  Background: Matrix-assisted laser desorption/ionization mass spectrometry
imaging (MALDI MSI) displays significant potential for applications in cancer
research, especially in tumor typing and subtyping. Lung cancer is the primary
cause of tumor-related deaths, where the most lethal entities are
adenocarcinoma (ADC) and squamous cell carcinoma (SqCC). Distinguishing between
these two common subtypes is crucial for therapy decisions and successful
patient management.
  Results: We propose a new algebraic topological framework, which obtains
intrinsic information from MALDI data and transforms it to reflect topological
persistence. Our framework offers two main advantages. Firstly, topological
persistence aids in distinguishing the signal from noise. Secondly, it
compresses the MALDI data, saving storage space and optimizes computational
time for subsequent classification tasks. We present an algorithm that
efficiently implements our topological framework, relying on a single tuning
parameter. Afterwards, logistic regression and random forest classifiers are
employed on the extracted persistence features, thereby accomplishing an
automated tumor (sub-)typing process. To demonstrate the competitiveness of our
proposed framework, we conduct experiments on a real-world MALDI dataset using
cross-validation. Furthermore, we showcase the effectiveness of the single
denoising parameter by evaluating its performance on synthetic MALDI images
with varying levels of noise.
  Conclusion: Our empirical experiments demonstrate that the proposed algebraic
topological framework successfully captures and leverages the intrinsic
spectral information from MALDI data, leading to competitive results in
classifying lung cancer subtypes. Moreover, the frameworks ability to be
fine-tuned for denoising highlights its versatility and potential for enhancing
data analysis in MALDI applications.
