On ill-conceived initialization in archetypal analysis

Suleman, Abdul

doi:10.1007/s11634-017-0303-0

Cited by 3 publications

(3 citation statements)

References 27 publications

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“…Note that AA++ can also be used as an initialization for archetypoid analysis. Suleman (2017) stresses that an improper initialization of archetypal analysis is problematic and that the FurthestSum method is prone to selecting redundant archetypes, especially when having many archetypes. This is contradicted by our experiments, which show that FurthestSum's problem is rather the poor choice of boundary points.…”

Section: Related Workmentioning

confidence: 99%

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Archetypal Analysis++: Rethinking the Initialization Strategy

Mair¹,

Sjölund²

2023

Preprint

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Archetypal analysis is a matrix factorization method with convexity constraints. Due to local minima, a good initialization is essential. Frequently used initialization methods yield either suboptimal starting points or are prone to get stuck in poor local minima. In this paper, we propose archetypal analysis++ (AA++), a probabilistic initialization strategy for archetypal analysis that sequentially samples points based on their in uence on the objective, similar to -means++. In fact, we argue that -means++ already approximates the proposed initialization method. Furthermore, we suggest to adapt an e cient Monte Carlo approximation of -means++ to AA++. In an extensive empirical evaluation of 13 real-world data sets of varying sizes and dimensionalities and considering two pre-processing strategies, we show that AA++ almost consistently outperforms all baselines, including the most frequently used ones.

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Section: Related Workmentioning

confidence: 99%

“…Despite its popularity, FurthestSum has also been criticized. For example, Suleman (2017) states that FurthestSum is prone to selecting redundant archetypes, primarily when many archetypes are used. Redundant archetypes lie in the convex hull of the already selected archetypes and thus do not lower the overall error.…”

Section: Introductionmentioning

confidence: 99%

Archetypal Analysis++: Rethinking the Initialization Strategy

Mair¹,

Sjölund²

2023

Preprint

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“…Therefore a balance has to be struck between AA cardinality and representation of extremes conditions in the original data set. To avoid the pitfalls of archetype redundancy mentioned by Suleman (2017a) for example, several initialisation procedures, dimension reduction truncation and aggregation levels have to be tested for a number of archetype orders and the results compared (Bauckhage and Thurau 2009;Suleman 2017b).…”

Section: B Archetype Cardinalitymentioning

confidence: 99%

Archetypal Analysis of Geophysical Data Illustrated by Sea Surface Temperature

Black

Monselesan

Risbey

et al. 2022

Artificial Intelligence for the Earth Systems

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The ability to find and recognize patterns in high-dimensional geophysical data is fundamental to climate science and critical for meaningful interpretation of weather and climate processes. Archetypal analysis (AA) is one technique that has recently gained traction in the geophysical science community for its ability to find patterns based on extreme conditions. While traditional empirical orthogonal function (EOF) analysis can reveal patterns based on data covariance, AA seeks patterns from the points located at the edges of the data distribution. The utility of any objective pattern method depends on the properties of the data to which it is applied and the choices made in implementing the method. Given the relative novelty of the application of AA in geophysics it is important to develop experience in applying the method. We provide an assessment of the method, implementation, sensitivity, and interpretation of AA with respect to geophysical data. As an example for demonstration, we apply AA to a 39-year sea surface temperature (SST) reanalysis data set. We show that the decisions made to implement AA can significantly affect the interpretation of results, but also, in the case of SST, that the analysis is exceptionally robust under both spatial and temporal coarse-graining.

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A Review on Initialization Methods for Nonnegative Matrix Factorization: Towards Omics Data Experiments

Esposito

2021

Mathematics

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Nonnegative Matrix Factorization (NMF) has acquired a relevant role in the panorama of knowledge extraction, thanks to the peculiarity that non-negativity applies to both bases and weights, which allows meaningful interpretations and is consistent with the natural human part-based learning process. Nevertheless, most NMF algorithms are iterative, so initialization methods affect convergence behaviour, the quality of the final solution, and NMF performance in terms of the residual of the cost function. Studies on the impact of NMF initialization techniques have been conducted for text or image datasets, but very few considerations can be found in the literature when biological datasets are studied, even though NMFs have largely demonstrated their usefulness in better understanding biological mechanisms with omic datasets. This paper aims to present the state-of-the-art on NMF initialization schemes along with some initial considerations on the impact of initialization methods when microarrays (a simple instance of omic data) are evaluated with NMF mechanisms. Using a series of measures to qualitatively examine the biological information extracted by a given NMF scheme, it preliminary appears that some information (e.g., represented by genes) can be extracted regardless of the initialization scheme used.

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On ill-conceived initialization in archetypal analysis

Cited by 3 publications

References 27 publications

Archetypal Analysis++: Rethinking the Initialization Strategy

Archetypal Analysis++: Rethinking the Initialization Strategy

Archetypal Analysis of Geophysical Data Illustrated by Sea Surface Temperature

A Review on Initialization Methods for Nonnegative Matrix Factorization: Towards Omics Data Experiments

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