High-veracity functional imaging in scanning probe microscopy via Graph-Bootstrapping

Abstract

The key objective of scanning probe microscopy (SPM) techniques is the optimal representation of the nanoscale surface structure and functionality inferred from the dynamics of the cantilever. This is particularly pertinent today, as the SPM community has seen a rapidly growing trend towards simultaneous capture of multiple imaging channels and complex modes of operation involving high-dimensional information-rich datasets, bringing forward the challenges of visualization and analysis, particularly for cases where the underlying dynamic model is poorly understood. To meet this challenge, we present a data-driven approach, Graph-Bootstrapping, based on low-dimensional manifold learning of the full SPM spectra and demonstrate its successes for high-veracity mechanical mapping on a mixed polymer thin film and resolving irregular hydration structure of calcite at atomic resolution. Using the proposed methodology, we can efficiently reveal and hierarchically represent salient material features with rich local details, further enabling denoising, classification, and high-resolution functional imaging.

Manifold learning of four-dimensional scanning transmission electron microscopy

“…The primary tuning parameter of HDBSCAN is the minimum cluster size k. We follow a similar procedure in Ref 29 to choose k. We first consider all integer k values in the range [20,149]. In supplementary Figure 2, we then plot the trend of total number of estimated clusters against every k value and fit this trend by the exponential decay.…”

Distilling Nanoscale Heterogeneity of Amorphous Silicon using Tip-enhanced Raman Spectroscopy (TERS) via Multiresolution Manifold Learning

“…Clustering can be subsequently performed on the lowdimensional manifold to underpin the intrinsic structure within the manifold that corresponds to the material structure heterogeneity. To better partition intrinsic manifold clusters (facilitating clustering tasks), Li et al recently proposed a Graph-Bootstrapping procedure 25,26 that iteratively reconstructed the NN graph based on previous manifold positions and then recalculated manifold coordinates based on the reconstructed NN graph. The projected low dimensional manifold clusters represent featured spectral property of the materials, thereby allowing for gaining insights of latent material structures via external validations such as rst principle theories.…”

“…Low-dimensional manifold embedding for TERS measurements is calculated via a modi ed Graph-Bootstrapping approach. 25,26 Graph-Bootstrapping is an iterative procedure that consists of two main steps: construction of nearest neighbor graph and manifold layout of nearest neighbor graph. During the initialization (iteration 0) of Graph-Bootstrapping, a nearest neighbor graph is calculated based on the high-dimensional TERS measurements, which we call this graph as root graph.…”

“…Unlike traditional manifold learning methods targeting solely on overlaying the prior-known labels over the manifold points, 24 the MML proposed here does not require any prior bias regarding the material structure and instrumental modality. 25,26 Bene ting from this nature, the underlying a-Si structural and physical properties, such as the average Si-Si distortion angle and the strain free energy can be quanti ed without a human-speci ed threshold at a lateral spatial resolution of 20 nm. Further, the multiresolution feature of the MML algorithm allows for extracting child clusters at the ner resolution grid, which carries structural characteristics of minor abundance (< 0.3% of the sampling points) that would have been hidden in the large dataset.…”

A machine perspective of atomic defects in scanning transmission electron microscopy

“…Manifold learning has been applied in many fields including text mining, social network visualization, and so on. In the domain of microscopy imaging, Li et al reported functional imaging and mapping of AFM images and 4D‐STEM data based on manifold learning, and 10 types of Ronchigrams from experimental 4D‐STEM data of monolayer graphene doped with Si were identified. The clusters in the low dimensional space exhibit improved separability after a graph‐bootstrapping process .…”