Dr. Alenka Trpin has recently obtained her PhD theses with title “Learning with hyperbolic metric in machine learning algorithms for application in oncology”. The dissertation introduces a novel image classification methodology, meticulously developed and empirically evaluated, that significantly enhances accuracy, particularly within the challenging domain of cancer image analysis. At its core, the approach synergistically combines Convolutional Neural Networks (CNNs), Large Margin Nearest Neighbors (LMNN), and k-Nearest Neighbors (kNN) algorithms, leveraging the unique strengths of each component.
The process begins with CNNs, which serve as feature extractors, transforming raw image data into meaningful attribute vectors. These vectors are then strategically embedded within a hyperbolic space, specifically the Poincaré ball. This embedding process ingeniously utilizes the geometric properties of the hyperbolic space: clear, low-noise images are positioned closer to the ball’s edge, while noisier, more complex images reside near the center. This spatial arrangement inherently reflects the image’s clarity and complexity, facilitating more accurate classification.
Subsequently, the LMNN method is applied to refine the embedded feature space. This metric learning technique effectively pulls similar data points closer together while pushing dissimilar points further apart, enhancing the discriminative power of the feature representation. Finally, the kNN algorithm performs the classification, utilizing both the traditional Euclidean metric and the Poincaré metric, which is particularly suited for hyperbolic spaces.
The empirical evaluation of this methodology yielded remarkable results. Notably, the ChkNN+LMNN+PM variant achieved perfect 100% accuracy on breast cancer images and 98.80% accuracy on skin melanoma images, demonstrating its exceptional performance on these balanced datasets. Furthermore, derived methods such as ChkNN+LMNN, GkNN+LMNN+PM, and RkNN+LMNN+PM exhibited superior accuracy on various cancer image datasets, including brain tumors, cervical cancer, and lung cancer, surpassing existing classification techniques.
Beyond cancer images, the dissertation explored the method’s applicability to other image and numerical datasets. The results indicated that the method’s performance depends on dataset characteristics, the number of nearest neighbours, and data balance. However, the proposed method consistently outperformed baseline methods on benchmark image datasets like Face and Digits, and on most numerical datasets, with the exceptions of datasets Cancer and Letter.
A key aspect of the research involved investigating the impact of modifying the norm within the Poincaré metric in the kNN classifier. The empirical findings revealed that adjusting the p parameter, which controls the norm, significantly affects classification accuracy. Specifically, higher p values often improved accuracy compared to the baseline p=2.
Furthermore, the study examined the influence of the attribute extractor’s architectural depth. It was observed that the accuracy of the kNN method is indeed influenced by the number of layers in the CNN. In addition to the proposed method, established deep learning architectures like ResNet (18 layers) and GoogLeNet (22 layers) also demonstrated strong performance on cancer image datasets.
When compared to traditional classification techniques such as traditional kNN, Support Vector Machines (SVM), Random Forests (RF), and Decision Trees (DT), the proposed hyperbolic embedding and classification approach yielded comparable or superior results. Notably, the method proved particularly effective for SVM classification on benchmark image datasets with distinct structural features, such as numbers and letters, and also demonstrated enhanced performance on numerical datasets compared to traditional classifiers.
Looking towards future research, the dissertation proposes several promising directions. Firstly, the methodology nas to be applied to real-world datasets, enabling a direct comparison with conventional clinical approaches and validating the method’s robustness and reliability in practical settings.
Secondly, the method’s flexibility opens up applications in diverse domains such as mechanical engineering (e.g., autonomous vehicles, turbomachinery analysis) and chemistry (e.g., atomic simulations). Exploring these diverse datasets will further demonstrate the method’s adaptability and broaden its impact.
Thirdly, a deeper mathematical and geometric analysis of the variations in the norm within the Poincaré metric will be conducted to optimise metric designs and improve model effectiveness.
Fourthly, the impact of hyperbolic embeddings on clustering algorithms like k-means will be investigated, assessing the method’s potential for unlabelled data analysis.
Finally, the influence of different CNN architectural configurations, notably the optimal number of layers and filters, will be explored to enhance the efficiency and accuracy of the classification process. The dissertation presents a robust and effective image classification methodology that leverages the strengths of CNNs, hyperbolic geometry, and metric learning. The empirical results demonstrate its superior performance, particularly in cancer image analysis, and its potential for broader applications across various domains. Continued research and refinement of this methodology promise to significantly advance the field of image classification, leading to more accurate diagnoses and improved outcomes.
