Spectral Clustering to Analyze the Hidden Events in Single-Molecule Break Junctions

Abstract

The single-molecule break junction technique provides a high-throughput method to explore the charge transport phenomena through a molecular junction at the ultimate scale of a single molecule. The most probable conductance of a molecular junction is normally extracted from histogram generated from repeated and massive break junction data. However, this conventional data analysis method only exhibits general charge transport properties of molecular junctions, and insightful information hidden in those recorded data remains unexplored. Among them, some of the conductance variations corresponding to different molecular junction conformations that occur during the break junction process might easily be overlooked. To accurately extract those hidden events, here we demonstrated a customized spectral clustering method with the evaluation of the Calinski–Harabasz index, which could be employed to analyze a large amount of data and to automatically extract different molecular junction conformations without subjective bias. Our approach was first validated through simulated data sets and was confirmed to be suitable for the product analysis during a chemical reaction. Moreover, using this method, an easily overlooked but unignorable junction conformation was found during the carborane molecular junction measurement, suggesting that spectral clustering with the Calinski–Harabasz index as a criterion offers a promising algorithm for junction conformation analysis in massive break junction data.

Using Weakly Supervised Deep Learning to Classify and Segment Single‐Molecule Break‐Junction Conductance Traces

“…Here the classification accuracy is defined as the proportion of correctly classified traces in the test set (by comparing the algorithm-generated class label of each conductance trace against its manual label). For comparison, we also apply alternative models to sort the conductance traces in the test set, including five unsupervised methods [tdistributed stochastic neighbor embedding (t-SNE) combined with graph average linkage (GAL), [32][33][34]18] uniform manifold approximation and projection (UMAP) combined with Gaussian mixed model (GMM), [35,36,18] DAK, [11] PCA combined with Kmeans + + [12,13] and spectral clustering [19] ], one supervised method (directly trained CNN) and one semi-supervised method (label propagation [37] ). For the former two unsupervised methods, the cosine (cos.) distance measure approach is used.…”

“…Recently machine learning has been introduced into molecular electronics, [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27] as a powerful tool to analyze break junction data. Supervised and unsupervised learning are the two main classes of machine learning algorithms, their main difference being whether or not a manually labeled training set is needed.…”

“…Supervised and unsupervised learning are the two main classes of machine learning algorithms, their main difference being whether or not a manually labeled training set is needed. Due to limited labor costs and the potential advantage of avoiding predefined bias in solving specific problems, many previous studies prefer unsupervised learning methods, [10][11][12][13][14][15][16][17][18][19][20][21][22] such as multi-parameter vector-based classification (MPVC), [10] deep auto-encoder K-means (DAK), [11] K-means + + , [12] principal component analysis (PCA), [13] Alexnet-enhanced autoencoder [14] and spectral clustering. [19] In general, the conductance traces collected for a certain molecule or different molecules are grouped by their mutual similarities to uncover the underlying features.…”

Grid-Based Correlation Analysis to Identify Rare Quantum Transport Behaviors

“…One strategy for separating qualitatively different behaviors that may overlap in 1D and 2D histograms is to employ clustering. Indeed, over the past five years several clustering approaches have been designed specifically for breaking traces 34,[43][44][45][46][47][48][49][50][51][52][53] and related data, 54,55 and these approaches have had varied success in extracting known and potential features, including "hidden" features, from real and simulated datasets. However, clustering algorithms by definition look for groupings of similar data, and so they will always struggle with truly rare behaviors that may not be common enough to form a clear grouping.…”

The Evolution of the Charge Transport Mechanism in Single‐Molecule Break Junctions Revealed by Flicker Noise Analysis

“…In the past decade, numerous data analysis methods were introduced to process the conductance traces, including statistical methods, [4][5][6][7] analytical modeling, [8,9] electronic noise analysis, [10][11][12][13][14][15] and machine learning and deep learning methods. [16][17][18] Among these methods, analysis of flicker noise from the single-molecule junctions has suggested to shed new light on the understanding of charge transport mechanisms of singlemolecule junctions. [19][20][21][22] The electronic noise of single-molecule junctions can be categorized into highfrequency noise and low-frequency noise, and the latter, including flicker noise and random telegraph signal (RTS) noise (that is 1/f noise and 1/f 2 noise, respectively due to their frequency dependence nature), is the result of rearrangement of metal atom on the electrode surface and the fluctuation of the microenvironment of molecule junctions.…”