The mean-shift algorithm is a popular algorithm in computer vision and image processing. It can also be cast as a minimum gamma-divergence estimation. In this paper we focus on the "blurring" mean shift algorithm, which is one version of the mean-shift process that successively blurs the dataset. The analysis of the blurring mean-shift is relatively more complicated compared to the nonblurring version, yet the algorithm convergence and the estimation consistency have not been well studied in the literature. In this paper we prove both the convergence and the consistency of the blurring mean-shift. We also perform simulation studies to compare the efficiency of the blurring and the nonblurring versions of the mean-shift algorithms. Our results show that the blurring mean-shift has more efficiency.

We define the notion of rational closure in the context of Description Logics extended with a tipicality operator. We start from ALC+T, an extension of ALC with a typicality operator T: intuitively allowing to express concepts of the form T(C), meant to select the "most normal" instances of a concept C. The semantics we consider is based on rational model. But we further restrict the semantics to minimal models, that is to say, to models that minimise the rank of domain elements. We show that this semantics captures exactly a notion of rational closure which is a natural extension to Description Logics of Lehmann and Magidor's original one. We also extend the notion of rational closure to the Abox component. We provide an ExpTime algorithm for computing the rational closure of an Abox and we show that it is sound and complete with respect to the minimal model semantics.

Understanding human activities and object affordances are two very important skills, especially for personal robots which operate in human environments. In this work, we consider the problem of extracting a descriptive labeling of the sequence of sub-activities being performed by a human, and more importantly, of their interactions with the objects in the form of associated affordances. Given a RGB-D video, we jointly model the human activities and object affordances as a Markov random field where the nodes represent objects and sub-activities, and the edges represent the relationships between object affordances, their relations with sub-activities, and their evolution over time. We formulate the learning problem using a structural support vector machine (SSVM) approach, where labelings over various alternate temporal segmentations are considered as latent variables. We tested our method on a challenging dataset comprising 120 activity videos collected from 4 subjects, and obtained an accuracy of 79.4% for affordance, 63.4% for sub-activity and 75.0% for high-level activity labeling. We then demonstrate the use of such descriptive labeling in performing assistive tasks by a PR2 robot.

In high-dimensional data analysis, penalized likelihood estimators are shown to provide superior results in both variable selection and parameter estimation. A new algorithm, APPLE, is proposed for calculating the Approximate Path for Penalized Likelihood Estimators. Both the convex penalty (such as LASSO) and the nonconvex penalty (such as SCAD and MCP) cases are considered. The APPLE efficiently computes the solution path for the penalized likelihood estimator using a hybrid of the modified predictor-corrector method and the coordinate-descent algorithm. APPLE is compared with several well-known packages via simulation and analysis of two gene expression data sets.

I introduce Forecastable Component Analysis (ForeCA), a novel dimension reduction technique for temporally dependent signals. Based on a new forecastability measure, ForeCA finds an optimal transformation to separate a multivariate time series into a forecastable and an orthogonal white noise space. I present a converging algorithm with a fast eigenvector solution. Applications to financial and macroeconomic time series show that ForeCA can successfully discover informative structure, which can be used for forecasting as well as classification. The R package ForeCA accompanies this work and is publicly available on CRAN.

March 22, 2018 Abstract We propose a new algorithm to do posterior sampling of Kingman's coalescent, based upon the Particle Markov Chain Monte Carlo methodology. Specifically, the algorithm is an instantiation of the Particle Gibbs Sampling method, which alternately samples coalescent times conditioned on coalescent tree structures, and tree structures conditioned on coalescent times via the conditional Sequential Monte Carlo procedure. We implement our algorithm as a C package, and demonstrate its utility via a parameter estimation task in population genetics on both single-and multiple-locus data. The experiment results show that the proposed algorithm performs comparable to or better than several well-developed methods. 1 Introduction Data shows hierarchical structure in many domains. For example, computer vision problems often involve hierarchical representation of images [Lee et al., 2009]. In text mining, documents can be modeled as hierarchical generative processes [Blei et al., 2003, Teh et al., 2006]. Algorithms that can effectively deal with hierarchical structure play an important role in uncovering the intrinsic structures of data.

Much work has been done on feature selection. Existing methods are based on document frequency, such as Chi-Square Statistic, Information Gain etc. However, these methods have two shortcomings: one is that they are not reliable for low-frequency terms, and the other is that they only count whether one term occurs in a document and ignore the term frequency. Actually, high-frequency terms within a specific category are often regards as discriminators. This paper focuses on how to construct the feature selection function based on term frequency, and proposes a new approach based on $t$-test, which is used to measure the diversity of the distributions of a term between the specific category and the entire corpus. Extensive comparative experiments on two text corpora using three classifiers show that our new approach is comparable to or or slightly better than the state-of-the-art feature selection methods (i.e., $\chi^2$, and IG) in terms of macro-$F_1$ and micro-$F_1$.

The effect of errors in variables in quantization is investigated. We prove general exact and non-exact oracle inequalities with fast rates for an empirical minimization based on a noisy sample $Z_i=X_i+\epsilon_i,i=1,\ldots,n$, where $X_i$ are i.i.d. with density $f$ and $\epsilon_i$ are i.i.d. with density $\eta$. These rates depend on the geometry of the density $f$ and the asymptotic behaviour of the characteristic function of $\eta$. This general study can be applied to the problem of $k$-means clustering with noisy data. For this purpose, we introduce a deconvolution $k$-means stochastic minimization which reaches fast rates of convergence under standard Pollard's regularity assumptions.

There are many methods developed to approximate a cloud of vectors embedded in high-dimensional space by simpler objects: starting from principal points and linear manifolds to self-organizing maps, neural gas, elastic maps, various types of principal curves and principal trees, and so on. For each type of approximators the measure of the approximator complexity was developed too. These measures are necessary to find the balance between accuracy and complexity and to define the optimal approximations of a given type. We propose a measure of complexity (geometrical complexity) which is applicable to approximators of several types and which allows comparing data approximations of different types.

In this paper, we firstly give a brief introduction of expectation maximization (EM) algorithm, and then discuss the initial value sensitivity of expectation maximization algorithm. Subsequently, we give a short proof of EM's convergence. Then, we implement experiments with the expectation maximization algorithm (We implement all the experiments on Gaussion mixture model (GMM)). Our experiment with expectation maximization is performed in the following three cases: initialize randomly; initialize with result of K-means; initialize with result of K-medoids. The experiment result shows that expectation maximization algorithm depend on its initial state or parameters. And we found that EM initialized with K-medoids performed better than both the one initialized with K-means and the one initialized randomly.