Application of persistent homology classification algorithm on MNIST fashion image database.

The classification of data is a crucial machine learning activity. The No Free Lunch Theorems assert that no single algorithm can provide the best results for all classification issues. The persistent homology classification algorithm, or Persistent Homology Classifier (PHC), is a new classification technique based on persistent homology (PH) developed to perform classification tasks involving various datasets, including image datasets. It is a supervised method that utilizes the lifespan of the topological features formed through the filtration process of each point cloud of observations with the same classes. Due to PH's robustness, the insertion of a new observation from the same class will not significantly alter the lifespans of the formed topological features. This was established as the criterion for determining the new observation's class. PHC's performance in categorizing the fashion MNIST image dataset has been compared with that of other well-known classifiers. The feature of each image was extracted using Histogram of Oriented Gradients (HOG) and was reduced using Principal Component Analysis (PCA). The research demonstrates that PHC outperformed classification and regression trees (CART), was comparable to k-nearest neighbors (KNN) and random forests (RF) but underperformed to support vector machines (SVM) and linear discriminant analysis (LDA). Additionally, PHC outperforms RF and CART in terms of accuracy. Moreover, an increase in dataset size indicates a significant improvement in the accuracy of PHC. In general, the study shows that PHC can satisfactorily perform image classification tasks. [ABSTRACT FROM AUTHOR]