Statistically-Robust Clustering Techniques for Mapping Spatial Hotspots: A Survey

Xie, Yiqun; Shekhar, Shashi; Li, Yan

doi:10.1145/3487893

Cited by 25 publications

(7 citation statements)

References 200 publications

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“…Possible examples include the famous Watershed segmentation algorithm (see later for a brief description), k-means clustering or more recent AI-based techniques. Xie et al [26] provide a comprehensive review on spatial hot-spot detection methodology.…”

Section: Hybridizationmentioning

confidence: 99%

Toward quantitative super-resolution microscopy: molecular maps with statistical guarantees

Proksch,

Werner,

Keller–Findeisen

et al. 2023

Microscopy

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Quantifying the number of molecules from fluorescence microscopy measurements is an important topic in cell biology and medical research. In this work, we present a consecutive algorithm for super-resolution (stimulated emission depletion (STED)) scanning microscopy that provides molecule counts in automatically generated image segments and offers statistical guarantees in form of asymptotic confidence intervals. To this end, we first apply a multiscale scanning procedure on STED microscopy measurements of the sample to obtain a system of significant regions, each of which contains at least one molecule with prescribed uniform probability. This system of regions will typically be highly redundant and consists of rectangular building blocks. To choose an informative but non-redundant subset of more naturally shaped regions, we hybridize our system with the result of a generic segmentation algorithm. The diameter of the segments can be of the order of the resolution of the microscope. Using multiple photon coincidence measurements of the same sample in confocal mode, we are then able to estimate the brightness and number of molecules and give uniform confidence intervals on the molecule counts for each previously constructed segment. In other words, we establish a so-called molecular map with uniform error control. The performance of the algorithm is investigated on simulated and real data.

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Section: Hybridizationmentioning

confidence: 99%

Toward quantitative super-resolution microscopy: molecular maps with statistical guarantees

Proksch,

Werner,

Keller–Findeisen

et al. 2023

Microscopy

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“…FNO and implicit neural representation [25] can be used to downsample data to an arbitrary resolution after they are trained on a specific spatial resolution. Existing works on building heterogeneity-aware models over a large number of different locations can also be viewed as simplified foundation models that are specifically designed for spatial generalization [85,94,169]. For example, Xie et al [169] create a general pipeline for transforming deep learning models to predict land covers for locations with statistically different distributions.…”

Section: Foundation Models In Environmental Sciencementioning

confidence: 99%

“…Existing works on building heterogeneity-aware models over a large number of different locations can also be viewed as simplified foundation models that are specifically designed for spatial generalization [85,94,169]. For example, Xie et al [169] create a general pipeline for transforming deep learning models to predict land covers for locations with statistically different distributions. These models could be further extended to address the problems of different spatial scales.…”

Section: Foundation Models In Environmental Sciencementioning

confidence: 99%

Knowledge-Guided Machine Learning

Karpatne¹,

Kannan²,

Kumar³

2022

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This paper presents an overview of scientific modeling and discusses the complementary strengths and weaknesses of ML methods for scientific modeling in comparison to process-based models. It also provides an introduction to the current state of research in the emerging field of scientific knowledge-guided machine learning (KGML) that aims to use both scientific knowledge and data in ML frameworks to achieve better generalizability, scientific consistency, and explainability of results. We discuss different facets of KGML research in terms of the type of scientific knowledge used, the form of knowledge-ML integration explored, and the method for incorporating scientific knowledge in ML. We also discuss some of the common categories of use cases in environmental sciences where KGML methods are being developed, using illustrative examples in each category.

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“…Many studies of clustering [1,3,5,6,20,22,23] are concerned with noise robustness or poisoning attacks (e.g., [13]), and demonstrate how sensitive the algorithm may become upon insertion of (even a few) adversarial examples. Our work extends these thoughts to not only poisoning the input to the algorithm, but also its configuration by replacing the distance functions a posteriori to justify some (desired) behavior.…”

Section: Related Workmentioning

confidence: 99%

Metricizing the Euclidean Space towards Desired Distance Relations in Point Clouds

Raß¹,

König²,

Ahmad³

et al. 2022

Preprint

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Given a set of points in the Euclidean space R with > 1, the pairwise distances between the points are determined by their spatial location and the metric d that we endow R with. Hence, the distance d(x, y) = δ between two points is fixed by the choice of x and y and d. We study the related problem of fixing the value δ, and the points x, y, and ask if there is a topological metric d that computes the desired distance δ. We demonstrate this problem to be solvable by constructing a metric to simultaneously give desired pairwise distances between up to O( √ ) many points in R . In particular, these distances can be chosen independent of any "natural" distance between the given points, such as Euclidean or others. Towards dropping the limit on how many points (at fixed locations) we can put into desired distance from one another, we then introduce the notion of an ε-semimetric d. This function has all properties of a metric, but allows violations of the triangle inequality up to an additive error < ε. With this (mild) generalization of a topological metric, we formulate our main result: for all ε > 0, for all m ≥ 1, for any choice of m points y1, . . . , ym ∈ R , and all chosen sets of values {δij ≥ 0 : 1 ≤ i < j ≤ m}, there exists an ε-semimetric δ : R ×R → R such that d(yi, yj) = δij, i.e., the desired distances are accomplished, irrespectively of the topology that the Euclidean or other norms would induce. The order of quantifiers is important here: we first can choose the accuracy ε by which our semi-metric may be violate the triangle inequality (while leaving the other metric axioms to hold as usual for d), then fix the spatial locations of points, and after that step, choose the distances that we wish between our points. We showcase our results by using them to "attack" unsupervised learning algorithms, specifically k-Means and density-based (DBSCAN) clustering algorithms. These have manifold applications in artificial intelligence, and letting them run with externally provided distance measures constructed in the way as shown here, can make clustering algorithms produce results that are pre-determined and hence malleable. This demonstrates that the

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Statistically-Robust Clustering Techniques for Mapping Spatial Hotspots: A Survey

Cited by 25 publications

References 200 publications

Toward quantitative super-resolution microscopy: molecular maps with statistical guarantees

Toward quantitative super-resolution microscopy: molecular maps with statistical guarantees

Knowledge-Guided Machine Learning

Metricizing the Euclidean Space towards Desired Distance Relations in Point Clouds

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