### Who are alike? Use BigObject feature vector to find similarities

Cluster Analysis is a common technique to group a set of objects in the way that the objects in the same group share certain attributes. It's commonly used in marketing and sales planning to define market segmentations. Here at BigObject we adopt a simple approach to exploring the similarities between objects. We simply calculate the "Feature Vector" based on given attributes and use the score to determine which objects are "alike." This is a simple example to show how to use BigObject to extract product features and then find similar products in your retail data.

### Multi-armed bandits on implicit metric spaces

The multi-armed bandit (MAB) setting is a useful abstraction of many online learning tasks which focuses on the trade-off between exploration and exploitation. In this setting, an online algorithm has a fixed set of alternatives ("arms"), and in each round it selects one arm and then observes the corresponding reward. While the case of small number of arms is by now well-understood, a lot of recent work has focused on multi-armed bandits with (infinitely) many arms, where one needs to assume extra structure in order to make the problem tractable. In particular, in the Lipschitz MAB problem there is an underlying similarity metric space, known to the algorithm, such that any two arms that are close in this metric space have similar payoffs. In this paper we consider the more realistic scenario in which the metric space is *implicit* -- it is defined by the available structure but not revealed to the algorithm directly. Specifically, we assume that an algorithm is given a tree-based classification of arms. For any given problem instance such a classification implicitly defines a similarity metric space, but the numerical similarity information is not available to the algorithm. We provide an algorithm for this setting, whose performance guarantees (almost) match the best known guarantees for the corresponding instance of the Lipschitz MAB problem.

### Multi-Armed Bandits with Metric Movement Costs

We consider the non-stochastic Multi-Armed Bandit problem in a setting where there is a fixed and known metric on the action space that determines a cost for switching between any pair of actions. The loss of the online learner has two components: the first is the usual loss of the selected actions, and the second is an additional loss due to switching between actions. Our main contribution gives a tight characterization of the expected minimax regret in this setting, in terms of a complexity measure $\mathcal{C}$ of the underlying metric which depends on its covering numbers. In finite metric spaces with $k$ actions, we give an efficient algorithm that achieves regret of the form $\widetilde(\max\set{\mathcal{C}^{1/3}T^{2/3},\sqrt{kT}})$, and show that this is the best possible. Our regret bound generalizes previous known regret bounds for some special cases: (i) the unit-switching cost regret $\widetilde{\Theta}(\max\set{k^{1/3}T^{2/3},\sqrt{kT}})$ where $\mathcal{C}=\Theta(k)$, and (ii) the interval metric with regret $\widetilde{\Theta}(\max\set{T^{2/3},\sqrt{kT}})$ where $\mathcal{C}=\Theta(1)$. For infinite metrics spaces with Lipschitz loss functions, we derive a tight regret bound of $\widetilde{\Theta}(T^{\frac{d+1}{d+2}})$ where $d \ge 1$ is the Minkowski dimension of the space, which is known to be tight even when there are no switching costs.

### Extraction of feature lines on triangulated surfaces using morphological operators

Triangle meshes are a popular representation of surfaces in computer graphics. Our aim is to detect feature on such surfaces. Feature regions distinguish themselves by high curvature. We are using discrete curvature analysis on triangle meshes to obtain curvature values in every vertex of a mesh. These values are then thresholded resulting in a so called binary feature vector. By adapting morphological operators to triangle meshes, noise and artifacts can be removed from the feature. We introduce an operator that determines the skeleton of the feature region. This skeleton can then be converted into a graph representing the desired feature. Therefore a description of the surface's geometrical characteristics is constructed.

### From Frequency to Meaning: Vector Space Models of Semantics

Computers understand very little of the meaning of human language. This profoundly limits our ability to give instructions to computers, the ability of computers to explain their actions to us, and the ability of computers to analyse and process text. Vector space models (VSMs) of semantics are beginning to address these limits. This paper surveys the use of VSMs for semantic processing of text. We organize the literature on VSMs according to the structure of the matrix in a VSM. There are currently three broad classes of VSMs, based on term-document, word-context, and pair-pattern matrices, yielding three classes of applications. We survey a broad range of applications in these three categories and we take a detailed look at a specific open source project in each category. Our goal in this survey is to show the breadth of applications of VSMs for semantics, to provide a new perspective on VSMs for those who are already familiar with the area, and to provide pointers into the literature for those who are less familiar with the field.