When applying eigenvalue decomposition on the quadratic term matrix in a type of linear equally constrained quadratic programming (EQP), there exists a linear mapping to project optimal solutions between the new EQP formulation where $Q$ is diagonalized and the original formulation. Although such a mapping requires a particular type of equality constraints, it is generalizable to some real problems such as efficient frontier for portfolio allocation and classification of Least Square Support Vector Machines (LSSVM). The established mapping could be potentially useful to explore optimal solutions in subspace, but it is not very clear to the author. This work was inspired by similar work proved on unconstrained formulation discussed earlier in \cite{Tan}, but its current proof is much improved and generalized. To the author's knowledge, very few similar discussion appears in literature.

Patients who undergo mechanical heart valve replacements or have conditions like Atrial Fibrillation have to take Vitamin K Antagonists (VKA) drugs to prevent coagulation of blood. These drugs have narrow therapeutic range and need to be very closely monitored due to life threatening side effects. The dosage of VKA drug is determined and revised by a physician based on Prothrombin Time - International Normalised Ratio (PT-INR) value obtained through a blood test. Our work aimed at predicting the maintenance dosage of warfarin, the present most widely recommended anticoagulant drug, using the de-identified medical data collected from 109 patients from Kerala. A Support Vector Machine (SVM) Regression model was built to predict the maintenance dosage of warfarin, for patients who have been undergoing treatment from a physician and have reached stable INR values between 2.0 and 4.0.

Multi-class classification with a very large number of classes, or extreme classification, is a challenging problem from both statistical and computational perspectives. Most of the classical approaches to multi-class classification, including one-vs-rest or multi-class support vector machines, require the exact estimation of the classifier's margin, at both the training and the prediction steps making them intractable in extreme classification scenarios. In this paper, we study the impact of computing an approximate margin using nearest neighbor (ANN) search structures combined with locality-sensitive hashing (LSH). This approximation allows to dramatically reduce both the training and the prediction time without a significant loss in performance. We theoretically prove that this approximation does not lead to a significant loss of the risk of the model and provide empirical evidence over five publicly available large scale datasets, showing that the proposed approach is highly competitive with respect to state-of-the-art approaches on time, memory and performance measures.

Not all classification predictive models support multi-class classification. Algorithms such as the Perceptron, Logistic Regression, and Support Vector Machines were designed for binary classification and do not natively support classification tasks with more than two classes. One approach for using binary classification algorithms for multi-classification problems is to split the multi-class classification dataset into multiple binary classification datasets and fit a binary classification model on each. Two different examples of this approach are the One-vs-Rest and One-vs-One strategies. In this tutorial, you will discover One-vs-Rest and One-vs-One strategies for multi-class classification.

Scenario optimization is by now a well established technique to perform designs in the presence of uncertainty. It relies on domain knowledge integrated with first-hand information that comes from data and generates solutions that are also accompanied by precise statements of reliability. In this paper, following recent developments in (Garatti and Campi, 2019), we venture beyond the traditional set-up of scenario optimization by analyzing the concept of constraints relaxation. By a solid theoretical underpinning, this new paradigm furnishes fundamental tools to perform designs that meet a proper compromise between robustness and performance. After suitably expanding the scope of constraints relaxation as proposed in (Garatti and Campi, 2019), we focus on various classical Support Vector methods in machine learning - including SVM (Support Vector Machine), SVR (Support Vector Regression) and SVDD (Support Vector Data Description) - and derive new results for the ability of these methods to generalize.

