Multi-view data clustering refers to categorizing a data set by making good use of related information from multiple representations of the data. It becomes important nowadays because more and more data can be collected in a variety of ways, in different settings and from different sources, so each data set can be represented by different sets of features to form different views of it. Many approaches have been proposed to improve clustering performance by exploring and integrating heterogeneous information underlying different views. In this paper, we propose a new multi-view fuzzy clustering approach called MinimaxFCM by using minimax optimization based on well-known Fuzzy c means. In MinimaxFCM the consensus clustering results are generated based on minimax optimization in which the maximum disagreements of different weighted views are minimized. Moreover, the weight of each view can be learned automatically in the clustering process. In addition, there is only one parameter to be set besides the fuzzifier. The detailed problem formulation, updating rules derivation, and the in-depth analysis of the proposed MinimaxFCM are provided here. Experimental studies on nine multi-view data sets including real world image and document data sets have been conducted. We observed that MinimaxFCM outperforms related multi-view clustering approaches in terms of clustering accuracy, demonstrating the great potential of MinimaxFCM for multi-view data analysis.

It always amazes me how I can hear a statement uttered in the space of a few seconds about some aspect of machine learning that then takes me countless hours to understand. I first heard about Gaussian Processes on an episode of the Talking Machines podcast and thought it sounded like a really neat idea. I promptly procured myself a copy of the classic text on the subject, Gaussian Processes for Machine Learning by Rasmussen and Williams, but my tenuous grasp on the Bayesian approach to machine learning meant I got stumped pretty quickly. That's when I began the journey I described in my last post, From both sides now: the math of linear regression. Gaussian Processes (GPs) are the natural next step in that journey as they provide an alternative approach to regression problems.

They are currently in the NYC Data Science Academy 12 week full time Data Science Bootcamp program taking place between January 11th to April 1st, 2016. This post is based on their fourth class project - Machine learning(due on the 8th week of the program). The Higgs Boson is a landmark discovery that will help us to understand the basic nature of the universe. It was discovered first by the ATLAS experiment at the Large Hadron Collider, CERN in 2012. The Higg's Boson decays into two tau particles giving rise to a small signal buried in background noise. The goal of the Higgs Boson Machine Learning Challenge was to classify the characterizing events detected by ATLAS into "tau tau decay of a Higgs boson" versus "background."

Over the past few weeks, we've started to learn more and more about machine learning and the role it plays in computer vision, image classification, and deep learning. We've seen how Convolutional Neural Networks (CNNs) such as LetNet can be used to classify handwritten digits from the MNIST dataset. We've applied the k-NN algorithm to classify whether or not an image contains a dog or a cat. And we've learned how to apply hyperparameter tuning to optimize our model to obtain higher classification accuracy. However, there is another very important machine learning algorithm we have yet to explore -- one that can be built upon and extended naturally to Neural Networks and Convolutional Neural Networks.

To construct flexible nonlinear predictive distributions, the paper introduces a family of softplus function based regression models that convolve, stack, or combine both operations by convolving countably infinite stacked gamma distributions, whose scales depend on the covariates. Generalizing logistic regression that uses a single hyperplane to partition the covariate space into two halves, softplus regressions employ multiple hyperplanes to construct a confined space, related to a single convex polytope defined by the intersection of multiple half-spaces or a union of multiple convex polytopes, to separate one class from the other. The gamma process is introduced to support the convolution of countably infinite (stacked) covariate-dependent gamma distributions. For Bayesian inference, Gibbs sampling derived via novel data augmentation and marginalization techniques is used to deconvolve and/or demix the highly complex nonlinear predictive distribution. Example results demonstrate that softplus regressions provide flexible nonlinear decision boundaries, achieving classification accuracies comparable to that of kernel support vector machine while requiring significant less computation for out-of-sample prediction.

Perceptron is a classic online algorithm for learning a classification function. In this paper, we provide a novel extension of the perceptron algorithm to the learning to rank problem in information retrieval. We consider popular listwise performance measures such as Normalized Discounted Cumulative Gain (NDCG) and Average Precision (AP). A modern perspective on perceptron for classification is that it is simply an instance of online gradient descent (OGD), during mistake rounds, using the hinge loss function. Motivated by this interpretation, we propose a novel family of listwise, large margin ranking surrogates. Members of this family can be thought of as analogs of the hinge loss. Exploiting a certain self-bounding property of the proposed family, we provide a guarantee on the cumulative NDCG (or AP) induced loss incurred by our perceptron-like algorithm. We show that, if there exists a perfect oracle ranker which can correctly rank each instance in an online sequence of ranking data, with some margin, the cumulative loss of perceptron algorithm on that sequence is bounded by a constant, irrespective of the length of the sequence. This result is reminiscent of Novikoff's convergence theorem for the classification perceptron. Moreover, we prove a lower bound on the cumulative loss achievable by any deterministic algorithm, under the assumption of existence of perfect oracle ranker. The lower bound shows that our perceptron bound is not tight, and we propose another, \emph{purely online}, algorithm which achieves the lower bound. We provide empirical results on simulated and large commercial datasets to corroborate our theoretical results.

This post was contributed by Chelsea Douglas, a Software Engineer at Plotly. Want to play with the code from this post? I recently had the chance to team up with Domino Data Lab to produce a webinar that demonstrated how to use Plotly to create data visualizations inside of Domino notebooks. In this post, I'll share a few of the benefits that I discovered while using Plotly and Domino together. Plotly is a web-based data visualization platform for data scientists and engineers.

This short tutorial will not only guide you through some basic data analysis methods but it will also show you how to implement some of the more sophisticated techniques available today. We will look into traffic accident data from the National Highway Traffic Safety Administration and try to predict fatal accidents using state-of-the-art statistical learning techniques. If you are interested, download the code at the bottom and follow along as we work through a real world data set. This post is in R while a companion post covers the same techniques in Python. The swirl package is designed to teach people R.

Wyatt Earp was the most famous lawman in the Wild West who is glorified beyond means for his abilities as a fearless gunman. He may not have been the quickest draw in the west, but was the most deadliest of his times. Neural Net training is a bit like the wild west. The errors are quite lawless and unhinged. They can behave erratically without rules, rhyme or reason.

Most machine learning algorithms have been developed and statistically validated for linearly separable data. Popular examples are linear classifiers like Support Vector Machines (SVMs) or the (standard) Principal Component Analysis (PCA) for dimensionality reduction. However, most real world data requires nonlinear methods in order to perform tasks that involve the analysis and discovery of patterns successfully. The focus of this article is to briefly introduce the idea of kernel methods and to implement a Gaussian radius basis function (RBF) kernel that is used to perform nonlinear dimensionality reduction via BF kernel principal component analysis (kPCA). The main purpose of principal component analysis (PCA) is the analysis of data to identify patterns that represent the data "well." The principal components can be understood as new axes of the dataset that maximize the variance along those axes (the eigenvectors of the covariance matrix).