Simultaneous Dimensionality Reduction for Extracting Useful Representations of Large Empirical Multimodal Datasets
The quest for simplification in physics drives the exploration of concise mathematical representations for complex systems. This Dissertation focuses on the concept of dimensionality reduction as a means to obtain low-dimensional descriptions from high-dimensional data, facilitating comprehension and analysis. We address the challenges posed by real-world data that defy conventional assumptions, such as complex interactions within neural systems or high-dimensional dynamical systems. Leveraging insights from both theoretical physics and machine learning, this work unifies diverse reduction methods under a comprehensive framework, the Deep Variational Multivariate Information Bottleneck. This framework enables the design of tailored reduction algorithms based on specific research questions. We explore and assert the efficacy of simultaneous reduction approaches over their independent reduction counterparts, demonstrating their superiority in capturing covariation between multiple modalities, while requiring less data. We also introduced novel techniques, such as the Deep Variational Symmetric Information Bottleneck, for general nonlinear simultaneous reduction. We show that the same principle of simultaneous reduction is the key to efficient estimation of mutual information. We show that our new method is able to discover the coordinates of high-dimensional observations of dynamical systems. Through analytical investigations and empirical validations, we shed light on the intricacies of dimensionality reduction methods, paving the way for enhanced data analysis across various domains. We underscore the potential of these methodologies to extract meaningful insights from complex datasets, driving advancements in fundamental research and applied sciences. As these methods evolve, they promise to deepen our understanding of complex systems and inform more effective data analysis strategies.
Code (0)
등록된 구현이 없습니다.
Tasks
Dimensionality ReductionSimilar Papers 제목 키워드 기반
Unsupervised low-rank representations for speech emotion recognition
We examine the use of linear and non-linear dimensionality reduction algorithms for extracting low-rank feature representations for speech emotion recognition. Two feature sets are used, one based on low-level descriptor…
Dimensionality ReductionEmotion RecognitionGeneral ClassificationSpeech Emotion RecognitionDimensionality Reduction for Data in Multiple Feature Representations
In solving complex visual learning tasks, adopting multiple descriptors to more precisely characterize the data has been a feasible way for improving performance. These representations are typically high dimensional and …
ClusteringDimensionality ReductionGraph EmbeddingObject RecognitionSimultaneous Dimensionality Reduction: A Data Efficient Approach for Multimodal Representations Learning
We explore two primary classes of approaches to dimensionality reduction (DR): Independent Dimensionality Reduction (IDR) and Simultaneous Dimensionality Reduction (SDR). In IDR methods, of which Principal Components Ana…
Dimensionality ReductionA GPU-Oriented Algorithm Design for Secant-Based Dimensionality Reduction
Dimensionality-reduction techniques are a fundamental tool for extracting useful information from high-dimensional data sets. Because secant sets encode manifold geometry, they are a useful tool for designing meaningful …
Dimensionality ReductionGPUImplicit Neural Representations for Simultaneous Reduction and Continuous Reconstruction of Multi-Altitude Climate Data
The world is moving towards clean and renewable energy sources, such as wind energy, in an attempt to reduce greenhouse gas emissions that contribute to global warming. To enhance the analysis and storage of wind data, w…
Dimensionality ReductionSuper-Resolution