Many datasets can be viewed as a noisy sampling of an underlying space, and tools from topological data analysis can characterize this structure for the purpose of knowledge discovery. One such tool is persistent homology, which provides a multiscale description of the homological features within a dataset. A useful representation of this homological information is a persistence diagram (PD). Efforts have been made to map PDs into spaces with additional structure valuable to machine learning tasks. We convert a PD to a finite-dimensional vector representation which we call a persistence image (PI), and prove the stability of this transformation with respect to small perturbations in the inputs. The discriminatory power of PIs is compared against existing methods, showing significant performance gains. We explore the use of PIs with vector-based machine learning tools, such as linear sparse support vector machines, which identify features containing discriminating topological information. Finally, high accuracy inference of parameter values from the dynamic output of a discrete dynamical system (the linked twist map) and a partial differential equation (the anisotropic Kuramoto-Sivashinsky equation) provide a novel application of the discriminatory power of PIs.

The early identification of toxic paraquat (PQ) poisoning in patients critical to ensure timely and accurate prognosis. Though plasma PQ concentration has been reported as a clinical indicator of PQ poisoning, it is not commonly applied in practice due to the inconvenient necessary instruments and operation. In this study, we explored the use of blood routine indexes to identify the degree of PQ toxicity and/or diagnose PQ poisoning in patients via machine learning approach. Specifically, we developed a method based on support vector machine combined with the feature selection technique to accurately predict PQ poisoning risk status, then tested the method on 79 (42 male and 37 female; 41 living and 38 deceased) patients. The detection method was rigorously evaluated against a real-world dataset to determine its accuracy, sensitivity and specificity. Feature selection was also applied to identify factors correlated with risk status, and results showed that there are significant differences in blood routine indexes between dead and living PQ-poisoned individuals (p-value 0.01).

Celestion loudspeakers have powered the performances of many noted guitar and bass players, including legends such as Jimi Hendrix. Deciding whether a loudspeaker is good enough for professional musicians is a lengthy and painstaking process. Each speaker has its own unique sound based on a combination of sonic characteristics, such as midrange character and brightness. Evaluating a musical instrument loudspeaker involves subjective judgement about whether it generates a "good" sound. Only engineers with years of experience can reliably make that decision, and then only after repeated listening to a single loudspeaker and comparing the sounds it produces with those produced by a reference speaker.

The story starts in Paris in 1989, when I benchmarked neural networks against kernel methods, but the real invention of SVMs happened when Bernhard decided to implement Vladimir Vapnik algorithm.

There is a widespread need for effective forecasting of financial risk using readily available financial measures, but the complicated environment facing financial practitioners and business institutions makes this very challenging. The concept of financial volatility, a required parameter for pricing many kinds of financial assets and derivatives, is critical, because it is widely expected that financial volatility implies financial risk. Therefore, accurate prediction of financial volatility is extremely important. Efficient prediction of financial volatility has been an extremely difficult task, but we can now offer a scalable and customizable mathematical model to achieve this goal, employing two approaches to forecast the volatility using financial information available online. First, we carry out a comparative study between two different machine-learning techniques -- artificial neural networks (ANN) and support vector machines (SVM) -- to forecast trading volume volatility.

The use of MRI as a diagnostic tool for mental disorders has been a consistent goal of neuroimaging research. Despite this, the vast majority of prior work is descriptive rather than predictive. The current study examines the utility of applying support vector machine (SVM) learning to MRI measures of brain white matter in order to classify individuals with major depressive disorder (MDD). In a precisely matched group of individuals with MDD (n 25) and healthy controls (n 25), SVM learning accurately (70%) classified patients and controls across an unselected brain map of white matter fractional anisotropy values (FA). Using a feature selection approach, where maximal discriminative voxels were selected, classification accuracy increased to over 90%.

We are interested in estimating individual labels given only coarse, aggregated signal over the data points. In our setting, we receive sets ("bags") of unlabeled instances with constraints on label proportions. We relax the unrealistic assumption of known label proportions, made in previous work; instead, we assume only to have upper and lower bounds, and constraints on bag differences. We motivate the problem, propose an intuitive formulation and algorithm, and apply our methods to real-world scenarios. Across several domains, we show how using only proportion constraints and no labeled examples, we can achieve surprisingly high accuracy. In particular, we demonstrate how to predict income level using rough stereotypes and how to perform sentiment analysis using very little information. We also apply our method to guide exploratory analysis, recovering geographical differences in twitter dialect.

We propose a general model explanation system (MES) for "explaining" the output of black box classifiers. This paper describes extensions to Turner (2015), which is referred to frequently in the text. We use the motivating example of a classifier trained to detect fraud in a credit card transaction history. The key aspect is that we provide explanations applicable to a single prediction, rather than provide an interpretable set of parameters. We focus on explaining positive predictions (alerts). However, the presented methodology is symmetrically applicable to negative predictions.

Motivated by big data applications, first-order methods have been extremely popular in recent years. However, naive gradient methods generally converge slowly. Hence, much efforts have been made to accelerate various first-order methods. This paper proposes two accelerated methods towards solving structured linearly constrained convex programming, for which we assume composite convex objective. The first method is the accelerated linearized augmented Lagrangian method (LALM). At each update to the primal variable, it allows linearization to the differentiable function and also the augmented term, and thus it enables easy subproblems. Assuming merely weak convexity, we show that LALM owns $O(1/t)$ convergence if parameters are kept fixed during all the iterations and can be accelerated to $O(1/t^2)$ if the parameters are adapted, where $t$ is the number of total iterations. The second method is the accelerated linearized alternating direction method of multipliers (LADMM). In addition to the composite convexity, it further assumes two-block structure on the objective. Different from classic ADMM, our method allows linearization to the objective and also augmented term to make the update simple. Assuming strong convexity on one block variable, we show that LADMM also enjoys $O(1/t^2)$ convergence with adaptive parameters. This result is a significant improvement over that in [Goldstein et. al, SIIMS'14], which requires strong convexity on both block variables and no linearization to the objective or augmented term. Numerical experiments are performed on quadratic programming, image denoising, and support vector machine. The proposed accelerated methods are compared to nonaccelerated ones and also existing accelerated methods. The results demonstrate the validness of acceleration and superior performance of the proposed methods over existing ones.

Currently, more than 30 million people in the world have speech impairments and thus to communicate have to use sign language resulting in a language barrier between sign language and non-sign language users. This project explores the development of a sign language to speech translation glove by implementing a Support Vector Machine(SVM) on the Intel Edison to recognize various letters signed by sign language users. The data for the predicted signed gesture is then transmitted to an Android application where it is vocalized. The sign language glove has five flex sensors mounted on each finger to quantify how much a finger is bent. Flex sensors are sensors that change their resistance depending on the amount of bend on the sensor.