Results

**1 - 5**of**5**### Efficient Learning on Point Sets

"... Abstract—Recently several methods have been proposed to learn from data that are represented as sets of multidimensional vectors. Such algorithms usually suffer from the high demand of computational resources, making them impractical on large-scale problems. We propose to solve this problem by conde ..."

Abstract
- Add to MetaCart

(Show Context)
Abstract—Recently several methods have been proposed to learn from data that are represented as sets of multidimensional vectors. Such algorithms usually suffer from the high demand of computational resources, making them impractical on large-scale problems. We propose to solve this problem by condensing i.e. reducing the sizes of the sets while maintaining the learning performance. Three methods are examined and evaluated with a wide spectrum of set learning algorithms on several large-scale image data sets. We discover that k-Means can successfully achieve the goal of condensing. In many cases, k-Means condens-ing can improve the algorithms ’ speed, space requirements, and surprisingly, learning performances simultaneously. I.

### On Learning from Collective Data

, 2013

"... In many machine learning problems and application domains, the data are naturally organized by groups. For example, a video sequence is a group of images, an image is a group of patches, a document is a group of paragraphs/words, and a community is a group of people. We call them the collective data ..."

Abstract
- Add to MetaCart

(Show Context)
In many machine learning problems and application domains, the data are naturally organized by groups. For example, a video sequence is a group of images, an image is a group of patches, a document is a group of paragraphs/words, and a community is a group of people. We call them the collective data. In this thesis, we study how and what we can learn from collective data. Usually, machine learning focuses on individual objects, each of which is described by a feature vector and studied as a point in some metric space. When approaching collective data, researchers often reduce the groups into vectors to which traditional methods can be applied. We, on the other hand, will try to develop machine learning methods that

### 1Dissimilarity-based Sparse Subset Selection

"... Abstract—Finding an informative subset of a large number of data points or models is at the center of many problems in machine learning, computer vision, bio/health informatics and image/signal processing. Given pairwise dissimilarities between the elements of a ‘source set ’ and a ‘target set, ’ we ..."

Abstract
- Add to MetaCart

Abstract—Finding an informative subset of a large number of data points or models is at the center of many problems in machine learning, computer vision, bio/health informatics and image/signal 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, an NP-hard problem, we consider a convex relaxation. The solution of our proposed optimization program finds the representatives and the probability that each element of the target set is associated with the representatives. 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, the solution of our proposed optimization program finds representatives from all groups and reveals clustering of the sets. In addition, we show that our proposed formulation can effectively deal with outliers. Our algorithm works with arbitrary dissimilarities, which can be asymmetric or violate the triangle inequality. To efficiently implement our proposed 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 cost. 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. Index Terms—Representatives, pairwise dissimilarities, simultaneous sparse recovery, encoding, convex programming, ADMM optimization, sampling, clustering, outlier detection, model identification, time-series data, video summarization, activity cluster-ing, scene recognition F 1

### arXiv Manuscript No.1306.6677 Supersparse Linear Integer Models for Interpretable Classification

, 2014

"... Abstract Scoring systems are classification models that only require users to add, subtract and multiply a few meaningful numbers to make a prediction. These models are often used because they are practical and interpretable. In this paper, we introduce an off-the-shelf tool to create scoring system ..."

Abstract
- Add to MetaCart

(Show Context)
Abstract Scoring systems are classification models that only require users to add, subtract and multiply a few meaningful numbers to make a prediction. These models are often used because they are practical and interpretable. In this paper, we introduce an off-the-shelf tool to create scoring systems that both accurate and interpretable, known as a Supersparse Linear Integer Model (SLIM). SLIM is a discrete optimization problem that minimizes the 0-1 loss to encourage a high level of accuracy, regularizes the `0-norm to encourage a high level of sparsity, and constrains coefficients to a set of interpretable values. We illustrate the practical and interpretable nature of SLIM scoring systems through applications in medicine and criminology, and show that they are are accurate and sparse in comparison to state-of-the-art classification models using numerical experiments.

### 4. TITLE AND SUBTITLE On Learning from Collective Data

, 2013

"... Public reporting burden for the collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments ..."

Abstract
- Add to MetaCart

(Show Context)
Public reporting burden for the collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information,