Xiaoye Jiang

Human action recognition by learning bases of action attributes and parts

In this work, we propose to use attributes and parts for recognizing human actions in still images. We define action attributes as the verbs that describe the properties of human actions, while the parts of actions are objects and poselets that are closely related to the actions. We jointly model the attributes and parts by learning a set of sparse bases that are shown to carry much semantic meaning. Then, the attributes and parts of an action image can be reconstructed from sparse coefficients with respect to the learned bases. This dual sparsity provides theoretical guarantee of our bases learning and feature reconstruction approach. On the PASCAL action dataset and a new “Stanford 40 Actions” dataset, we show that our method extracts meaningful high-order interactions between attributes and parts in human actions while achieving state-of-the-art classification performance.

Statistical ranking and combinatorial Hodge theory

We propose a technique that we call HodgeRank for ranking data that may be incomplete and imbalanced, characteristics common in modern datasets coming from e-commerce and internet applications. We are primarily interested in cardinal data based on scores or ratings though our methods also give specific insights on ordinal data. From raw ranking data, we construct pairwise rankings, represented as edge flows on an appropriate graph. Our statistical ranking method exploits the graph Helmholtzian, which is the graph theoretic analogue of the Helmholtz operator or vector Laplacian, in much the same way the graph Laplacian is an analogue of the Laplace operator or scalar Laplacian. We shall study the graph Helmholtzian using combinatorial Hodge theory, which provides a way to unravel ranking information from edge flows. In particular, we show that every edge flow representing pairwise ranking can be resolved into two orthogonal components, a gradient flow that represents the l2-optimal global ranking and a divergence-free flow (cyclic) that measures the validity of the global ranking obtained—if this is large, then it indicates that the data does not have a good global ranking. This divergence-free flow can be further decomposed orthogonally into a curl flow (locally cyclic) and a harmonic flow (locally acyclic but globally cyclic); these provides information on whether inconsistency in the ranking data arises locally or globally. When applied to statistical ranking problems, Hodge decomposition sheds light on whether a given dataset may be globally ranked in a meaningful way or if the data is inherently inconsistent and thus could not have any reasonable global ranking; in the latter case it provides information on the nature of the inconsistencies. An obvious advantage over the NP-hardness of Kemeny optimization is that HodgeRank may be easily computed via a linear least squares regression. We also discuss connections with well-known ordinal ranking techniques such as Kemeny optimization and Borda count from social choice theory.

Data-driven trajectory smoothing

Motivated by the increasing availability of large collections of noisy GPS traces, we present a new data-driven framework for smoothing trajectory data. The framework, which can be viewed of as a generalization of the classical moving average technique, naturally leads to efficient algorithms for various smoothing objectives. We analyze an algorithm based on this framework and provide connections to previous smoothing techniques. We implement a variation of the algorithm to smooth an entire collection of trajectories and show that it performs well on both synthetic data and massive collections of GPS traces.

Fingerprinting Mobile User Positions in Sensor Networks: Attacks and Countermeasures

We demonstrate that the network flux over the sensor network provides fingerprint information about the mobile users within the field. Such information is exoteric in the physical space and easy to access through passive sniffing. We present a theoretical model to abstract the network flux according to the statuses of mobile users. We fit the theoretical model with the network flux measurements through Nonlinear Least Squares (NLS) and develop an algorithm that iteratively approaches the NLS solution by Sequential Monte Carlo Estimation. With sparse measurements of the flux information at individual sensor nodes, we show that it is easy to identify the mobile users within the network and instantly track their movements without breaking into the details of the communicational packets. Our study indicates that most of existing systems are vulnerable to such attack against the privacy of mobile users. We further propose a set of countermeasures that redistribute and reshape the network traffic to preserve the location privacy of mobile users. With a trace driven simulation, we demonstrate the substantial threats of the attacks and the effectiveness of the proposed countermeasures.

Fingerprinting Mobile User Positions in Sensor Networks

We demonstrate that the network flux over the sensor network provides us fingerprint information about the mobile users within the field. Such information is exoteric in the physical space and easy to access through passive sniffing. We present a theoretical model to the network flux according to the statuses of mobile users. We fit the theoretical model with the network flux measurements through Non-linear Least Squares (NLS) and develop an algorithm that iteratively approaches the NLS solution by Sequential Monte Carlo Estimation. With sparse measurements of the flux information at individual sensor nodes, we are able to identify the mobile users within the network and instantly track their movements without breaking into the details of the communicational packets. A particular advantage of this approach is that compared to the vast information we can reveal the required knowledge is extremely cheap. As all fingerprint information comes from the network flux that is public under current wireless communication medium, our study indicates that most of existing systems are vulnerable in protecting the privacy of mobile users.

Compressive Network Analysis

Modern data acquisition routinely produces massive amounts of network data. Though many methods and models have been proposed to analyze such data, the research of network data is largely disconnected with the classical theory of statistical learning and signal processing. In this paper, we present a new framework for modeling network data, which connects two seemingly different areas: network data analysis and compressed sensing. From a nonparametric perspective, we model an observed network using a large dictionary. In particular, we consider the network clique detection problem and show connections between our formulation with a new algebraic tool, namely Randon basis pursuit in homogeneous spaces. Such a connection allows us to identify rigorous recovery conditions for clique detection problems. Though this paper is mainly conceptual, we also develop practical approximation algorithms for solving empirical problems and demonstrate their usefulness on real-world datasets.

A Fourier-theoretic approach for inferring symmetries

In this paper, we propose a novel Fourier-theoretic approach for estimating the symmetry group G of a geometric object X. Our approach takes as input a geometric similarity matrix between low-order combinations of features of X and then searches within the tree of all feature permutations to detect the sparse subset that defines the symmetry group G of X. Using the Fourier-theoretic approach, we construct an efficient marginal-based search strategy, which can recover the symmetry group G effectively. The framework introduced in this paper can be used to discover symmetries of more abstract geometric spaces and is robust to deformation noise. Experimental results show that our approach can fully determine the symmetries of various geometric objects.

Fourier-information duality in the identity management problem

We compare two recently proposed approaches for representing probability distributions over the space of permutations in the context of multi-target tracking. We show that these two representations, the Fourier approximation and the information form approximation can both be viewed as low dimensional projections of a true distribution, but with respect to different metrics. We identify the strengths and weaknesses of each approximation, and propose an algorithm for converting between the two forms, allowing for a hybrid approach that draws on the strengths of both representations. We show experimental evidence that there are situations where hybrid algorithms are favorable.

Property management in wireless sensor networks with overcomplete radon bases

This article presents a scalable algorithm for managing property information about moving objects tracked by a sensor network. Property information is obtained via distributed sensor observations, but will be corrupted when objects mix up with each other. The association between properties and objects then becomes ambiguous. We build a novel representation framework, exploiting an overcomplete Radon basis dictionary to model property uncertainty in such circumstances. By making use of the combinatorial structure of the basis design and sparse representations we can efficiently approximate the underlying probability distribution of the association between target properties and tracks, overcoming the exponential space that would otherwise be required. Based on the proposed theories, we design a fully distributed algorithm on wireless sensor networks. We conduct comparative simulations and the results validate the effectiveness of our approach.