This is a preliminary theoretical discussion on the computational requirements of the state of the art smoothed particle hydrodynamics (SPH) from the optics of pattern recognition and artificial intelligence. It is pointed out in the present paper that, when including anisotropy detection to improve resolution on shock layer, SPH is a very peculiar case of unsupervised machine learning. On the other hand, the free particle nature of SPH opens an opportunity for artificial intelligence to study particles as agents acting in a collaborative framework in which the timed outcomes of a fluid simulation forms a large knowledge base, which might be very attractive in computational astrophysics phenomenological problems like self-propagating star formation.

Cepstral features have been widely used in audio applications. Domain knowledge has played an important role in designing different types of cepstral features proposed in the literature. In this paper, we present a novel approach for learning optimized cepstral features directly from audio data to better discriminate between different categories of signals in classification tasks. We employ multi-layer feedforward neural networks to model the cepstral feature extraction process. The network weights are initialized to replicate a reference cepstral feature like the mel frequency cepstral coefficient. We then propose a embedded approach that integrates feature learning with the training of a support vector machine (SVM) classifier. A single optimization problem is formulated where the feature and classifier variables are optimized simultaneously so as to refine the initial features and minimize the classification risk. Experimental results have demonstrated the effectiveness of the proposed feature learning approach, outperforming competing methods by a large margin on benchmark data.

Matrix factorization (MF) is a popular collaborative filtering approach for recommender systems due to its simplicity and effectiveness. Existing MF methods either assume that all latent features are uncorrelated or assume that all are correlated. To address the important issue of what structure should be imposed on the features, we investigate the covariance matrix of the latent features learned from real data. Based on the findings, we propose an MF model with a sparse covariance prior which favors a sparse yet non-diagonal covariance matrix. Not only can this reflect the semantics more faithfully, but imposing sparsity can also have a side effect of preventing overfitting. Starting from a probabilistic generative model with a sparse covariance prior, we formulate the model inference problem as a maximum a posteriori (MAP) estimation problem. The optimization procedure makes use of stochastic gradient descent and majorization-minimization. For empirical validation, we conduct experiments using the MovieLens and Netflix datasets to compare the proposed method with two strong baselines which use different priors. Experimental results show that our sparse covariance prior can lead to performance improvement.

We propose to measure statistical dependence between two random variables by the mutual information dimension (MID), and present a scalable parameter-free estimation method for this task. Supported by sound dimension theory, our method gives an effective solution to the problem of detecting interesting relationships of variables in massive data, which is nowadays a heavily studied topic in many scientific disciplines. Different from classical Pearson's correlation coefficient, MID is zero if and only if two random variables are statistically independent and is translation and scaling invariant. We experimentally show superior performance of MID in detecting various types of relationships in the presence of noise data. Moreover, we illustrate that MID can be effectively used for feature selection in regression.

We study an interesting phenomenon of social influence locality in a large microblogging network, which suggests that users' behaviors are mainly influenced by close friends in their ego networks. We provide a formal definition for the notion of social influence locality and develop two instantiation functions based on pairwise influence and structural diversity. The defined influence locality functions have strong predictive power. Without any additional features, we can obtain a F1-score of 71.65% for predicting users' retweet behaviors by training a logistic regression classifier based on the defined functions. Our analysis also reveals several intriguing discoveries. For example, though the probability of a user retweeting a microblog is positively correlated with the number of friends who have retweeted the microblog, it is surprisingly negatively correlated with the number of connected circles that are formed by those friends.

In past decade, more and more data are collected from multiple sources or represented by multiple views, where different views describe distinct perspectives of the data. Although each view could be individually used for finding patterns by clustering, the clustering performance could be more accurate by exploring the rich information among multiple views. Several multi-view clustering methods have been proposed to unsupervised integrate different views of data. However, they are graph based approaches, e.g. based on spectral clustering, such that they cannot handle the large-scale data. How to combine these heterogeneous features for unsupervised large-scale data clustering has become a challenging problem. In this paper, we propose a new robust large-scale multi-view clustering method to integrate heterogeneous representations of large-scale data. We evaluate the proposed new methods by six benchmark data sets and compared the performance with several commonly used clustering approaches as well as the baseline multi-view clustering methods. In all experimental results, our proposed methods consistently achieve superiors clustering performances.

Parsing human poses in images is fundamental in extracting critical visual information for artificial intelligent agents. Our goal is to learn self-contained body part representations from images, which we call visual symbols, and their symbol-wise geometric contexts in this parsing process. Each symbol is individually learned by categorizing visual features leveraged by geometric information. In the categorization, we use Latent Support Vector Machine followed by an efficient cross validation procedure. Then, these symbols naturally define geometric contexts of body parts in a fine granularity for effective inference. When the structure of the compositional parts is a tree, we derive an efficient approach to estimating human poses in images. Experiments on two large datasets suggest our approach outperforms state of the art methods.

Bag-of-Words approach has played an important role in recent works for image classification. In consideration of efficiency, most methods use k-means clustering to generate the codebook. The obtained codebooks often lose the cluster size and shape information with distortion errors and low discriminative power. Though some efforts have been made to optimize codebook in sparse coding, they usually incur higher computational cost. Moreover, they ignore the correlations between codes in the following coding stage, that leads to low discriminative power of the final representation. In this paper, we propose a bilevel visual words coding approach in consideration of representation ability, discriminative power and efficiency. In the bilevel codebook generation stage, k-means and an efficient spectral clustering are respectively run in each level by taking both class information and the shapes of each visual word cluster into account. To obtain discriminative representation in the coding stage, we design a certain localized coding rule with bilevel codebook to select local bases. To further achieve an efficient coding referring to this rule, an online method is proposed to efficiently learn a projection of local descriptor to the visual words in the codebook. After projection, coding can be efficiently completed by a low dimensional localized soft-assignment. Experimental results show that our proposed bilevel visual words coding approach outperforms the state-of-the-art approaches for image classification.

The Nyström method is a well known sampling based low-rank matrix approximation approach. It is usually considered to be originated from the numerical treatment of integral equations and eigendecomposition of matrices. In this paper, we present a novel point of view for the Nyström approximation. We show that theoretically the Nyström method can be regraded as a set of point-wise ordinary least square linear regressions of the kernel matrix, sharing the same design matrix. With the new interpretation, we are able to analyze the approximation quality based on the fulfillment of the homoscedasticity assumption and explain the success and deficiency of various sampling methods. We also empirically show that positively skewed explanatory variable distributions can lead to heteroscedasticity. Based on this discovery, we propose to use non-symmetric explanatory functions to improve the quality of the Nyström approximation with almost no extra computational cost. Experiments show that positively skewed datasets widely exist, and our method exhibits good improvements on these datasets.

We study robust high-dimensional estimation of generalized linear models (GLMs); where a small number k of the n observations can be arbitrarily corrupted, and where the true parameter is high dimensional in the “p >> n” regime, but only has a small number s of non-zero entries. There has been some recent work connecting robustness and sparsity, in the context of linear regression with corrupted observations, by using an explicitly modeled outlier response vector that is assumed to be sparse. Interestingly, we show, in the GLM setting, such explicit outlier response modeling can be performed in two distinct ways. For each of these two approaches, we give l 2 error bounds for parameter estimation for general values of the tuple (n,p,s,k).