In pattern recognition, the K-Nearest Neighbor algorithm (KNN) is a method for classifying objects based on the closest training examples in the feature space. KNN is a type of instance-based learning, or lazy learning where the function is only approximated locally and all computation is deferred until classification. The KNN algorithm is amongst the simplest of all machine learning algorithms: an object is classified by a majority vote of its neighbors, with the object being assigned to the class most common amongst its k nearest neighbors (k is a positive integer, typically small). If k 1, then the object is simply assigned to the class of its nearest neighbor [Source: Wikipedia]. In today's post, we explore the application of KNN to an automobile manufacturer that has developed prototypes for two new vehicles, a car and a truck.

In this paper, we consider clustering data that is assumed to come from one of finitely many pointed convex polyhedral cones. This model is referred to as the Union of Polyhedral Cones (UOPC) model. Similar to the Union of Subspaces (UOS) model where each data from each subspace is generated from a (unknown) basis, in the UOPC model each data from each cone is assumed to be generated from a finite number of (unknown) \emph{extreme rays}.To cluster data under this model, we consider several algorithms - (a) Sparse Subspace Clustering by Non-negative constraints Lasso (NCL), (b) Least squares approximation (LSA), and (c) K-nearest neighbor (KNN) algorithm to arrive at affinity between data points. Spectral Clustering (SC) is then applied on the resulting affinity matrix to cluster data into different polyhedral cones. We show that on an average KNN outperforms both NCL and LSA and for this algorithm we provide the deterministic conditions for correct clustering. For an affinity measure between the cones it is shown that as long as the cones are not very coherent and as long as the density of data within each cone exceeds a threshold, KNN leads to accurate clustering. Finally, simulation results on real datasets (MNIST and YaleFace datasets) depict that the proposed algorithm works well on real data indicating the utility of the UOPC model and the proposed algorithm.

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Last time we investigated the k-nearest-neighbors algorithm and the underlying idea that one can learn a classification rule by copying the known classification of nearby data points. This required that we view our data as sitting inside a metric space; that is, we imposed a kind of geometric structure on our data. One glaring problem is that there may be no reasonable way to do this. While we mentioned scaling issues and provided a number of possible metrics in our primer, a more common problem is that the data simply isn't numeric. For instance, a poll of US citizens might ask the respondent to select which of a number of issues he cares most about. There could be 50 choices, and there is no reasonable way to assign these numerical values so that all are equidistant in the resulting metric space. Another issue is that the quality of the data could be bad. For instance, there may be missing values for some attributes (e.g., a respondent may neglect to answer one or more questions).

K-nearest neighbors, or KNN, is a supervised learning algorithm for either classification or regression. It's super intuitive and has been applied to many types of problems. To make a personalized offer to one customer, you might employ KNN to find similar customers and base your offer on their purchase behaviors. KNN has also been applied to medical diagnosis and credit scoring. This is a post about the K-nearest neighbors algorithm and Python.

In an earlier post, I described work that I had initially done as an Insight Data Engineering Fellow. That work, now merged into Flink's master branch, was to do an efficient exact k-nearest neighbors (KNN) query using quadtrees. I have since worked on an approximate version of the KNN algorithm, and I will discuss one method I used for the approximate version using Z-value based hashing. For large and high dimensional data sets, an exact k-nearest neighbors query can become infeasible. There are many algorithms that reduce the dimensionality of the points by hashing them to lower dimensions.

In part 1 I gave a brief introduction to classification. Just to recap, classification is the problem of identifying which group a piece of data belongs to. It's an example of supervised learning because the classifier predicts the classes based on the training data fed to it. An example of classification is finding out whether an email is spam or not. More formally, classification is about finding out a model that distinguishes one class of data from another so as to predict the class of data whose class is unknown.

Wasserstein Discriminant Analysis (WDA) is a new supervised method that can improve classification of high-dimensional data by computing a suitable linear map onto a lower dimensional subspace. Following the blueprint of classical Linear Discriminant Analysis (LDA), WDA selects the projection matrix that maximizes the ratio of two quantities: the dispersion of projected points coming from different classes, divided by the dispersion of projected points coming from the same class. To quantify dispersion, WDA uses regularized Wasserstein distances, rather than cross-variance measures which have been usually considered, notably in LDA. Thanks to the the underlying principles of optimal transport, WDA is able to capture both global (at distribution scale) and local (at samples scale) interactions between classes. Regularized Wasserstein distances can be computed using the Sinkhorn matrix scaling algorithm; We show that the optimization of WDA can be tackled using automatic differentiation of Sinkhorn iterations. Numerical experiments show promising results both in terms of prediction and visualization on toy examples and real life datasets such as MNIST and on deep features obtained from a subset of the Caltech dataset.

Data science interviews are daunting, complicated gauntlets for many. But despite the ways they're evolving, the technical portion of the typical data science interview tends to be pretty predictable. The questions most candidates face usually cover behavior, mathematics, statistics, coding, and scenarios. However they differ in their particulars, those questions may be easier to answer if you can identify which bucket each one falls into. Here's a breakdown, and what you can do to prepare.

The result of standardization (or Z-score normalization) is that the features will be rescaled so that they'll have the properties of a standard normal distribution with Standardizing the features so that they are centered around 0 with a standard deviation of 1 is not only important if we are comparing measurements that have different units, but it is also a general requirement for many machine learning algorithms. Intuitively, we can think of gradient descent as a prominent example (an optimization algorithm often used in logistic regression, SVMs, perceptrons, neural networks etc.); with features being on different scales, certain weights may update faster than others since the feature values play a role in the weight updates Other intuitive examples include K-Nearest Neighbor algorithms and clustering algorithms that use, for example, Euclidean distance measures – in fact, tree-based classifier are probably the only classifiers where feature scaling doesn't make a difference. In fact, the only family of algorithms that I could think of being scale-invariant are tree-based methods. Let's take the general CART decision tree algorithm. Intuitively, we can see that it really doesn't matter on which scale this feature is (centimeters, Fahrenheit, a standardized scale – it really doesn't matter).