Clustering genotypes based upon their phenotypic characteristics is used to obtain diverse sets of parents that are useful in their breeding programs. The Hierarchical Clustering (HC) algorithm is the current standard in clustering of phenotypic data. This algorithm suffers from low accuracy and high computational complexity issues. To address the accuracy challenge, we propose the use of Spectral Clustering (SC) algorithm. To make the algorithm computationally cheap, we propose using sampling, specifically, Pivotal Sampling that is probability based. Since application of samplings to phenotypic data has not been explored much, for effective comparison, another sampling technique called Vector Quantization (VQ) is adapted for this data as well. VQ has recently given promising results for genome data. The novelty of our SC with Pivotal Sampling algorithm is in constructing the crucial similarity matrix for the clustering algorithm and defining probabilities for the sampling technique. Although our algorithm can be applied to any plant genotypes, we test it on the phenotypic data obtained from about 2400 Soybean genotypes. SC with Pivotal Sampling achieves substantially more accuracy (in terms of Silhouette Values) than all the other proposed competitive clustering with sampling algorithms (i.e. SC with VQ, HC with Pivotal Sampling, and HC with VQ). The complexities of our SC with Pivotal Sampling algorithm and these three variants are almost same because of the involved sampling. In addition to this, SC with Pivotal Sampling outperforms the standard HC algorithm in both accuracy and computational complexity. We experimentally show that we are up to 45% more accurate than HC in terms of clustering accuracy. The computational complexity of our algorithm is more than a magnitude lesser than HC.

Scalable kernel methods, including kernel ridge regression, often rely on low-rank matrix approximations using the Nystrom method, which involves selecting landmark points from large data sets. The existing approaches to selecting landmarks are typically computationally demanding as they require manipulating and performing computations with large matrices in the input or feature space. In this paper, our contribution is twofold. The first contribution is to propose a novel landmark selection method that promotes diversity using an efficient two-step approach. Our landmark selection technique follows a coarse to fine strategy, where the first step computes importance scores with a single pass over the whole data. The second step performs K-means clustering on the constructed coreset to use the obtained centroids as landmarks. Hence, the introduced method provides tunable trade-offs between accuracy and efficiency. Our second contribution is to investigate the performance of several landmark selection techniques using a novel application of kernel methods for predicting structural responses due to earthquake load and material uncertainties. Our experiments exhibit the merits of our proposed landmark selection scheme against baselines.

This is a comprehensive tutorial on using the Spark distributed machine learning framework to build a scalable ML data pipeline. I will cover the basic machine learning algorithms implemented in Spark MLlib library and through this tutorial, I will use the PySpark in python environment. Machine learning is getting popular in solving real-world problems in almost every business domain. It helps solve the problems using the data which is often unstructured, noisy, and in huge size. With the increase in data sizes and various sources of data, solving machine learning problems using standard techniques pose a big challenge.

One of the central goals in precision health is the understanding and interpretation of high-dimensional biological data to identify genes and markers associated with disease initiation, development, and outcomes. Though significant effort has been committed to harness gene expression data for multiple analyses while accounting for time-to-event modeling by including survival times, many traditional analyses have focused separately on non-negative matrix factorization (NMF) of the gene expression data matrix and survival regression with Cox proportional hazards model. In this work, Cox proportional hazards regression is integrated with NMF by imposing survival constraints. This is accomplished by jointly optimizing the Frobenius norm and partial log likelihood for events such as death or relapse. Simulation results on synthetic data demonstrated the superiority of the proposed method, when compared to other algorithms, in finding survival associated gene clusters. In addition, using human cancer gene expression data, the proposed technique can unravel critical clusters of cancer genes. The discovered gene clusters reflect rich biological implications and can help identify survival-related biomarkers. Towards the goal of precision health and cancer treatments, the proposed algorithm can help understand and interpret high-dimensional heterogeneous genomics data with accurate identification of survival-associated gene clusters.

Clustering Algorithms are essential aspects of Data Science and every data scientist must be aware of its concepts. Before discussing the top 5 clustering algorithms, we shall briefly see what clustering is and how it helps in Data Science. Clustering is a Machine Learning technique involving the grouping of data points. It is an unsupervised learning method and a famous technique for statistical data analysis. For a given set of data points, you can use clustering algorithms to classify these into specific groups.

Clustering is part of an unsupervised algorithm in machine learning. Unlike supervised algorithms like linear regression, logistic regression, etc, clustering works with unlabeled data or data without target variables. The task of clustering is to group similar data points. Clustering comes under the data mining topic and there is a lot of research going on in this field and there exist many clustering algorithms. The following are the main types of clustering algorithms.

