In this task, you are given a part of an article. Your task is to generate headline (title) for this text. Preferred headlines are under fifteen words.

Input: Consider Input: CUR matrix decomposition computes the low rank approximation of a given matrix by using the actual rows and columns of the matrix. It has been a very useful tool for handling large matrices. One limitation with the existing algorithms for CUR matrix decomposition is that they need an access to the full matrix, a requirement that can be difficult to fulfill in many real world applications. In this work, we alleviate this limitation by developing a CUR decomposition algorithm for partially observed matrices. In particular, the proposed algorithm computes the low rank approximation of the target matrix based on (i) the randomly sampled rows and columns, and (ii) a subset of observed entries that are randomly sampled from the matrix. Our analysis shows the relative error bound, measured by spectral norm, for the proposed algorithm when the target matrix is of full rank. We also show that only O(nr ln r) observed entries are needed by the proposed algorithm to perfectly recover a rank r matrix of size n n, which improves the sample complexity of the existing algorithms for matrix completion. Empirical studies on both synthetic and real-world datasets verify our theoretical claims and demonstrate the effectiveness of the proposed algorithm.

Output: CUR Algorithm for Partially Observed Matrices

Input: Consider Input: Visual representation is crucial for a visual tracking method's performances. Conventionally, visual representations adopted in visual tracking rely on hand-crafted computer vision descriptors. These descriptors were developed generically without considering tracking-specific information. In this paper, we propose to learn complex-valued invariant representations from tracked sequential image patches, via strong temporal slowness constraint and stacked convolutional autoencoders. The deep slow local representations are learned offline on unlabeled data and transferred to the observational model of our proposed tracker. The proposed observational model retains old training samples to alleviate drift, and collect negative samples which are coherent with target's motion pattern for better discriminative tracking. With the learned representation and online training samples, a logistic regression classifier is adopted to distinguish target from background, and retrained online to adapt to appearance changes. Subsequently, the observational model is integrated into a particle filter framework to peform visual tracking. Experimental results on various challenging benchmark sequences demonstrate that the proposed tracker performs favourably against several state-of-the-art trackers.

Output: Self-taught learning of a deep invariant representation for visual tracking via temporal slowness principle

Input: Consider Input: We propose and compare various sentence selection strategies for active learning for the task of detecting mentions of entities. The best strategy employs the sum of con dences of two statistical classi ers trained on di erent views of the data. Our experimental results show that, compared to the random selection strategy, this strategy reduces the amount of required labeled training data by over 50% while achieving the same performance. The e ect is even more signi cant when only named mentions are considered: the system achieves the same performance by using only 42% of the training data required by the random selection strategy.
Output: Active Learning for Mention Detection: A Comparison of Sentence Selection Strategies