In many datasets, different parts of the data may have their own patterns of correlation, a structure that can be modeled as a mixture of local linear correlation models. The task of finding these mixtures is known as correlation clustering. In this work, we propose a linear correlation clustering method for datasets whose features are pre-divided into two views. The method, called Canonical Least Squares (CLS) clustering, is inspired by multi-output regression and Canonical Correlation Analysis. CLS clusters can be interpreted as variations in the regression relationship between the two views. The method is useful for data mining and data interpretation. Its utility is demonstrated on a synthetic dataset and stock market dataset.

The random dot product graph (RDPG) is an independent-edge random graph that is analytically tractable and, simultaneously, either encompasses or can successfully approximate a wide range of random graphs, from relatively simple stochastic block models to complex latent position graphs. In this survey paper, we describe a comprehensive paradigm for statistical inference on random dot product graphs, a paradigm centered on spectral embeddings of adjacency and Laplacian matrices. We examine the analogues, in graph inference, of several canonical tenets of classical Euclidean inference: in particular, we summarize a body of existing results on the consistency and asymptotic normality of the adjacency and Laplacian spectral embeddings, and the role these spectral embeddings can play in the construction of single- and multi-sample hypothesis tests for graph data. We investigate several real-world applications, including community detection and classification in large social networks and the determination of functional and biologically relevant network properties from an exploratory data analysis of the Drosophila connectome. We outline requisite background and current open problems in spectral graph inference.

In spite of the rapid development in data acquisition technology resulting in the explosive collection of acquired datasets, techniques such as data organization and classification, manipulation, and analysis of very large, diverse, heterogeneous datasets have only evolved modestly. This has led to hindrances in effective utility and better understanding of the acquired, large-scale data for knowledge discovery. In an industrial setting, an interesting visual from McKinsey illustrates that despite collecting data from tens of thousands of sensors, less than 1% is actually utilized. Data clustering is the classification of data objects into different groups (clusters) such that data objects in one group are similar together and dissimilar from another group. Typically, homogeneous data objects, i.e. data objects having the same data type, are grouped together using some of the well-known clustering algorithms.

In modern computer vision problems such as facial recognition [1] and object tracking [2], researchers have found success applying the union of subspaces (UoS) model, in which data vectors lie near one of several subspaces. Under this model, the goal is to simultaneously identify these underlying subspaces and cluster the points according to their nearest subspace. Algorithms designed to solve this problem fall under the category of subspace clustering, a topic that has received a great deal of attention in recent years [3] due to its efficacy on real-world datasets such as the Extended Yale Face Database B [4] and the MNIST handwritten digit database [5]. One of the earliest approaches to solving the subspace clustering problem involves an iterative method in the spirit of K-means, known as K-subspaces (KSS) [6], [7], [8], which alternates between assigning points to clusters and estimating the subspace basis associated with each cluster. As this algorithm is only guaranteed to converge to a local minimum, in practice one runs many instances of the algorithm and chooses the final clustering as the one that produces the minimum cost. Although its empirical performance is limited, KSS continues to serve as a benchmark for subspace clustering algorithms, in part due to its computational efficiency and simplicity. Therefore, a deeper understanding of this method is an important contribution in the area of subspace clustering and a contribution of this paper. While the KSS cost function and alternating algorithm are perhaps the most natural approach for the subspace clustering problem, it is known that there is a set of initializations of nonzero measure from which the algorithm will convergence to a point other than the global minimizer.

The current work characterizes the users of a VoD streaming space through user-personas based on a tenure timeline and temporal behavioral features in the absence of explicit user profiles. A combination of tenure timeline and temporal characteristics caters to business needs of understanding the evolution and phases of user behavior as their accounts age. The personas constructed in this work successfully represent both dominant and niche characterizations while providing insightful maturation of user behavior in the system. The two major highlights of our personas are demonstration of stability along tenure timelines on a population level, while exhibiting interesting migrations between labels on an individual granularity and clear interpretability of user labels. Finally, we show a trade-off between an indispensable trio of guarantees, relevance-scalability-interpretability by using summary information from personas in a CTR (Click through rate) predictive model. The proposed method of uncovering latent personas, consequent insights from these and application of information from personas to predictive models are broadly applicable to other streaming based products.