Clustering is one of the most fundamental tools in the artificial intelligence area, particularly in the pattern recognition and learning theory. In this paper, we propose a simple, but novel approach for variance-based k-clustering tasks, included in which is the widely known k-means clustering. The proposed approach picks a sampling subset from the given dataset and makes decisions based on the data information in the subset only. With certain assumptions, the resulting clustering is provably good to estimate the optimum of the variance-based objective with high probability. Extensive experiments on synthetic datasets and real-world datasets show that to obtain competitive results compared with k-means method (Llyod 1982) and k-means++ method (Arthur and Vassilvitskii 2007), we only need 7% information of the dataset. If we have up to 15% information of the dataset, then our algorithm outperforms both the k-means method and k-means++ method in at least 80% of the clustering tasks, in terms of the quality of clustering. Also, an extended algorithm based on the same idea guarantees a balanced k-clustering result.

Spectral clustering (SC) is one of the most popular clustering methods and often outperforms traditional clustering methods. SC uses the eigenvectors of a Laplacian matrix calculated from a similarity matrix of a dataset. SC has serious drawbacks that are the significant increase in the computational complexity derived from the eigendecomposition and the memory space complexities to store the similarity matrix. To address the issues, I develop a new approximate spectral clustering using the network generated by growing neural gas (GNG), called ASC with GNG in this study. The proposed method uses not only reference vectors for vector quantization but also the topology of the network for extraction of the topological relationship between data points in a dataset. The similarity matrix used by ASC with GNG is made from both the reference vectors and the topology of the network generated by GNG. Using the network generated from a dataset by GNG, we achieve to reduce the computational and space complexities and to improve clustering quality. This paper demonstrates that the proposed method effectively reduces the computational time. Moreover, the results of this study show that the proposed method displays equal to or better performance of clustering than SC.

Dynamical systems arise in a wide variety of mathematical models from science and engineering. A common challenge is to quantify uncertainties on model inputs (parameters) that correspond to a quantitative characterization of uncertainties on observable Quantities of Interest (QoI). To this end, we consider a stochastic inverse problem (SIP) with a solution described by a pullback probability measure. We call this an observation-consistent solution, as its subsequent push-forward through the QoI map matches the observed probability distribution on model outputs. A distinction is made between QoI useful for solving the SIP and arbitrary model output data. In dynamical systems, model output data are often given as a series of state variable responses recorded over a particular time window. Consequently, the dimension of output data can easily exceed $\mathcal{O}(1E4)$ or more due to the frequency of observations, and the correct choice or construction of a QoI from this data is not self-evident. We present a new framework, Learning Uncertain Quantities (LUQ), that facilitates the tractable solution of SIPs for dynamical systems. Given ensembles of predicted (simulated) time series and (noisy) observed data, LUQ provides routines for filtering data, unsupervised learning of the underlying dynamics, classifying observations, and feature extraction to learn the QoI map. Subsequently, time series data are transformed into samples of the underlying predicted and observed distributions associated with the QoI so that solutions to the SIP are computable. Following the introduction and demonstration of LUQ, numerical results from several SIPs are presented for a variety of dynamical systems arising in the life and physical sciences. For scientific reproducibility, we provide links to our Python implementation of LUQ and to all data and scripts required to reproduce the results in this manuscript.

This thesis focuses on the research and development of the Hemodynamic Tissue Signature (HTS) method: an unsupervised machine learning approach to describe the vascular heterogeneity of glioblastomas by means of perfusion MRI analysis. The HTS builds on the concept of habitats. An habitat is defined as a sub-region of the lesion with a particular MRI profile describing a specific physiological behavior. The HTS method delineates four habitats within the glioblastoma: the High Angiogenic Tumor (HAT) habitat, as the most perfused region of the enhancing tumor; the Low Angiogenic Tumor (LAT) habitat, as the region of the enhancing tumor with a lower angiogenic profile; the potentially Infiltrated Peripheral Edema (IPE) habitat, as the non-enhancing region adjacent to the tumor with elevated perfusion indexes; and the Vasogenic Peripheral Edema (VPE) habitat, as the remaining edema of the lesion with the lowest perfusion profile. The results of this thesis have been published in ten scientific contributions, including top-ranked journals and conferences in the areas of Medical Informatics, Statistics and Probability, Radiology & Nuclear Medicine, Machine Learning and Data Mining and Biomedical Engineering. An industrial patent registered in Spain (ES201431289A), Europe (EP3190542A1) and EEUU (US20170287133A1) was also issued, summarizing the efforts of the thesis to generate tangible assets besides the academic revenue obtained from research publications. Finally, the methods, technologies and original ideas conceived in this thesis led to the foundation of ONCOANALYTICS CDX, a company framed into the business model of companion diagnostics for pharmaceutical compounds, thought as a vehicle to facilitate the industrialization of the ONCOhabitats technology.