## 1 Introduction  
Due to the recent advancements in Computed Tomography (CT) technology, and with more than 57,000 colon cancer deaths per year in the United States, CT Colonography (CTC), also known as virtual colonoscopy, is becoming a promising tool for early diagnosis of colon cancer. CTC is a minimally invasive technique that detects colorectal polyps and masses based on the CT scans of distended colon [1]. One of the major obstacles for CTC to be an effective tool for detecting polyps is that radiologists' expertise is required for analyzing the CTC images, in particular, for the detection of small polyps. Because diagnosis interpretation is a complicated task and any erroneous decision may lead to painful consequences for patients, computer-aided detection (CAD) of polyps would provide clinical decision support systems that benefit patients from correct clinical decisions by reducing the variability of the detection accuracy among radiologists [1]. Such a CAD system typically employs a shape-based method for the initial detection of polyp candidates, followed by a machine learning (ML) method for the classification of polyps from non-polyps (normal colonic structures). The CAD system then generates the final list of polyps that are provided to the radiologist as a \"second opinion\" [2]. Typically, the input to a CAD system is a large number of CT images, ranging from 300 to 3000 images per patient.  
The large amount of data is one of the major obstacles for the ML method in any CAD system to be trained. Moreover, to update the CAD system, the ML method needs to be retrained when new CTC patient image data become available. Therefore, the need to scale up inductive learning algorithms in CAD systems is drastically increasing in order to extract valid and novel patterns from incremental data without a major ML retrain. Dynamic, incremental, or online learning refers, in this context, to the situation where a training image data set is not fully available at the beginning of the learning process. The data can arrive at different time intervals and need to be incorporated into the training data to preserve the class concept. Thus, constructing a ML method capable of incremental classification as opposed to batch-mode learning is very attractive and will become a strategic necessity for CTC because of a few reasons. First, the training period is the most significant resource-intensive element in ML. Second, the CTC data has a continuous, large and unbalanced stream by nature which makes it an ideal candidate for online learning.  
To the best of our knowledge, no prior work has addressed incremental multi-classification of polyps using a support vector machine (SVM) approach within the framework of dynamic learning. The novel method we present in this work is called Weighted Proximal Support Vector Machine (_WP-SVM_) and extends traditional SVM beyond its existing static learning context to handle dynamic and multiple classifications of unbalanced data sets of polyps. The selection of SVM as a machine learning tool for assisting in CTC clinical decisions stems from several of its main advantages: SVM has its roots in statistical learning theory which ensures strong learning and generalization capabilities. It is computationally efficient in learning a hyper-plane that correctly classifies the high dimensional feature space and it is also highly resistant to noisy data [3].  
The remainder of this paper is organized as follows: Section 2 presents an overview of multi-classification Least Square SVM (LS-SVM) principles. Section 3 covers our proposed multi-classification _WP-SVM_ techniques for unbalanced data sets. Section 4 validates the effectiveness of_WP-SVM_ in terms of detection performance, computation time, and storage requirements. Finally, Section 5 concludes this work with remarks and outlines for future research.