysis is a matrix factorization method with convexity constraints. Due to local minima, a good initialization is essential, but frequently used initialization methods yield either sub-optimal starting points or are prone to…
The study of neural computation aims to understand the function of a neural system as an information processing machine. Neural systems are undoubtedly complex, necessitating principled and automated tools to abstract away details to…
We revisit a pioneer unsupervised learning technique called archetypal analysis, which is related to successful data analysis methods such as sparse coding and non-negative matrix factorization. Since it was proposed, archetypal analysis…
Archetypal analysis and non-negative matrix factorization (NMF) are staples in a statisticians toolbox for dimension reduction and exploratory data analysis. We describe a geometric approach to both NMF and archetypal analysis by…
The use of a hypothetical generative model was been suggested for causal analysis of observational data. The very assumption of a particular model is a commitment to a certain set of variables and therefore to a certain set of possible…
Groups -- such as clusters of points or communities of nodes -- are fundamental when addressing various data mining tasks. In temporal data, the predominant approach for characterizing group evolution has been through the identification of…
This contribution proposes a new approach towards developing a class of probabilistic methods for classifying attributed graphs. The key concept is random attributed graph, which is defined as an attributed graph whose nodes and edges are…
In this paper, we introduce an unsupervised learning approach to automatically discover, summarize, and manipulate artistic styles from large collections of paintings. Our method is based on archetypal analysis, which is an unsupervised…