arXiv subjects

Anyu Zhang

Publications and source records attributed to Anyu Zhang.

4 recordsLinked to original sources

arXiv2022

Cross-View-Prediction: Exploring Contrastive Feature for Hyperspectral Image Classification

This paper presents a self-supervised feature learning method for hyperspectral image classification. Our method tries to construct two different views of the raw hyperspectral image through a cross-representation learning method. And then to learn semantically consistent representation over the created views by contrastive learning method. Specifically, four cross-channel-prediction based augmentation methods are naturally designed to utilize the high dimension characteristic of hyperspectral data for the view construction. And the better representative features are learned by maximizing mutual information and minimizing conditional entropy across different views from our contrastive network. This 'Cross-View-Predicton' style is straightforward and gets the state-of-the-art performance of unsupervised classification with a simple SVM classifier.

cs.CV↗

arXiv2021

Algebraic Model Selection and Experimental Design in Biological Data Science

Design of experiments and model selection, though essential steps in data science, are usually viewed as unrelated processes in the study and analysis of biological networks. Not accounting for their inter-relatedness has the potential to introduce bias and increase the risk of missing salient features in the modeling process. We propose a data-driven computational framework to unify experimental design and model selection for discrete data sets and minimal polynomial models. We use a special affine transformation, called a linear shift, to provide both the data sets and the polynomial terms that form a basis for a model. This framework enables us to address two important questions that arise in biological data science research: finding the data which identify a set of known interactions and finding identifiable interactions given a set of data. We present the theoretical foundation for a web-accessible database. As an example, we apply this methodology to a previously constructed pharmacodynamic model of epidermal derived growth factor receptor (EGFR) signaling.

math.AG↗

arXiv2020

Geometric characterization of data sets with unique reduced Gröbner bases

Model selection based on experimental data is an important challenge in biological data science. Particularly when collecting data is expensive or time consuming, as it is often the case with clinical trial and biomolecular experiments, the problem of selecting information-rich data becomes crucial for creating relevant models. We identify geometric properties of input data that result in a unique algebraic model and we show that if the data form a staircase, or a so-called linear shift of a staircase, the ideal of the points has a unique reduced Gro bner basis and thus corresponds to a unique model. We use linear shifts to partition data into equivalence classes with the same basis. We demonstrate the utility of the results by applying them to a Boolean model of the well-studied lac operon in E. coli.

math.AG↗

arXiv2019

The Number of Gr\"obner Bases in Finite Fields

In the field of algebraic systems biology, the number of minimal polynomial models constructed using discretized data from an underlying system is related to the number of distinct reduced Gr\"obner bases for the ideal of the data points. While the theory of Gr\"obner bases is extensive, what is missing is a closed form for their number for a given ideal. This work contributes connections between the geometry of data points and the number of Gr\"obner bases associated to small data sets. Furthermore we improve an existing upper bound for the number of Gr\"obner bases specialized for data over a finite field.

math.AG↗