A Proposal for a Problem-Driven Mathematics Curriculum Framework

A framework for a problem-driven mathematics curriculum is proposed, grounded in the assumption that students learn mathematics while engaged in complex problem-solving activity. The framework is envisioned as a dynamic technologicallydriven multi-dimensional representation that can highlight the nature of the curriculum (e.g., revealing the relationship among modeling, conceptual, and procedural knowledge), can be used for programmatic, classroom and individual assessment, and can be easily revised to reflect ongoing changes in disciplinary knowledge development and important applications of mathematics. The discussion prompts ideas and questions for future development of the envisioned software needed to enact such a framework

Increasing the Efficiency of Policy Learning for Autonomous Vehicles by Multi-Task Representation Learning

Driving in a dynamic, multi-agent, and complex urban environment is a difficult task requiring a complex decision-making policy. The learning of such a policy requires a state representation that can encode the entire environment. Mid-level representations that encode a vehicle's environment as images have become a popular choice. Still, they are quite high-dimensional, limiting their use in data-hungry approaches such as reinforcement learning. In this article, we propose to learn a low-dimensional and rich latent representation of the environment by leveraging the knowledge of relevant semantic factors. To do this, we train an encoder-decoder deep neural network to predict multiple application-relevant factors such as the trajectories of other agents and the ego car. Furthermore, we propose a hazard signal based on other vehicles' future trajectories and the planned route which is used in conjunction with the learned latent representation as input to a down-stream policy. We demonstrate that using the multi-head encoder-decoder neural network results in a more informative representation than a standard single-head model. In particular, the proposed representation learning and the hazard signal help reinforcement learning to learn faster, with increased performance and less data than baseline methods

Multi-view representation learning for data stream clustering

open access articleData stream clustering provides valuable insights into the evolving patterns of long sequences of continuously generated data objects. Most existing clustering methods focus on single-view data streams. In this paper, we propose a multi-view representation learning (MVRL) method for multi-view clustering of data streams. We first introduce an integrated representation learning model to learn a fused sparse affinity matrix across multiple views for spectral clustering. Motivated by the optimization procedure of the integrated representation learning model, we propose three consecutive stages: collaborative representation, the construction of individual global affinity matrices using a mapping function, and the calculation of a fused sparse affinity matrix using Euclidean projection. These stages allow the effective capture of the global and local structures of high-dimensional data objects. Moreover, each stage has a closed-form solution, which determines the upper bound of the computational cost and memory consumption. We then employ the construction residuals of the collaborative representation to adaptively update a dynamic set, which is used to preserve the representative data objects. The dynamic set efficiently transfers previously learned useful knowledge to the arriving data objects. Extensive experimental results on multi-view data stream datasets demonstrate the effectiveness of the proposed MVRL method

An information-driven framework for image mining

[Abstract]: Image mining systems that can automatically extract semantically meaningful information (knowledge) from image data are increasingly in demand. The fundamental challenge in image mining is to determine how low-level, pixel representation contained in a raw image or image sequence can be processed to identify high-level spatial objects and relationships. To meet this challenge, we propose an efficient information-driven framework for image mining. We distinguish four levels of information: the Pixel Level, the Object Level, the Semantic Concept Level, and the Pattern and Knowledge Level. High-dimensional indexing schemes and retrieval techniques are also included in the framework to support the flow of information among the levels. We believe this framework represents the first step towards capturing the different levels of information present in image data and addressing the issues and challenges of discovering useful patterns/knowledge from each level

Node Embedding over Temporal Graphs

In this work, we present a method for node embedding in temporal graphs. We propose an algorithm that learns the evolution of a temporal graph's nodes and edges over time and incorporates this dynamics in a temporal node embedding framework for different graph prediction tasks. We present a joint loss function that creates a temporal embedding of a node by learning to combine its historical temporal embeddings, such that it optimizes per given task (e.g., link prediction). The algorithm is initialized using static node embeddings, which are then aligned over the representations of a node at different time points, and eventually adapted for the given task in a joint optimization. We evaluate the effectiveness of our approach over a variety of temporal graphs for the two fundamental tasks of temporal link prediction and multi-label node classification, comparing to competitive baselines and algorithmic alternatives. Our algorithm shows performance improvements across many of the datasets and baselines and is found particularly effective for graphs that are less cohesive, with a lower clustering coefficient

Fusion of Learned Multi-Modal Representations and Dense Trajectories for Emotional Analysis in Videos

When designing a video affective content analysis algorithm, one of the most important steps is the selection of discriminative features for the effective representation of video segments. The majority of existing affective content analysis methods either use low-level audio-visual features or generate handcrafted higher level representations based on these low-level features. We propose in this work to use deep learning methods, in particular convolutional neural networks (CNNs), in order to automatically learn and extract mid-level representations from raw data. To this end, we exploit the audio and visual modality of videos by employing Mel-Frequency Cepstral Coefficients (MFCC) and color values in the HSV color space. We also incorporate dense trajectory based motion features in order to further enhance the performance of the analysis. By means of multi-class support vector machines (SVMs) and fusion mechanisms, music video clips are classified into one of four affective categories representing the four quadrants of the Valence-Arousal (VA) space. Results obtained on a subset of the DEAP dataset show (1) that higher level representations perform better than low-level features, and (2) that incorporating motion information leads to a notable performance gain, independently from the chosen representation

Image mining: trends and developments

[Abstract]: Advances in image acquisition and storage technology have led to tremendous growth in very large and detailed image databases. These images, if analyzed, can reveal useful information to the human users. Image mining deals with the extraction of implicit knowledge, image data relationship, or other patterns not explicitly stored in the images. Image mining is more than just an extension of data mining to image domain. It is an interdisciplinary endeavor that draws upon expertise in computer vision, image processing, image retrieval, data mining, machine learning, database, and artificial intelligence. In this paper, we will examine the research issues in image mining, current developments in image mining, particularly, image mining frameworks, state-of-the-art techniques and systems. We will also identify some future research directions for image mining