Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

Pattern Recognition and Machine Learning

Data Mining - Concepts and Techniques.

Feature matching is at the base of many computer vision problems, such as object recognition or structure from motion. Current methods rely on costly descriptors for detection and matching. In this paper, we propose a very fast binary descriptor based on BRIEF, called ORB, which is rotation invariant and resistant to noise. We demonstrate through experiments how ORB is at two orders of magnitude faster than SIFT, while performing as well in many situations. The efficiency is tested on several real-world applications, including object detection and patch-tracking on a smart phone.

ORB: An efficient alternative to SIFT or SURF

We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.

Random graphs

We present two algorithms for the approximate nearest neighbor problem in high-dimensional spaces. For data sets of size n living in R d , the algorithms require space that is only polynomial in n and d, while achieving query times that are sub-linear in n and polynomial in d. We also show applications to other high-dimensional geometric problems, such as the approximate minimum spanning tree. The article is based on the material from the authors' STOC'98 and FOCS'01 papers. It unifies, generalizes and simplifies the results from those papers.

/pdf/approximate-nearest-neighbors-towards-removing-the-curse-of-27lmlz5prr.pdf

Approximate nearest neighbors: towards removing the curse of dimensionality

Many 0/1 datasets have a very large number of variables; on the other hand, they are sparse and the dependency structure of the variables is simpler than the number of variables would suggest. Defining the effective dimensionality of such a dataset is a nontrivial problem. We consider the problem of defining a robust measure of dimension for 0/1 datasets, and show that the basic idea of fractal dimension can be adapted for binary data. However, as such the fractal dimension is difficult to interpret. Hence we introduce the concept of normalized fractal dimension. For a dataset $D$, its normalized fractal dimension is the number of columns in a dataset $D'$ with independent columns and having the same (unnormalized) fractal dimension as $D$. The normalized fractal dimension measures the degree of dependency structure of the data. We study the properties of the normalized fractal dimension and discuss its computation. We give empirical results on the normalized fractal dimension, comparing it against baseline measures such as PCA. We also study the relationship of the dimension of the whole dataset and the dimensions of subgroups formed by clustering. The results indicate interesting differences between and within datasets.

What is the dimension of your binary data

The problem of assessing the significance of data mining results on high-dimensional 0-1 data sets has been studied extensively in the literature. For problems such as mining frequent sets and finding correlations, significance testing can be done by, e.g., chi-square tests, or many other methods. However, the results of such tests depend only on the specific attributes and not on the dataset as a whole. Moreover, the tests are more difficult to apply to sets of patterns or other complex results of data mining. In this paper, we consider a simple randomization technique that deals with this shortcoming. The approach consists of producing random datasets that have the same row and column margins with the given dataset, computing the results of interest on the randomized instances, and comparing them against the results on the actual data. This randomization technique can be used to assess the results of many different types of data mining algorithms, such as frequent sets, clustering, and rankings. To generate random datasets with given margins, we use variations of a Markov chain approach, which is based on a simple swap operation. We give theoretical results on the efficiency of different randomization methods, and apply the swap randomization method to several well-known datasets. Our results indicate that for some datasets the structure discovered by the data mining algorithms is a random artifact, while for other datasets the discovered structure conveys meaningful information.

/pdf/assessing-data-mining-results-via-swap-randomization-44trjwb7pe.pdf

Assessing data mining results via swap randomization

The process of opinion formation through synthesis and contrast of different viewpoints has been the subject of many studies in economics and social sciences. Today, this process manifests itself also in online social networks and social media. The key characteristic of successful promotion campaigns is that they take into consideration such opinion-formation dynamics in order to create a overall favorable opinion about a specific information item, such as a person, a product, or an idea. In this paper, we adopt a well-established model for social-opinion dynamics and formalize the campaigndesign problem as the problem of identifying a set of target individuals whose positive opinion about an information item will maximize the overall positive opinion for the item in the social network. We call this problem Campaign. We study the complexity of the Campaign problem, and design algorithms for solving it. Our experiments on real data demonstrate the efficiency and practical utility of our algorithms.

/pdf/opinion-maximization-in-social-networks-2608qf1y7q.pdf

Opinion Maximization in Social Networks.

Sequence segmentation and dimensionality reduction have been used as methods for studying high-dimensional sequences — they both reduce the complexity of the representation of the original data. In this paper we study the interplay of these two techniques. We formulate the problem of segmenting a sequence while modeling it with a basis of small size, thus essentially reducing the dimension of the input sequence. We give three different algorithms for this problem: all combine existing methods for sequence segmentation and dimensionality reduction. For two of the proposed algorithms we prove guarantees for the quality of the solutions obtained. We describe experimental results on synthetic and real datasets, including data on exchange rates and genomic sequences. Our experiments show that the algorithms indeed discover underlying structure in the data, including both segmental structure and interdependencies between the dimensions.

http://www.siam.org/meetings/sdm06/proceedings/034BinghamE.pdf

Segmentation and Dimensionality Reduction

Set value attributes are a concise and natural way to model complex data sets. Modern Object Relational systems support set value attributes and allow various query capabilities on them. In this paper we initiate a formal study of indexing techniques for set value attributes based on similarity, for suitably defined notions of similarity between sets. Such techniques are necessary in modern applications such as recommendations through collaborative filtering and automated advertising. Our techniques are probabilistic and approximate in nature. As a design principle we create structures that make use of well known and widely used data structuring techniques, as a means to ease integration with existing infrastructure.We show how the problem of indexing a collection of sets based on similarity can be reduced to the problem of indexing suitably encoded (in a way that preserves similarity) binary vectors in Hamming space thus, reducing the problem to one of similarity query processing in Hamming space. Then, we introduce and analyze two data structure primitives that we use in cooperation to perform similarity query processing in a Hamming space. We show how the resulting indexing technique can be optimized for properties of interest by formulating constraint optimization problems based on the space one is willing to devote for indexing. Finally we present experimental results from a prototype implementation of our techniques using real life datasets exploring the accuracy and efficiency of our overall approach as well as the quality of our solutions to problems related to the optimization of the indexing scheme.

Aristides Gionis

Papers

What is the dimension of your binary data

Assessing data mining results via swap randomization

Opinion Maximization in Social Networks.

Segmentation and Dimensionality Reduction

Efficient and tumble similar set retrieval