We describe a new iteration of ICGS that outperforms state-of-the-art scRNA-Seq detection workflows when applied to well-established benchmarks. This approach combines multiple complementary subtype detection methods (HOPACH, sparse-NMF, cluster "fitness", SVM) to resolve rare and common cell-states, while minimizing differences due to donor or batch effects. Using data from multiple cell atlases, we show that the PageRank algorithm effectively down-samples ultra-large scRNA-Seq datasets, without losing extremely rare or transcriptionally similar yet distinct cell-types and while recovering novel transcriptionally distinct cell populations. We believe this new approach holds tremendous promise in reproducibly resolving hidden cell populations in complex datasets.

Time-varying classifiers, namely, evolving classifiers, play an important role in a scenario in which information is available as a never-ending online data stream. We present a new unsupervised learning method for numerical data called evolving Internal-eXternal Fuzzy clustering method (Fuzzy eIX). We develop the notion of double-boundary fuzzy granules and elaborate on its implications. Type 1 and type 2 fuzzy inference systems can be obtained from the projection of Fuzzy eIX granules. We perform the principle of the balanced information granularity within Fuzzy eIX classifiers to achieve a higher level of model understandability. Internal and external granules are updated from a numerical data stream at the same time that the global granular structure of the classifier is autonomously evolved. A synthetic nonstationary problem called Rotation of Twin Gaussians shows the behavior of the classifier. The Fuzzy eIX classifier could keep up with its accuracy in a scenario in which offline-trained classifiers would clearly have their accuracy drastically dropped.

Graph clustering has been studied extensively on both plain graphs and attributed graphs. However, all these methods need to partition the whole graph to find cluster structures. Sometimes, based on domain knowledge, people may have information about a specific target region in the graph and only want to find a single cluster concentrated on this local region. Such a task is called local clustering. In contrast to global clustering, local clustering aims to find only one cluster that is concentrating on the given seed vertex (and also on the designated attributes for attributed graphs). Currently, very few methods can deal with this kind of task. To this end, we propose two quality measures for a local cluster: Graph Unimodality (GU) and Attribute Unimodality (AU). The former measures the homogeneity of the graph structure while the latter measures the homogeneity of the subspace that is composed of the designated attributes. We call their linear combination as Compactness. Further, we propose LOCLU to optimize the Compactness score. The local cluster detected by LOCLU concentrates on the region of interest, provides efficient information flow in the graph and exhibits a unimodal data distribution in the subspace of the designated attributes.

We introduce a cluster evaluation technique called Tree Index. Our Tree Index algorithm aims at describing the structural information of the clustering rather than the quantitative format of cluster-quality indexes (where the representation power of clustering is some cumulative error similar to vector quantization). Our Tree Index is finding margins amongst clusters for easy learning without the complications of Minimum Description Length. Our Tree Index produces a decision tree from the clustered data set, using the cluster identifiers as labels. It combines the entropy of each leaf with their depth. Intuitively, a shorter tree with pure leaves generalizes the data well (the clusters are easy to learn because they are well separated). So, the labels are meaningful clusters. If the clustering algorithm does not separate well, trees learned from their results will be large and too detailed. We show that, on the clustering results (obtained by various techniques) on a brain dataset, Tree Index discriminates between reasonable and non-sensible clusters. We confirm the effectiveness of Tree Index through graphical visualizations. Tree Index evaluates the sensible solutions higher than the non-sensible solutions while existing cluster-quality indexes fail to do so.

An unprecedented volume of data is currently being generated across the globe with no less than an estimated 2.5 quintillion (1018) bytes of data each day at our current pace. The variety of formats in which this data is being produced, and its structural complexity, are also on the rise. Collectively, these factors are driving demand among institutions for advanced analytics to generate actionable insights. At the most basic level, machine learning encompasses the use of computational algorithms more advanced than the analytics methods (data mining approaches, for example) traditionally employed to deliver insights into large datasets. Machine learning techniques are firmly rooted in the science of statistics and have valuable applications not least in financial services.

Machine learning is driving development across many fields in science and engineering. A simple and efficient programming language could accelerate applications of machine learning in various fields. Currently, the programming languages most commonly used to develop machine learning algorithms include Python, MATLAB, and C/C ++. However, none of these languages well balance both efficiency and simplicity. The Julia language is a fast, easy-to-use, and open-source programming language that was originally designed for high-performance computing, which can well balance the efficiency and simplicity. This paper summarizes the related research work and developments in the application of the Julia language in machine learning. It first surveys the popular machine learning algorithms that are developed in the Julia language. Then, it investigates applications of the machine learning algorithms implemented with the Julia language. Finally, it discusses the open issues and the potential future directions that arise in the use of the Julia language in machine learning.

We study hypergraph clustering under the weighted $d$-uniform hypergraph stochastic block model ($d$-WHSBM), where each edge consisting of $d$ nodes has higher expected weight if $d$ nodes are from the same community compared to edges consisting of nodes from different communities. We propose a new hypergraph clustering algorithm, which is a convex relaxation of truncated maximum likelihood estimator (CRTMLE), that can handle the relatively sparse, high-dimensional regime of the $d$-WHSBM with community sizes of different orders. We provide performance guarantees of this algorithm under a unified framework for different parameter regimes, and show that it achieves the order-wise optimal or the best existing results for approximately balanced community sizes. We also demonstrate the first recovery guarantees for the setting with growing number of communities of unbalanced sizes.

This paper considers a canonical clustering problem where one receives unlabeled samples drawn from a balanced mixture of two elliptical distributions and aims for a classifier to estimate the labels. Many popular methods including PCA and k-means require individual components of the mixture to be somewhat spherical, and perform poorly when they are stretched. To overcome this issue, we propose a non-convex program seeking for an affine transform to turn the data into a one-dimensional point cloud concentrating around -1 and 1, after which clustering becomes easy. Our theoretical contributions are two-fold: (1) we show that the non-convex loss function exhibits desirable landscape properties as long as the sample size exceeds some constant multiple of the dimension, and (2) we leverage this to prove that an efficient first-order algorithm achieves near-optimal statistical precision even without good initialization. We also propose a general methodology for multi-class clustering tasks with flexible choices of feature transforms and loss objectives.

We consider the problem of data clustering with unidentified feature quality but the existence of small amount of label data. In the first case a sparse clustering method can be employed in order to detect the subgroup of features necessary for clustering and in the second case a semi-supervised method can use the labelled data to create constraints and enhance the clustering solution. In this paper we propose a K-Means inspired algorithm that employs these techniques. We show that the algorithm maintains the high performance of other similar semi-supervised algorthms as well as keeping the ability to identify informative from uninformative features. We examine the performance of the algorithm on real world data sets with unknown features quality as well as a real world data set with a known uninformative feature. We use a series of scenarios with different number and types of constraints.

We investigate active learning by pairwise similarity over the leaves of trees originating from hierarchical clustering procedures. In the realizable setting, we provide a full characterization of the number of queries needed to achieve perfect reconstruction of the tree cut. In the non-realizable setting, we rely on known important-sampling procedures to obtain regret and query complexity bounds. Our algorithms come with theoretical guarantees on the statistical error and, more importantly, lend themselves to {\em linear-time} implementations in the relevant parameters of the problem. We discuss such implementations, prove running time guarantees for them, and present preliminary experiments on real-world datasets showing the compelling practical performance of our algorithms as compared to both passive learning and simple active learning baselines.