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: The preimage of the activities of all the nodes at a certain level of a deep network is the set of inputs that result in the same node activity. For fully connected multi layer rectifier networks we demonstrate how to compute the preimages of activities at arbitrary levels from knowledge of the parameters in a deep rectifying network by disregarding the effects of max-pooling. If the preimage set of a certain activity in the network contains elements from more than one class it means that these classes are irreversibly mixed. This implies that preimage sets which are piecewise linear manifolds are building blocks for describing the input manifolds specific classes, i.e. all preimages should ideally be from the same class. We believe that the knowledge of how to compute preimages will be valuable in understanding the efficiency displayed by deep learning networks and could potentially be used in designing more efficient training algorithms

Output: THE PREIMAGE OF RECTIFIER NETWORK ACTIVITIES


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: The number of computers, tablets and smartphones is increasing rapidly, which entails the ownership and use of multiple devices to perform online tasks. As people move across devices to complete these tasks, their identities becomes fragmented. Understanding the usage and transition between those devices is essential to develop efficient applications in a multi-device world. In this paper we present a solution to deal with the cross-device identification of users based on semi-supervised machine learning methods to identify which cookies belong to an individual using a device. The method proposed in this paper scored third in the ICDM 2015 Drawbridge Cross-Device Connections challenge proving its good performance.


Output: Cross-Device Tracking: Matching Devices and Cookies