Shape Interaction Matrix Revisited and Robustified: Efficient Subspace Clustering with Corrupted and Incomplete Data

The Shape Interaction Matrix (SIM) is one of the earliest approaches to performing subspace clustering (i.e., separating points drawn from a union of subspaces). In this paper, we revisit the SIM and reveal its connections to several recent subspace clustering methods. Our analysis lets us derive a simple, yet effective algorithm to robustify the SIM and make it applicable to realistic scenarios where the data is corrupted by noise. We justify our method by intuitive examples and the matrix perturbation theory. We then show how this approach can be extended to handle missing data, thus yielding an efficient and general subspace clustering algorithm. We demonstrate the benefits of our approach over state-of-the-art subspace clustering methods on several challenging motion segmentation and face clustering problems, where the data includes corrupted and missing measurements.Comment: This is an extended version of our iccv15 pape

The reentry hypothesis: The putative interaction of the frontal eye field, ventrolateral prefrontal cortex, and areas V4, IT for attention and eye movement

Attention is known to play a key role in perception, including action selection, object recognition and memory. Despite findings revealing competitive interactions among cell populations, attention remains difficult to explain. The central purpose of this paper is to link up a large number of findings in a single computational approach. Our simulation results suggest that attention can be well explained on a network level involving many areas of the brain. We argue that attention is an emergent phenomenon that arises from reentry and competitive interactions. We hypothesize that guided visual search requires the usage of an object-specific template in prefrontal cortex to sensitize V4 and IT cells whose preferred stimuli match the target template. This induces a feature-specific bias and provides guidance for eye movements. Prior to an eye movement, a spatially organized reentry from occulomotor centers, specifically the movement cells of the frontal eye field, occurs and modulates the gain of V4 and IT cells. The processes involved are elucidated by quantitatively comparing the time course of simulated neural activity with experimental data. Using visual search tasks as an example, we provide clear and empirically testable predictions for the participation of IT, V4 and the frontal eye field in attention. Finally, we explain a possible physiological mechanism that can lead to non-flat search slopes as the result of a slow, parallel discrimination process

Learning Deployable Navigation Policies at Kilometer Scale from a Single Traversal

Model-free reinforcement learning has recently been shown to be effective at learning navigation policies from complex image input. However, these algorithms tend to require large amounts of interaction with the environment, which can be prohibitively costly to obtain on robots in the real world. We present an approach for efficiently learning goal-directed navigation policies on a mobile robot, from only a single coverage traversal of recorded data. The navigation agent learns an effective policy over a diverse action space in a large heterogeneous environment consisting of more than 2km of travel, through buildings and outdoor regions that collectively exhibit large variations in visual appearance, self-similarity, and connectivity. We compare pretrained visual encoders that enable precomputation of visual embeddings to achieve a throughput of tens of thousands of transitions per second at training time on a commodity desktop computer, allowing agents to learn from millions of trajectories of experience in a matter of hours. We propose multiple forms of computationally efficient stochastic augmentation to enable the learned policy to generalise beyond these precomputed embeddings, and demonstrate successful deployment of the learned policy on the real robot without fine tuning, despite environmental appearance differences at test time. The dataset and code required to reproduce these results and apply the technique to other datasets and robots is made publicly available at rl-navigation.github.io/deployable

Reconstructing dynamical networks via feature ranking

Empirical data on real complex systems are becoming increasingly available. Parallel to this is the need for new methods of reconstructing (inferring) the topology of networks from time-resolved observations of their node-dynamics. The methods based on physical insights often rely on strong assumptions about the properties and dynamics of the scrutinized network. Here, we use the insights from machine learning to design a new method of network reconstruction that essentially makes no such assumptions. Specifically, we interpret the available trajectories (data) as features, and use two independent feature ranking approaches -- Random forest and RReliefF -- to rank the importance of each node for predicting the value of each other node, which yields the reconstructed adjacency matrix. We show that our method is fairly robust to coupling strength, system size, trajectory length and noise. We also find that the reconstruction quality strongly depends on the dynamical regime

Efficient one- and two-qubit pulsed gates for an oscillator stabilized Josephson qubit

We present theoretical schemes for performing high-fidelity one- and two-qubit pulsed gates for a superconducting flux qubit. The "IBM qubit" consists of three Josephson junctions, three loops, and a superconducting transmission line. Assuming a fixed inductive qubit-qubit coupling, we show that the effective qubit-qubit interaction is tunable by changing the applied fluxes, and can be made negligible, allowing one to perform high fidelity single qubit gates. Our schemes are tailored to alleviate errors due to 1/f noise; we find gates with only 1% loss of fidelity due to this source, for pulse times in the range of 20-30ns for one-qubit gates (Z rotations, Hadamard), and 60ns for a two-qubit gate (controlled-Z). Our relaxation and dephasing time estimates indicate a comparable loss of fidelity from this source. The control of leakage plays an important role in the design of our shaped pulses, preventing shorter pulse times. However, we have found that imprecision in the control of the quantum phase plays the major role in the limitation of the fidelity of our gates.Comment: Published version. Added references. Corrected minor typos. Added discussion on how the influence of 1/f noise is modeled. 36 pages, 11 figure