In this paper, we investigate the common scenario where every candidate item for recommendation is characterized by a maximum capacity, i.e., number of seats in a Point-of-Interest (POI) or size of an item's inventory. Despite the prevalence of the task of recommending items under capacity constraints in a variety of settings, to the best of our knowledge, none of the known recommender methods is designed to respect capacity constraints. To close this gap, we extend three state-of-the art latent factor recommendation approaches: probabilistic matrix factorization (PMF), geographical matrix factorization (GeoMF), and bayesian personalized ranking (BPR), to optimize for both recommendation accuracy and expected item usage that respects the capacity constraints. We introduce the useful concepts of user propensity to listen and item capacity. Our experimental results in real-world datasets, both for the domain of item recommendation and POI recommendation, highlight the benefit of our method for the setting of recommendation under capacity constraints.

Inferring macroscopic properties of physical systems from their microscopic description is an ongoing work in many disciplines of physics, like condensed matter, ultra cold atoms or quantum chromo dynamics. The most drastic changes in the macroscopic properties of a physical system occur at phase transitions, which often involve a symmetry breaking process. The theory of such phase transitions was formulated by Landau as a phenomenological model [1] and later devised from microscopic principles using the renormalization group [2, 3]. One can identify phases by knowledge of an order parameter which is zero in the disordered phase and nonzero in the ordered phase. Whereas in many known models the order parameter can be determined by symmetry considerations of the underlying Hamiltonian, there are states of matter where such a parameter can only be defined in a complicated non-local way [4]. These systems include topological states like topological insulators, quantum spin hall states [5] or quantum spin liquids [6].

We study distributed learning with the least squares regularization scheme in a reproducing kernel Hilbert space (RKHS). By a divide-and-conquer approach, the algorithm partitions a data set into disjoint data subsets, applies the least squares regularization scheme to each data subset to produce an output function, and then takes an average of the individual output functions as a final global estimator or predictor. We show with error bounds in expectation in both the $L^2$-metric and RKHS-metric that the global output function of this distributed learning is a good approximation to the algorithm processing the whole data in one single machine. Our error bounds are sharp and stated in a general setting without any eigenfunction assumption. The analysis is achieved by a novel second order decomposition of operator differences in our integral operator approach. Even for the classical least squares regularization scheme in the RKHS associated with a general kernel, we give the best learning rate in the literature.

Multicollinearity (Collinearity) is not a new term especially when dealing with multiple regression models. This phenomenon of relationship in between one response variable with the set of predictor variables also include models like classification and regression trees as well as neural networks. Collinearity is infamously famous for inflating the variance of at least one estimated regression coefficient, which can cause the model to predict erroneously and in a business setup it can have an unrepairable consequence. So, the next logical question is how to identify collinearity? In this article we will only talk about the Variance Inflation Factor(VIF) identification technique which is very useful for identify high multicollinearity among the predictor variables when working with MLR (Multiple Linear Regression Models).

This post is a simple yet illustrative application of K-means clustering technique. Using K-means clustering, we will perform quantization of colours present in the image which will further help in compressing the image. In a coloured image, each pixel is of size 3 bytes (RGB), where each colour can have intensity values from 0 to 255. Following combinatorics, the total number of colours which can be represented are 256*256*256. Practically, we are able to visualize only a few colours in an image.

The first step is often the hardest to take, and when given too much choice in terms of direction it can often be debilitating. This post aims to take a newcomer from minimal knowledge of machine learning in Python all the way to knowledgeable practitioner in 7 steps, all while using freely available materials and resources along the way. The prime objective of this outline is to help you wade through the numerous free options that are available; there are many, to be sure, but which are the best? What is the best order in which to use selected resources? It would probably be helpful to have some basic understanding of one or both of the first 2 topics, but even that won't be necessary; some extra time spent on the earlier steps should help compensate.

At Flickr, we understand that the value in our image corpus is only unlocked when our members can find photos and photographers that inspire them, so we strive to enable the discovery and appreciation of new photos. To further that effort, today we are introducing similarity search on Flickr. If you hover over a photo on a search result page, you will reveal a "…" button that exposes a menu that gives you the option to search for photos similar to the photo you are currently viewing. In many ways, photo search is very different from traditional web or text search. First, the goal of web search is usually to satisfy a particular information need, while with photo search the goal is often one of discovery; as such, it should be delightful as well as functional.

Context: One of the black arts of data mining is learning the magic parameters which control the learners. In software analytics, at least for defect prediction, several methods, like grid search and differential evolution (DE), have been proposed to learn these parameters, which has been proved to be able to improve the performance scores of learners. Objective: We want to evaluate which method can find better parameters in terms of performance score and runtime cost. Methods: This paper compares grid search to differential evolution, which is an evolutionary algorithm that makes extensive use of stochastic jumps around the search space. Results: We find that the seemingly complete approach of grid search does no better, and sometimes worse, than the stochastic search. When repeated 20 times to check for conclusion validity, DE was over 210 times faster than grid search to tune Random Forests on 17 testing data sets with F-Measure Conclusions: These results are puzzling: why does a quick partial search be just as effective as a much slower, and much more, extensive search? To answer that question, we turned to the theoretical optimization literature. Bergstra and Bengio conjecture that grid search is not more effective than more randomized searchers if the underlying search space is inherently low dimensional. This is significant since recent results show that defect prediction exhibits very low intrinsic dimensionality-- an observation that explains why a fast method like DE may work as well as a seemingly more thorough grid search. This suggests, as a future research direction, that it might be possible to peek at data sets before doing any optimization in order to match the optimization algorithm to the problem at hand.

Non-linear kernel methods can be approximated by fast linear ones using suitable explicit feature maps allowing their application to large scale problems. To this end, explicit feature maps of kernels for vectorial data have been extensively studied. As many real-world data is structured, various kernels for complex data like graphs have been proposed. Indeed, many of them directly compute feature maps. However, the kernel trick is employed when the number of features is very large or the individual vertices of graphs are annotated by real-valued attributes. Can we still compute explicit feature maps efficiently under these circumstances? Triggered by this question, we investigate how general convolution kernels are composed from base kernels and construct corresponding feature maps. We apply our results to widely used graph kernels and analyze for which kernels and graph properties computation by explicit feature maps is feasible and actually more efficient. In particular, we derive feature maps for random walk and subgraph matching kernels and apply them to real-world graphs with discrete labels. Thereby, our theoretical results are confirmed experimentally by observing a phase transition when comparing running time with respect to label diversity, walk lengths and subgraph size, respectively. Moreover, we derive approximative, explicit feature maps for state-of-the-art kernels supporting real-valued attributes including the GraphHopper and Graph Invariant kernels. In extensive experiments we show that our approaches often achieve a classification accuracy close to the exact methods based on the kernel trick, but require only a fraction of their running time.

A framework is presented for unsupervised learning of representations based on infomax principle for large-scale neural populations. We use an asymptotic approximation to the Shannon's mutual information for a large neural population to demonstrate that a good initial approximation to the global information-theoretic optimum can be obtained by a hierarchical infomax method. Starting from the initial solution, an efficient algorithm based on gradient descent of the final objective function is proposed to learn representations from the input datasets, and the method works for complete, overcomplete, and undercomplete bases. As confirmed by numerical experiments, our method is robust and highly efficient for extracting salient features from input datasets. Compared with the main existing methods, our algorithm has a distinct advantage in both the training speed and the robustness of unsupervised representation learning. Furthermore, the proposed method is easily extended to the supervised or unsupervised model for training deep structure networks.