The below is an example of how sklearn in Python can be used to develop a k-means clustering algorithm. The purpose of k-means clustering is to be able to partition observations in a dataset into a specific number of clusters in order to aid in analysis of the data. From this perspective, it has particular value from a data visualisation perspective. The particular example used here is that of stock returns. Specifically, the k-means scatter plot will illustrate the clustering of specific stock returns according to their dividend yield.

If you ask any experienced analytics or data science professional, what differentiates a good model from a bad model – chances are that you will hear a uniform answer. Whether you call it "characteristics generation" or "variable generation" (as it was known traditionally) or "feature engineering" – the importance of this step is unanimously agreed in the data science / analytics world. This step involves creating a large and diverse set of derived variables from the base data. The richer the set of variables that are generated, the better will be your models. Most of our time and coding efforts are usually spent in the area of feature engineering. Therefore, understanding feature engineering for specific data sources is a key success factors for us.

You're refining your training set, and maybe you've even tried stuff out using Naive Bayes. But now you're feeling confident in your dataset, and want to take it one step further. Enter Support Vector Machines (SVM): a fast and dependable classification algorithm that performs very well with a limited amount of data. Perhaps you have dug a bit deeper, and ran into terms like linearly separable, kernel trick and kernel functions. The idea behind the SVM algorithm is simple, and applying it to natural language classification doesn't require most of the complicated stuff.

Hierarchical clustering methods produce dendrograms which contain more information than mere flat clustering, for instance cluster proximity. A particular hierarchical clustering method, namely Single-Linkage, enjoys several nice theoretical properties (Zadeh and Ben-David, 2009) and (Carlsson and Mémoli, 2010) despite being known to give poor results in practice. Nonetheless, in (Awasthi et al., 2012), authors show that if the center-based clustering instance verifies some perturbation resilient properties, finding the optimal center-based clustering is possible in polynomial time by cutting efficiently the Single-Linkage dendrogram while in the general case, finding the optimal clustering is NP-hard. The common practice to flatten dendrograms in $k$ clusters is to cut them off at constant height $k-1$. Yet it leads to poorer clusters than efficiently pruning the tree.

It is no doubt that the sub-field of machine learning / artificial intelligence has increasingly gained more popularity in the past couple of years. As Big Data is the hottest trend in the tech industry at the moment, machine learning is incredibly powerful to make predictions or calculated suggestions based on large amounts of data. Some of the most common examples of machine learning are Netflix's algorithms to make movie suggestions based on movies you have watched in the past or Amazon's algorithms that recommend books based on books you have bought before. So if you want to learn more about machine learning, how do you start? For me, my first introduction is when I took an Artificial Intelligence class when I was studying abroad in Copenhagen.

Mutual Information (MI) is often used for feature selection when developing classifier models. Estimating the MI for a subset of features is often intractable. We demonstrate, that under the assumptions of conditional independence, MI between a subset of features can be expressed as the Conditional Mutual Information (CMI) between pairs of features. But selecting features with the highest CMI turns out to be a hard combinatorial problem. In this work, we have applied two unique global methods, Truncated Power Method (TPower) and Low Rank Bilinear Approximation (LowRank), to solve the feature selection problem. These algorithms provide very good approximations to the NP-hard CMI based feature selection problem. We experimentally demonstrate the effectiveness of these procedures across multiple datasets and compare them with existing MI based global and iterative feature selection procedures.

In this paper, we initiate a rigorous theoretical study of clustering with noisy queries (or a faulty oracle). Given a set of $n$ elements, our goal is to recover the true clustering by asking minimum number of pairwise queries to an oracle. Oracle can answer queries of the form : "do elements $u$ and $v$ belong to the same cluster?" -- the queries can be asked interactively (adaptive queries), or non-adaptively up-front, but its answer can be erroneous with probability $p$. In this paper, we provide the first information theoretic lower bound on the number of queries for clustering with noisy oracle in both situations. We design novel algorithms that closely match this query complexity lower bound, even when the number of clusters is unknown. Moreover, we design computationally efficient algorithms both for the adaptive and non-adaptive settings. The problem captures/generalizes multiple application scenarios. It is directly motivated by the growing body of work that use crowdsourcing for {\em entity resolution}, a fundamental and challenging data mining task aimed to identify all records in a database referring to the same entity. Here crowd represents the noisy oracle, and the number of queries directly relates to the cost of crowdsourcing. Another application comes from the problem of {\em sign edge prediction} in social network, where social interactions can be both positive and negative, and one must identify the sign of all pair-wise interactions by querying a few pairs. Furthermore, clustering with noisy oracle is intimately connected to correlation clustering, leading to improvement therein. Finally, it introduces a new direction of study in the popular {\em stochastic block model} where one has an incomplete stochastic block model matrix to recover the clusters.

This paper describes an expectation propagation (EP) method for multi-class classification with Gaussian processes that scales well to very large datasets. In such a method the estimate of the log-marginal-likelihood involves a sum across the data instances. This enables efficient training using stochastic gradients and mini-batches. When this type of training is used, the computational cost does not depend on the number of data instances $N$. Furthermore, extra assumptions in the approximate inference process make the memory cost independent of $N$. The consequence is that the proposed EP method can be used on datasets with millions of instances. We compare empirically this method with alternative approaches that approximate the required computations using variational inference. The results show that it performs similar or even better than these techniques, which sometimes give significantly worse predictive distributions in terms of the test log-likelihood. Besides this, the training process of the proposed approach also seems to converge in a smaller number of iterations.

We propose a Frank-Wolfe (FW) solver to optimize the symmetric nonnegative matrix factorization problem under a simplicial constraint. Compared with existing solutions, this algorithm is extremely simple to implement, and has almost no hyperparameters to be tuned. Building on the recent advances of FW algorithms in nonconvex optimization, we prove an $O(1/\varepsilon^2)$ convergence rate to stationary points, via a tight bound $\Theta(n^2)$ on the curvature constant. Numerical results demonstrate the effectiveness of our algorithm. As a side contribution, we construct a simple nonsmooth convex problem where the FW algorithm fails to converge to the optimum. This result raises an interesting question about necessary conditions of the success of the FW algorithm on convex problems.

Probability distributions produced by the cross-entropy loss for ordinal classification problems can possess undesired properties. We propose a straightforward technique to constrain discrete ordinal probability distributions to be unimodal via the use of the Poisson and binomial probability distributions. We evaluate this approach in the context of deep learning on two large ordinal image datasets, obtaining promising results.