Supervised classification and mathematical optimization

Data Mining techniques often ask for the resolution of optimization problems. Supervised Classification, and, in particular, Support Vector Machines, can be seen as a paradigmatic instance. In this paper, some links between Mathematical Optimization methods and Supervised Classification are emphasized. It is shown that many different areas of Mathematical Optimization play a central role in off-the-shelf Supervised Classification methods. Moreover, Mathematical Optimization turns out to be extremely useful to address important issues in Classification, such as identifying relevant variables, improving the interpretability of classifiers or dealing with vagueness/noise in the data.Ministerio de Ciencia e InnovaciónJunta de Andalucí

Supervised Classification and Mathematical Optimization

Data Mining techniques often ask for the resolution of optimization problems. Supervised Classification, and, in particular, Support Vector Machines, can be seen as a paradigmatic instance. In this paper, some links between Mathematical Optimization methods and Supervised Classification are emphasized. It is shown that many different areas of Mathematical Optimization play a central role in off-the-shelf Supervised Classification methods. Moreover, Mathematical Optimization turns out to be extremely useful to address important issues in Classification, such as identifying relevant variables, improving the interpretability of classifiers or dealing with vagueness/noise in the data

Clustering System and Clustering Support Vector Machine for Local Protein Structure Prediction

Protein tertiary structure plays a very important role in determining its possible functional sites and chemical interactions with other related proteins. Experimental methods to determine protein structure are time consuming and expensive. As a result, the gap between protein sequence and its structure has widened substantially due to the high throughput sequencing techniques. Problems of experimental methods motivate us to develop the computational algorithms for protein structure prediction. In this work, the clustering system is used to predict local protein structure. At first, recurring sequence clusters are explored with an improved K-means clustering algorithm. Carefully constructed sequence clusters are used to predict local protein structure. After obtaining the sequence clusters and motifs, we study how sequence variation for sequence clusters may influence its structural similarity. Analysis of the relationship between sequence variation and structural similarity for sequence clusters shows that sequence clusters with tight sequence variation have high structural similarity and sequence clusters with wide sequence variation have poor structural similarity. Based on above knowledge, the established clustering system is used to predict the tertiary structure for local sequence segments. Test results indicate that highest quality clusters can give highly reliable prediction results and high quality clusters can give reliable prediction results. In order to improve the performance of the clustering system for local protein structure prediction, a novel computational model called Clustering Support Vector Machines (CSVMs) is proposed. In our previous work, the sequence-to-structure relationship with the K-means algorithm has been explored by the conventional K-means algorithm. The K-means clustering algorithm may not capture nonlinear sequence-to-structure relationship effectively. As a result, we consider using Support Vector Machine (SVM) to capture the nonlinear sequence-to-structure relationship. However, SVM is not favorable for huge datasets including millions of samples. Therefore, we propose a novel computational model called CSVMs. Taking advantage of both the theory of granular computing and advanced statistical learning methodology, CSVMs are built specifically for each information granule partitioned intelligently by the clustering algorithm. Compared with the clustering system introduced previously, our experimental results show that accuracy for local structure prediction has been improved noticeably when CSVMs are applied

Iterative regularization in classification via hinge loss diagonal descent

Iterative regularization is a classic idea in regularization theory, that has recently become popular in machine learning. On the one hand, it allows to design efficient algorithms controlling at the same time numerical and statistical accuracy. On the other hand it allows to shed light on the learning curves observed while training neural networks. In this paper, we focus on iterative regularization in the context of classification. After contrasting this setting with that of regression and inverse problems, we develop an iterative regularization approach based on the use of the hinge loss function. More precisely we consider a diagonal approach for a family of algorithms for which we prove convergence as well as rates of convergence. Our approach compares favorably with other alternatives, as confirmed also in numerical simulations