Let's say you have to cluster 10 million points, for instance keywords. So, in short, you can perform k-NN (k-nearest neighbors) clustering or some other types of clustering, which typically is O(n 2) or worse, from a computational complexity point of view. Has anyone ever used a clustering method based on sampling? The idea is to start by sampling 1% (or less) of the 100,000,000 entries, and perform clustering on these pairs of keywords, to create a "seed" or "baseline" cluster structure. The next step is to browse sequentially your 10,000,000 keywords, and for each keyword, find the closest cluster from the baseline cluster structure.

In general, the clustering problem is NP-hard, and global optimality cannot be established for non-trivial instances. For high-dimensional data, distance-based methods for clustering or classification face an additional difficulty, the unreliability of distances in very high-dimensional spaces. We propose a distance-based iterative method for clustering data in very high-dimensional space, using the $\ell_1$-metric that is less sensitive to high dimensionality than the Euclidean distance. For $K$ clusters in $\mathbb{R}^n$, the problem decomposes to $K$ problems coupled by probabilities, and an iteration reduces to finding $Kn$ weighted medians of points on a line. The complexity of the algorithm is linear in the dimension of the data space, and its performance was observed to improve significantly as the dimension increases.

We propose to model the fixation locations of the human eye when observing a still image by a Markovian point process in R 2 . Our approach is data driven using k-means clustering of the fixation locations to identify distinct salient regions of the image, which in turn correspond to the states of our Markov chain. Bayes factors are computed as model selection criterion to determine the number of clusters. Furthermore, we demonstrate that the behaviour of the human eye differs from this model when colour information is removed from the given image.

A number of organizations ranging from terrorist groups such as ISIS to politicians and nation states reportedly conduct explicit campaigns to influence opinion on social media, posing a risk to democratic processes. There is thus a growing need to identify and eliminate "influence bots" - realistic, automated identities that illicitly shape discussion on sites like Twitter and Facebook - before they get too influential. Spurred by such events, DARPA held a 4-week competition in February/March 2015 in which multiple teams supported by the DARPA Social Media in Strategic Communications program competed to identify a set of previously identified "influence bots" serving as ground truth on a specific topic within Twitter. Past work regarding influence bots often has difficulty supporting claims about accuracy, since there is limited ground truth (though some exceptions do exist [3,7]). However, with the exception of [3], no past work has looked specifically at identifying influence bots on a specific topic. This paper describes the DARPA Challenge and describes the methods used by the three top-ranked teams.

The final homework assignment for CS545 Machine Learning was to implement a K-means clustering algorithm to cluster and classify the OptDigits data. The raw data looks something like the figures to the left. So these instances are fields of 0's whereby some 0's have been flipped to be 1's such that the image is recognizable (to humans) as a handwritten digit. For the K-means classifier, we ran 2 different experiments. The first expeiment used 10 centroids (one per digit), the second used 30 centroids to see if it could find clusters where the handwritten digits were different enough to notice differences.

In a wide range of statistical learning problems such as ranking, clustering or metric learning among others, the risk is accurately estimated by $U$-statistics of degree $d\geq 1$, i.e. functionals of the training data with low variance that take the form of averages over $k$-tuples. From a computational perspective, the calculation of such statistics is highly expensive even for a moderate sample size $n$, as it requires averaging $O(n^d)$ terms. This makes learning procedures relying on the optimization of such data functionals hardly feasible in practice. It is the major goal of this paper to show that, strikingly, such empirical risks can be replaced by drastically computationally simpler Monte-Carlo estimates based on $O(n)$ terms only, usually referred to as incomplete $U$-statistics, without damaging the $O_{\mathbb{P}}(1/\sqrt{n})$ learning rate of Empirical Risk Minimization (ERM) procedures. For this purpose, we establish uniform deviation results describing the error made when approximating a $U$-process by its incomplete version under appropriate complexity assumptions. Extensions to model selection, fast rate situations and various sampling techniques are also considered, as well as an application to stochastic gradient descent for ERM. Finally, numerical examples are displayed in order to provide strong empirical evidence that the approach we promote largely surpasses more naive subsampling techniques.

We have designed an open and modular course for data science and big data analytics using a workflow paradigm that allows students to easily experience big data through a sophisticated yet easy to use instrument that is an intelligent workflow system. A key aspect of this work is the use of semantic workflows to capture and reuse end-to-end analytic methods that experts would use to analyze big data, and the use of an intelligent workflow system to elaborate the workflow and manage its execution and resulting datasets. Through the exposure of big data analytics in a workflow framework, students will be able to get first-hand experiences with a breadth of big data topics, including multi-step data analytic and statistical methods, software reuse and composition, parallel distributed programming, high-end computing. In addition, students learn about a range of topics in AI, including semantic representations and ontologies, machine learning, natural language processing, and image analysis.

Kaczmarz algorithm is an efficient iterative algorithm to solve overdetermined consistent system of linear equations. During each updating step, Kaczmarz chooses a hyperplane based on an individual equation and projects the current estimate for the exact solution onto that space to get a new estimate.Many vairants of Kaczmarz algorithms are proposed on how to choose better hyperplanes.Using the property of randomly sampled data in high-dimensional space,we propose an accelerated algorithm based on clustering information to improve block Kaczmarz and Kaczmarz via Johnson-Lindenstrauss lemma. Additionally, we theoretically demonstrate convergence improvement on block Kaczmarz algorithm.

Most approaches to classifying data streams either divide the stream into fixed-size chunks or use gradual forgetting. Due to evolving nature of data streams, finding a proper size or choosing a forgetting rate without prior knowledge about time-scale of change is not a trivial task. These approaches hence suffer from a trade-off between performance and sensitivity. Existing dynamic sliding window based approaches address this problem by tracking changes in classifier error rate, but are supervised in nature. We propose an efficient semi-supervised framework in this paper which uses change detection on classifier confidence to detect concept drifts, and to determine chunk boundaries dynamically. It also addresses concept evolution problem by detecting outliers having strong cohesion among themselves. Experiment results on benchmark and synthetic data sets show effectiveness of the proposed approach.

In graph-oriented machine learning research, L1 graph is an efficient way to represent the connections of input data samples. Its construction algorithm is based on a numerical optimization motivated by Compressive Sensing theory. As a result, It is a nonparametric method which is highly demanded. However, the information of data such as geometry structure and density distribution are ignored. In this paper, we propose a Structure Aware (SA) L1 graph to improve the data clustering performance by capturing the manifold structure of input data. We use a local dictionary for each datum while calculating its sparse coefficients. SA-L1 graph not only preserves the locality of data but also captures the geometry structure of data. The experimental results show that our new algorithm has better clustering performance than L1 graph.