Another quite standard technique is called'Cluster Validity Index', Here are the two famous papers, Part1 [3] and Part2 [4]. Basically these methods perform internal evaluation of the quality of clusters, after the clustering is performed. For e.g. one common method called Dunn's method

Inora is not claiming that the free version of the RAE Linear Regression software can solve complex data challenges. The linear regression is just an application of the generalized core Math Engine to that specific task (y mx b). Of course, the free version is limited to a 2-class task (finding what is line and what is not line). The Inora Math Engine is also capable of detecting and analyzing multiple patterns in any size data set. So, even though the free linear regression software is limited, it will demonstrate how the Math Engine core is different from traditional statistics, random sample and Least Squares approaches.

If you've been using R for a while, and you've been working with basic data visualization and data exploration techniques, the next logical step is to start learning some machine learning. To help you begin learning about machine learning in R, I'm going to introduce you to an R package: the caret package. We'll build a very simple machine learning model as a way to learn some of caret's basic syntax and functionality. But before diving into caret, let's quickly discuss what machine learning is and why we use it. Machine learning is the study of data-driven, computational methods for making inferences and predictions. Without going into extreme depth here, let's unpack that by looking at an example.

I'm developing a program which uses a multi step classification process, with the idea being that after an initial classification is done, a new set of pixels are chosen by the program to be classed as training data for another iteration. I'm trying to figure out which classifiers do better with training data which is closer to the decision boundary, and which do better with training data which is more typical of the class it represents

Spring is the time when many sports fans are glued to their brackets in hopes of asserting their ability to correctly select amongst the 150 quintillion permutations of Teams who will win the NCAA Basketball Championship (see our blog post on this subject). My personal highlight of the spring sports calendar is the Masters Golf Tournament, which is held every year at the Augusta National Golf Club in Georgia. The professional golf schedule contains four major tournaments each year: The Masters, The US Open, The Open Championship, and The PGA Championship. Of these tournaments, only the Masters is played on the same course every year and its champion is awarded the iconic Masters Champion green jacket. Having participated in a number of fantasy sports leagues and being a Data Scientist at MapR gives me a unique perspective on my approach to choosing who I think will most likely "win" the tournament.

Understanding the behaviour of heuristic search methods is a challenge. This even holds for simple local search methods such as 2-OPT for the Traveling Salesperson problem. In this paper, we present a general framework that is able to construct a diverse set of instances that are hard or easy for a given search heuristic. Such a diverse set is obtained by using an evolutionary algorithm for constructing hard or easy instances that are diverse with respect to different features of the underlying problem. Examining the constructed instance sets, we show that many combinations of two or three features give a good classification of the TSP instances in terms of whether they are hard to be solved by 2-OPT.

As we enter into the big data age and an avalanche of images have become readily available, recognition systems face the need to move from close, lab settings where the number of classes and training data are fixed, to dynamic scenarios where the number of categories to be recognized grows continuously over time, as well as new data providing useful information to update the system. Recent attempts, like the open world recognition framework, tried to inject dynamics into the system by detecting new unknown classes and adding them incrementally, while at the same time continuously updating the models for the known classes. incrementally adding new classes and detecting instances from unknown classes, while at the same time continuously updating the models for the known classes. In this paper we argue that to properly capture the intrinsic dynamic of open world recognition, it is necessary to add to these aspects (a) the incremental learning of the underlying metric, (b) the incremental estimate of confidence thresholds for the unknown classes, and (c) the use of local learning to precisely describe the space of classes. We extend three existing metric learning algorithms towards these goals by using online metric learning. Experimentally we validate our approach on two large-scale datasets in different learning scenarios. For all these scenarios our proposed methods outperform their non-online counterparts. We conclude that local and online learning is important to capture the full dynamics of open world recognition.

Research on manifold learning within a density ridge estimation framework has shown great potential in recent work for both estimation and de-noising of manifolds, building on the intuitive and well-defined notion of principal curves and surfaces. However, the problem of unwrapping or unfolding manifolds has received relatively little attention within the density ridge approach, despite being an integral part of manifold learning in general. This paper proposes two novel algorithms for unwrapping manifolds based on estimated principal curves and surfaces for one- and multi-dimensional manifolds respectively. The methods of unwrapping are founded in the realization that both principal curves and principal surfaces will have inherent local maxima of the probability density function. Following this observation, coordinate systems that follow the shape of the manifold can be computed by following the integral curves of the gradient flow of a kernel density estimate on the manifold. Furthermore, since integral curves of the gradient flow of a kernel density estimate is inherently local, we propose to stitch together local coordinate systems using parallel transport along the manifold. We provide numerical experiments on both real and synthetic data that illustrates clear and intuitive unwrapping results comparable to state-of-the-art manifold learning algorithms.

Finding an informative subset of a large collection of data points or models is at the center of many problems in computer vision, recommender systems, bio/health informatics as well as image and natural language processing. Given pairwise dissimilarities between the elements of a `source set' and a `target set,' we consider the problem of finding a subset of the source set, called representatives or exemplars, that can efficiently describe the target set. We formulate the problem as a row-sparsity regularized trace minimization problem. Since the proposed formulation is, in general, NP-hard, we consider a convex relaxation. The solution of our optimization finds representatives and the assignment of each element of the target set to each representative, hence, obtaining a clustering. We analyze the solution of our proposed optimization as a function of the regularization parameter. We show that when the two sets jointly partition into multiple groups, our algorithm finds representatives from all groups and reveals clustering of the sets. In addition, we show that the proposed framework can effectively deal with outliers. Our algorithm works with arbitrary dissimilarities, which can be asymmetric or violate the triangle inequality. To efficiently implement our algorithm, we consider an Alternating Direction Method of Multipliers (ADMM) framework, which results in quadratic complexity in the problem size. We show that the ADMM implementation allows to parallelize the algorithm, hence further reducing the computational time. Finally, by experiments on real-world datasets, we show that our proposed algorithm improves the state of the art on the two problems of scene categorization using representative images and time-series modeling and segmentation using representative~models.

This paper explores and analyzes two randomized designs for robust Principal Component Analysis (PCA) employing low-dimensional data sketching. In one design, a data sketch is constructed using random column sampling followed by low dimensional embedding, while in the other, sketching is based on random column and row sampling. Both designs are shown to bring about substantial savings in complexity and memory requirements for robust subspace learning over conventional approaches that use the full scale data. A characterization of the sample and computational complexity of both designs is derived in the context of two distinct outlier models, namely, sparse and independent outlier models. The proposed randomized approach can provably recover the correct subspace with computational and sample complexity that are almost independent of the size of the data. The results of the mathematical analysis are confirmed through numerical simulations using both synthetic and real data.