We derive an efficient method to perform clustering of nodes in Gaussian graphical models directly from sample data. Nodes are clustered based on the similarity of their network neighborhoods, with edge weights defined by partial correlations. In the limited-data scenario, where the covariance matrix would be rank-deficient, we are able to make use of matrix factors, and never need to estimate the actual covariance or precision matrix. We demonstrate the method on functional MRI data from the Human Connectome Project. A matlab implementation of the algorithm is provided.

Energy game-theoretic frameworks have emerged to be a successful strategy to encourage energy efficient behavior in large scale by leveraging human-in-the-loop strategy. A number of such frameworks have been introduced over the years which formulate the energy saving process as a competitive game with appropriate incentives for energy efficient players. However, prior works involve an incentive design mechanism which is dependent on knowledge of utility functions for all the players in the game, which is hard to compute especially when the number of players is high, common in energy game-theoretic frameworks. Our research proposes that the utilities of players in such a framework can be grouped together to a relatively small number of clusters, and the clusters can then be targeted with tailored incentives. The key to above segmentation analysis is to learn the features leading to human decision making towards energy usage in competitive environments. We propose a novel graphical lasso based approach to perform such segmentation, by studying the feature correlations in a real-world energy social game dataset. To further improve the explainability of the model, we perform causality study using grangers causality. Proposed segmentation analysis results in characteristic clusters demonstrating different energy usage behaviors. We also present avenues to implement intelligent incentive design using proposed segmentation method.

This work extends the randomized shortest paths model (RSP) by investigating the net flow RSP and adding capacity constraints on edge flows. The standard RSP is a model of movement, or spread, through a network interpolating between a random walk and a shortest path behavior. This framework assumes a unit flow injected into a source node and collected from a target node with flows minimizing the expected transportation cost together with a relative entropy regularization term. In this context, the present work first develops the net flow RSP model considering that edge flows in opposite directions neutralize each other (as in electrical networks) and proposes an algorithm for computing the expected routing costs between all pairs of nodes. This quantity is called the net flow RSP dissimilarity measure between nodes. Experimental comparisons on node clustering tasks show that the net flow RSP dissimilarity is competitive with other state-of-the-art techniques. In the second part of the paper, it is shown how to introduce capacity constraints on edge flows and a procedure solving this constrained problem by using Lagrangian duality is developed. These two extensions improve significantly the scope of applications of the RSP framework.

This paper provides statistical theory and intuition for Personalized PageRank (PPR), a popular technique that samples a small community from a massive network. We study a setting where the entire network is expensive to thoroughly obtain or maintain, but we can start from a seed node of interest and "crawl" the network to find other nodes through their connections. By crawling the graph in a designed way, the PPR vector can be approximated without querying the entire massive graph, making it an alternative to snowball sampling. Using the Degree-Corrected Stochastic Blockmodel, we study whether the PPR vector can select nodes that belong to the same block as the seed node. We provide a simple and interpretable form for the PPR vector, highlighting its biases towards high degree nodes outside of the target block. We examine a simple adjustment based on node degrees and establish consistency results for PPR clustering that allows for directed graphs. We illustrate the method with the Twitter friendship graph and find that (i) the adjusted and unadjusted PPR techniques are complementary approaches, where the adjustment makes the results particularly localized around the seed node and (ii) the bias adjustment greatly benefits from degree regularization.

The objective of the present paper is to study the Popularity Adjusted Block Model (PABM) in the sparse setting. Unlike in other block models, the flexibility of PABM allows to set some of the connection probabilities to zero while maintaining the rest of the probabilities non-negligible, leading to the Sparse Popularity Adjusted Block Model (SPABM). The latter reduces the size of parameter set and leads to improved precision of estimation and clustering. The theory is complemented by the simulation study and real data examples.

Feature selection is an important and challenging task in high dimensional clustering. For example, in genomics, there may only be a small number of genes that are differentially expressed, which are informative to the overall clustering structure. Existing feature selection methods, such as Sparse K-means, rarely tackle the problem of accounting features that can only separate a subset of clusters. In genomics, it is highly likely that a gene can only define one subtype against all the other subtypes or distinguish a pair of subtypes but not others. In this paper, we propose a K-means based clustering algorithm that discovers informative features as well as which cluster pairs are separable by each selected features. The method is essentially an EM algorithm, in which we introduce lasso-type constraints on each cluster pair in the M step, and make the E step possible by maximizing the raw cross-cluster distance instead of minimizing the intra-cluster distance. The results were demonstrated on simulated data and a leukemia gene expression dataset.

In this article, we will study the various types of machine learning algorithms and their use-cases. We will study how Baidu is using supervised learning-based facial recognition for intelligent airport check-in and how Google is making use of Reinforcement Learning to develop an intelligent platform that would answer your queries. Machine Learning is a broad field, but it is classified into three classes of supervised, unsupervised and reinforcement learning. All these three paradigms are used everywhere to power intelligent applications. We will look at the important use cases of these paradigms and how they are revolutionizing our world today.

The goal of lifetime clustering is to develop an inductive model that maps subjects into $K$ clusters according to their underlying (unobserved) lifetime distribution. We introduce a neural-network based lifetime clustering model that can find cluster assignments by directly maximizing the divergence between the empirical lifetime distributions of the clusters. Accordingly, we define a novel clustering loss function over the lifetime distributions (of entire clusters) based on a tight upper bound of the two-sample Kuiper test p-value. The resultant model is robust to the modeling issues associated with the unobservability of termination signals, and does not assume proportional hazards. Our results in real and synthetic datasets show significantly better lifetime clusters (as evaluated by C-index, Brier Score, Logrank score and adjusted Rand index) as compared to competing approaches.

Clustering is a technique that groups similar objects such that the objects in the same group are more similar to each other than the objects in the other groups. The group of similar objects is called a Cluster. Also called Hierarchical cluster analysis or HCA is an unsupervised clustering algorithm which involves creating clusters that have predominant ordering from top to bottom. For e.g: All files and folders on our hard disk are organized in a hierarchy. The algorithm groups similar objects into groups called clusters.

We propose a deep amortized clustering (DAC), a neural architecture which learns to cluster datasets efficiently using a few forward passes. DAC implicitly learns what makes a cluster, how to group data points into clusters, and how to count the number of clusters in datasets. DAC is meta-learned using labelled datasets for training, a process distinct from traditional clustering algorithms which usually require hand-specified prior knowledge about cluster shapes/structures. We empirically show, on both synthetic and image data, that DAC can efficiently and accurately cluster new datasets coming from the same distribution used to generate training datasets.