We advocate Laplacian K-modes for joint clustering and density mode finding, and propose a concave-convex relaxation of the problem, which yields a parallel algorithm that scales up to large datasets and high dimensions. We optimize a tight bound (auxiliary function) of our relaxation, which, at each iteration, amounts to computing an independent update for each cluster-assignment variable, with guar- anteed convergence. Therefore, our bound optimizer can be trivially distributed for large-scale data sets. Furthermore, we show that the density modes can be obtained as byproducts of the assignment variables via simple maximum-value operations whose additional computational cost is linear in the number of data points. Our formulation does not need storing a full affinity matrix and computing its eigenvalue decomposition, neither does it perform expensive projection steps and Lagrangian-dual inner iterates for the simplex constraints of each point. Fur- thermore, unlike mean-shift, our density-mode estimation does not require inner- loop gradient-ascent iterates. It has a complexity independent of feature-space dimension, yields modes that are valid data points in the input set and is appli- cable to discrete domains as well as arbitrary kernels. We report comprehensive experiments over various data sets, which show that our algorithm yields very competitive performances in term of optimization quality (i.e., the value of the discrete-variable objective at convergence) and clustering accuracy.

We advocate Laplacian K-modes for joint clustering and density mode finding, and propose a concave-convex relaxation of the problem, which yields a parallel algorithm that scales up to large datasets and high dimensions. We optimize a tight bound (auxiliary function) of our relaxation, which, at each iteration, amounts to computing an independent update for each cluster-assignment variable, with guaranteed convergence. Therefore, our bound optimizer can be trivially distributed for large-scale data sets. Furthermore, we show that the density modes can be obtained as byproducts of the assignment variables via simple maximum-value operations whose additional computational cost is linear in the number of data points. Our formulation does not need storing a full affinity matrix and computing its eigenvalue decomposition, neither does it perform expensive projection steps and Lagrangian-dual inner iterates for the simplex constraints of each point. Furthermore, unlike mean-shift, our density-mode estimation does not require inner-loop gradient-ascent iterates. It has a complexity independent of feature-space dimension, yields modes that are valid data points in the input set and is applicable to discrete domains as well as arbitrary kernels. We report comprehensive experiments over various data sets, which show that our algorithm yields very competitive performances in term of optimization quality (i.e., the value of the discrete-variable objective at convergence) and clustering accuracy.

This paper proposes a principled information theoretic analysis of classification for deep neural network structures, e.g. convolutional neural networks (CNN). The output of convolutional filters is modeled as a random variable Y conditioned on the object class C and network filter bank F. The conditional entropy (CENT) H(Y |C,F) is shown in theory and experiments to be a highly compact and class-informative code, that can be computed from the filter outputs throughout an existing CNN and used to obtain higher classification results than the original CNN itself. Experiments demonstrate the effectiveness of CENT feature analysis in two separate CNN classification contexts. 1) In the classification of neurodegeneration due to Alzheimer's disease (AD) and natural aging from 3D magnetic resonance image (MRI) volumes, 3 CENT features result in an AUC=94.6% for whole-brain AD classification, the highest reported accuracy on the public OASIS dataset used and 12% higher than the softmax output of the original CNN trained for the task. 2) In the context of visual object classification from 2D photographs, transfer learning based on a small set of CENT features identified throughout an existing CNN leads to AUC values comparable to the 1000-feature softmax output of the original network when classifying previously unseen object categories. The general information theoretical analysis explains various recent CNN design successes, e.g. densely connected CNN architectures, and provides insights for future research directions in deep learning.

Multiple instance learning (MIL) is a form of weakly supervised learning where training instances are arranged in sets, called bags, and a label is provided for the entire bag. This formulation is gaining interest because it naturally fits various problems and allows to leverage weakly labeled data. Consequently, it has been used in diverse application fields such as computer vision and document classification. However, learning from bags raises important challenges that are unique to MIL. This paper provides a comprehensive survey of the characteristics which define and differentiate the types of MIL problems. Until now, these problem characteristics have not been formally identified and described. As a result, the variations in performance of MIL algorithms from one data set to another are difficult to explain. In this paper, MIL problem characteristics are grouped into four broad categories: the composition of the bags, the types of data distribution, the ambiguity of instance labels, and the task to be performed. Methods specialized to address each category are reviewed. Then, the extent to which these characteristics manifest themselves in key MIL application areas are described. Finally, experiments are conducted to compare the performance of 16 state-of-the-art MIL methods on selected problem characteristics. This paper provides insight on how the problem characteristics affect MIL algorithms, recommendations for future benchmarking and promising avenues for research.

H3C 3A7 CANADA 2Department of Cognitive and Neural Systems, Boston University Boston, MA 02215 USA Abstract The ARTMAP-FD neural network performs both identification (placing test patterns in classes encountered during training) and familiarity discrimination (judging whether a test pattern belongs to any of the classes encountered during training). The performance ofARTMAP-FD is tested on radar pulse data obtained in the field, and compared to that of the nearest-neighbor-based NEN algorithm and to a k 1 extension of NEN. 1 Introduction The recognition process involves both identification and familiarity discrimination. Consider, for example, a neural network designed to identify aircraft based on their radar reflections and trained on sample reflections from ten types of aircraft A . . . After training, the network should correctly classify radar reflections belonging to the familiar classes A . Familiarity discrimination is also referred to as "novelty detection," a "reject option," and "recognition in partially exposed environments."

H3C 3A 7 CAN ADA 2Department of Cognitive and Neural Systems, Boston University Boston, MA 02215 USA Abstract The ARTMAP-FD neural network performs both identification (placing test patterns in classes encountered during training) and familiarity discrimination (judging whether a test pattern belongs to any of the classes encountered during training). The performance of ARTMAP-FD is tested on radar pulse data obtained in the field, and compared to that of the nearest-neighbor-based NEN algorithm and to a k 1 extension of NEN. 1 Introduction The recognition process involves both identification and familiarity discrimination. Consider, for example, a neural network designed to identify aircraft based on their radar reflections and trained on sample reflections from ten types of aircraft A... J. After training, the network should correctly classify radar reflections belonging to the familiar classes A... J, but it should also abstain from making a meaningless guess when presented with a radar reflection from an object belonging to a different, unfamiliar class. Familiarity discrimination is also referred to as "novelty detection," a "reject option," and "recognition in partially exposed environments."