ﻻ يوجد ملخص باللغة العربية
A simple and fast analysis method to sort large data sets into groups with shared distinguishing characteristics is described, and applied to single molecular break junction conductance versus electrode displacement data. The method, based on principal component analysis, successfully sorted data sets based on the projection of the data onto the first or second principal component of the correlation matrix without the need to assert any specific hypothesis about the expected features within the data. This was an improvement on the current correlation matrix analysis approach because it sorted data automatically, making it more objective and less time consuming, and our method is applicable to a wide range of multivariate data sets. Here the method was demonstrated on two systems. First, it was demonstrated on mixtures of two molecules with identical anchor groups, similar lengths, but either a $pi$ (high conductance) or $sigma$ (low conductance) bridge. The mixed data was automatically sorted into two groups containing one molecule or the other. Second, it was demonstrated on break junction data measured with the $pi$ bridged molecule alone. Again the method distinguished between two groups. These groups were tentatively assigned to different geometries of the molecule in the junction.
Single-molecule break junction measurements deliver a huge number of conductance vs. electrode separation traces. Along such measurements the target molecules may bind to the electrodes in different geometries, and the evolution and rupture of the si
Cryo-electron microscopy nowadays often requires the analysis of hundreds of thousands of 2D images as large as a few hundred pixels in each direction. Here we introduce an algorithm that efficiently and accurately performs principal component analys
We show how to efficiently project a vector onto the top principal components of a matrix, without explicitly computing these components. Specifically, we introduce an iterative algorithm that provably computes the projection using few calls to any b
Dimension reduction for high-dimensional compositional data plays an important role in many fields, where the principal component analysis of the basis covariance matrix is of scientific interest. In practice, however, the basis variables are latent
Principal component analysis (PCA) is an important tool in exploring data. The conventional approach to PCA leads to a solution which favours the structures with large variances. This is sensitive to outliers and could obfuscate interesting underlyin