Local learning methods are a popular class of machine learning algorithms. The basic idea for the entire cadre is to choose some non-local model family, to train many of them on small sections of neighboring data, and then to `stitch' the resulting models together in some way. Due to the limits of constraining a training dataset to a small neighborhood, research on locally-learned models has largely been restricted to simple model families. Also, since simple model families have no complex structure by design, this has limited use of the individual local models to predictive tasks. We hypothesize that, using a sufficiently complex local model family, various properties of the individual local models, such as their learned parameters, can be used as features for further learning. This dissertation improves upon the current state of research and works toward establishing this hypothesis by investigating algorithms for localization of more complex model families and by studying their applications beyond predictions as a feature extraction mechanism. We summarize this generic technique of using local models as a feature extraction step with the term ``local model feature transformations.'' In this document, we extend the local modeling paradigm to Gaussian processes, orthogonal quadric models and word embedding models, and extend the existing theory for localized linear classifiers. We then demonstrate applications of local model feature transformations to epileptic event classification from EEG readings, activity monitoring via chest accelerometry, 3D surface reconstruction, 3D point cloud segmentation, handwritten digit classification and event detection from Twitter feeds.

Multi-label learning has attracted the attention of the machine learning community. The problem conversion method Binary Relevance converts a familiar single label into a multi-label algorithm. The binary relevance method is widely used because of its simple structure and efficient algorithm. But binary relevance does not consider the links between labels, making it cumbersome to handle some tasks. This paper proposes a multi-label learning algorithm that can also be used for single-label classification. It is based on standard support vector machines and changes the original single decision hyperplane into two parallel decision hyper-planes, which call multi-label parallel support vector machine (MLPSVM). At the end of the article, MLPSVM is compared with other multi-label learning algorithms. The experimental results show that the algorithm performs well on data sets.

The transcriptomics of cancer tumors are characterized with tens of thousands of gene expression features. Patient prognosis or tumor stage can be assessed by machine learning techniques like supervised classification tasks given a gene expression profile. Feature selection is a useful approach to select the key genes which helps to classify tumors. In this work we propose a feature selection method based on Multiple Kernel Learning that results in a reduced subset of genes and a custom kernel that improves the classification performance when used in support vector classification. During the feature selection process this method performs a novel latent regularisation by relaxing the supervised target problem by introducing unsupervised structure obtained from the latent space learned by a non linear dimensionality reduction model. An improvement of the generalization capacity is obtained and assessed by the tumor classification performance on new unseen test samples when the classifier is trained with the features selected by the proposed method in comparison with other supervised feature selection approaches.

In this paper, we propose a Doppler-spectrum feature-based human–vehicle classification scheme for an FMCW (frequency-modulated continuous wave) radar sensor. We introduce three novel features referred to as the scattering point count, scattering point difference, and magnitude difference rate features based on the characteristics of the Doppler spectrum in two successive frames. We also use an SVM (support vector machine) and BDT (binary decision tree) for training and validation of the three aforementioned features. We measured the signals using a 24-GHz FMCW radar front-end module and a real-time data acquisition module and extracted three features from a walking human and a moving vehicle in the field. We then repeatedly measured the classification decision rate of the proposed algorithm using the SVM and BDT, finding that the average performance exceeded 99% and 96% for the walking human and the moving vehicle, respectively.

The objective of this study is to predict suicidal and non-suicidal deaths from DNA methylation data using a modern machine learning algorithm. We used support vector machines to classify existing secondary data consisting of normalized values of methylated DNA probe intensities from tissues of two cortical brain regions to distinguish suicide cases from control cases. Before classification, we employed Principal component analysis (PCA) and t-distributed Stochastic Neighbor Embedding (t-SNE) to reduce the dimension of the data. In comparison to PCA, the modern data visualization method t-SNE performs better in dimensionality reduction. t-SNE accounts for the possible non-linear patterns in low-dimensional data. We applied four-fold cross-validation in which the resulting output from t-SNE was used as training data for the Support Vector Machine (SVM). Despite the use of cross-validation, the nominally perfect prediction of suicidal deaths for BA11 data suggests possible over-fitting of the model. The study also may have suffered from 'spectrum bias' since the individuals were only studied from two extreme scenarios. This research constitutes a baseline study for classifying suicidal and non-suicidal deaths from DNA methylation data. Future studies with larger sample size, while possibly incorporating methylation data from living individuals, may reduce the bias and improve the accuracy of the results.