Flow cytometry is a high-throughput technology used to quantify multiple surface and intracellular markers at the level of a single cell. This enables to identify cell sub-types, and to determine their relative proportions. Improvements of this technology allow to describe millions of individual cells from a blood sample using multiple markers. This results in high-dimensional datasets, whose manual analysis is highly time-consuming and poorly reproducible. While several methods have been developed to perform automatic recognition of cell populations, most of them treat and analyze each sample independently. However, in practice, individual samples are rarely independent (e.g. longitudinal studies). Here, we propose to use a Bayesian nonparametric approach with Dirichlet process mixture (DPM) of multivariate skew $t$-distributions to perform model based clustering of flow-cytometry data. DPM models directly estimate the number of cell populations from the data, avoiding model selection issues, and skew $t$-distributions provides robustness to outliers and non-elliptical shape of cell populations. To accommodate repeated measurements, we propose a sequential strategy relying on a parametric approximation of the posterior. We illustrate the good performance of our method on simulated data, on an experimental benchmark dataset, and on new longitudinal data from the DALIA-1 trial which evaluates a therapeutic vaccine against HIV. On the benchmark dataset, the sequential strategy outperforms all other methods evaluated, and similarly, leads to improved performance on the DALIA-1 data. We have made the method available for the community in the R package NPflow.

Semi-supervised active clustering (SSAC) utilizes the knowledge of a domain expert to cluster data points by interactively making pairwise "same-cluster" queries. However, it is impractical to ask human oracles to answer every pairwise query. In this paper, we study the influence of allowing "not-sure" answers from a weak oracle and propose algorithms to efficiently handle uncertainties. Different types of model assumptions are analyzed to cover realistic scenarios of oracle abstraction. In the first model, random-weak oracle, an oracle randomly abstains with a certain probability. We also proposed two distance-weak oracle models which simulate the case of getting confused based on the distance between two points in a pairwise query. For each weak oracle model, we show that a small query complexity is adequate for the effective $k$ means clustering with high probability. Sufficient conditions for the guarantee include a $\gamma$-margin property of the data, and an existence of a point close to each cluster center. Furthermore, we provide a sample complexity with a reduced effect of the cluster's margin and only a logarithmic dependency on the data dimension. Our results allow significantly less number of same-cluster queries if the margin of the clusters is tight, i.e. $\gamma \approx 1$. Experimental results on synthetic data show the effective performance of our approach in overcoming uncertainties.

Topic models can provide us with an insight into the underlying latent structure of a large corpus of documents. A range of methods have been proposed in the literature, including probabilistic topic models and techniques based on matrix factorization. However, in both cases, standard implementations rely on stochastic elements in their initialization phase, which can potentially lead to different results being generated on the same corpus when using the same parameter values. This corresponds to the concept of "instability" which has previously been studied in the context of $k$-means clustering. In many applications of topic modeling, this problem of instability is not considered and topic models are treated as being definitive, even though the results may change considerably if the initialization process is altered. In this paper we demonstrate the inherent instability of popular topic modeling approaches, using a number of new measures to assess stability. To address this issue in the context of matrix factorization for topic modeling, we propose the use of ensemble learning strategies. Based on experiments performed on annotated text corpora, we show that a K-Fold ensemble strategy, combining both ensembles and structured initialization, can significantly reduce instability, while simultaneously yielding more accurate topic models.

Have you come across a situation when a Chief Marketing Officer of a company tells you – "Help me understand our customers better so that we can market our products to them in a better manner!" I did and the analyst in me was completely clueless what to do! I was used to getting specific problems, where there is an outcome to be predicted for various set of conditions. But I had no clue, what to do in this case. If the person would have asked me to calculate Life Time Value (LTV) or propensity of Cross-sell, I wouldn't have blinked.

How do you find the underlying structure of a dataset? How do you summarize it and group it most usefully? How do you effectively represent data in a compressed format? These are the goals of unsupervised learning, which is called "unsupervised" because you start with unlabeled data (there's no Y). The two unsupervised learning tasks we will explore are clustering the data into groups by similarity and reducing dimensionality to compress the data while maintaining its structure and usefulness.