Graph-RAT: Combining data sources in music recommendation systems

The complexity of music recommendation systems has increased rapidly in recent years, drawing upon different sources of information: content analysis, web-mining, social tagging, etc. Unfortunately, the tools to scientifically evaluate such integrated systems are not readily available; nor are the base algorithms available. This article describes Graph-RAT (Graph-based Relational Analysis Toolkit), an open source toolkit that provides a framework for developing and evaluating novel hybrid systems. While this toolkit is designed for music recommendation, it has applications outside its discipline as well. An experiment—indicative of the sort of procedure that can be configured using the toolkit—is provided to illustrate its usefulness

Methods of Hierarchical Clustering

We survey agglomerative hierarchical clustering algorithms and discuss efficient implementations that are available in R and other software environments. We look at hierarchical self-organizing maps, and mixture models. We review grid-based clustering, focusing on hierarchical density-based approaches. Finally we describe a recently developed very efficient (linear time) hierarchical clustering algorithm, which can also be viewed as a hierarchical grid-based algorithm.Comment: 21 pages, 2 figures, 1 table, 69 reference

Anytime Hierarchical Clustering

We propose a new anytime hierarchical clustering method that iteratively transforms an arbitrary initial hierarchy on the configuration of measurements along a sequence of trees we prove for a fixed data set must terminate in a chain of nested partitions that satisfies a natural homogeneity requirement. Each recursive step re-edits the tree so as to improve a local measure of cluster homogeneity that is compatible with a number of commonly used (e.g., single, average, complete) linkage functions. As an alternative to the standard batch algorithms, we present numerical evidence to suggest that appropriate adaptations of this method can yield decentralized, scalable algorithms suitable for distributed/parallel computation of clustering hierarchies and online tracking of clustering trees applicable to large, dynamically changing databases and anomaly detection.Comment: 13 pages, 6 figures, 5 tables, in preparation for submission to a conferenc

Axiomatic Construction of Hierarchical Clustering in Asymmetric Networks

This paper considers networks where relationships between nodes are represented by directed dissimilarities. The goal is to study methods for the determination of hierarchical clusters, i.e., a family of nested partitions indexed by a connectivity parameter, induced by the given dissimilarity structures. Our construction of hierarchical clustering methods is based on defining admissible methods to be those methods that abide by the axioms of value - nodes in a network with two nodes are clustered together at the maximum of the two dissimilarities between them - and transformation - when dissimilarities are reduced, the network may become more clustered but not less. Several admissible methods are constructed and two particular methods, termed reciprocal and nonreciprocal clustering, are shown to provide upper and lower bounds in the space of admissible methods. Alternative clustering methodologies and axioms are further considered. Allowing the outcome of hierarchical clustering to be asymmetric, so that it matches the asymmetry of the original data, leads to the inception of quasi-clustering methods. The existence of a unique quasi-clustering method is shown. Allowing clustering in a two-node network to proceed at the minimum of the two dissimilarities generates an alternative axiomatic construction. There is a unique clustering method in this case too. The paper also develops algorithms for the computation of hierarchical clusters using matrix powers on a min-max dioid algebra and studies the stability of the methods proposed. We proved that most of the methods introduced in this paper are such that similar networks yield similar hierarchical clustering results. Algorithms are exemplified through their application to networks describing internal migration within states of the United States (U.S.) and the interrelation between sectors of the U.S. economy.Comment: This is a largely extended version of the previous conference submission under the same title. The current version contains the material in the previous version (published in ICASSP 2013) as well as material presented at the Asilomar Conference on Signal, Systems, and Computers 2013, GlobalSIP 2013, and ICML 2014. Also, unpublished material is included in the current versio

Exhaustive and Efficient Constraint Propagation: A Semi-Supervised Learning Perspective and Its Applications

This paper presents a novel pairwise constraint propagation approach by decomposing the challenging constraint propagation problem into a set of independent semi-supervised learning subproblems which can be solved in quadratic time using label propagation based on k-nearest neighbor graphs. Considering that this time cost is proportional to the number of all possible pairwise constraints, our approach actually provides an efficient solution for exhaustively propagating pairwise constraints throughout the entire dataset. The resulting exhaustive set of propagated pairwise constraints are further used to adjust the similarity matrix for constrained spectral clustering. Other than the traditional constraint propagation on single-source data, our approach is also extended to more challenging constraint propagation on multi-source data where each pairwise constraint is defined over a pair of data points from different sources. This multi-source constraint propagation has an important application to cross-modal multimedia retrieval. Extensive results have shown the superior performance of our approach.Comment: The short version of this paper appears as oral paper in ECCV 201

Representation Learning for Clustering: A Statistical Framework

We address the problem of communicating domain knowledge from a user to the designer of a clustering algorithm. We propose a protocol in which the user provides a clustering of a relatively small random sample of a data set. The algorithm designer then uses that sample to come up with a data representation under which $k$-means clustering results in a clustering (of the full data set) that is aligned with the user's clustering. We provide a formal statistical model for analyzing the sample complexity of learning a clustering representation with this paradigm. We then introduce a notion of capacity of a class of possible representations, in the spirit of the VC-dimension, showing that classes of representations that have finite such dimension can be successfully learned with sample size error bounds, and end our discussion with an analysis of that dimension for classes of representations induced by linear embeddings.Comment: To be published in Proceedings of UAI 201

Distance Dependent Chinese Restaurant Processes

We develop the distance dependent Chinese restaurant process (CRP), a flexible class of distributions over partitions that allows for non-exchangeability. This class can be used to model many kinds of dependencies between data in infinite clustering models, including dependencies across time or space. We examine the properties of the distance dependent CRP, discuss its connections to Bayesian nonparametric mixture models, and derive a Gibbs sampler for both observed and mixture settings. We study its performance with three text corpora. We show that relaxing the assumption of exchangeability with distance dependent CRPs can provide a better fit to sequential data. We also show its alternative formulation of the traditional CRP leads to a faster-mixing Gibbs sampling algorithm than the one based on the original formulation

Uncovering Group Level Insights with Accordant Clustering

Clustering is a widely-used data mining tool, which aims to discover partitions of similar items in data. We introduce a new clustering paradigm, \emph{accordant clustering}, which enables the discovery of (predefined) group level insights. Unlike previous clustering paradigms that aim to understand relationships amongst the individual members, the goal of accordant clustering is to uncover insights at the group level through the analysis of their members. Group level insight can often support a call to action that cannot be informed through previous clustering techniques. We propose the first accordant clustering algorithm, and prove that it finds near-optimal solutions when data possesses inherent cluster structure. The insights revealed by accordant clusterings enabled experts in the field of medicine to isolate successful treatments for a neurodegenerative disease, and those in finance to discover patterns of unnecessary spending.Comment: accepted to SDM 2017 (oral