Generating Labels for Regression of Subjective Constructs using Triplet Embeddings

Human annotations serve an important role in computational models where the target constructs under study are hidden, such as dimensions of affect. This is especially relevant in machine learning, where subjective labels derived from related observable signals (e.g., audio, video, text) are needed to support model training and testing. Current research trends focus on correcting artifacts and biases introduced by annotators during the annotation process while fusing them into a single annotation. In this work, we propose a novel annotation approach using triplet embeddings. By lifting the absolute annotation process to relative annotations where the annotator compares individual target constructs in triplets, we leverage the accuracy of comparisons over absolute ratings by human annotators. We then build a 1-dimensional embedding in Euclidean space that is indexed in time and serves as a label for regression. In this setting, the annotation fusion occurs naturally as a union of sets of sampled triplet comparisons among different annotators. We show that by using our proposed sampling method to find an embedding, we are able to accurately represent synthetic hidden constructs in time under noisy sampling conditions. We further validate this approach using human annotations collected from Mechanical Turk and show that we can recover the underlying structure of the hidden construct up to bias and scaling factors.Comment: 9 pages, 5 figures, accepted journal pape

Making Laplacians commute

In this paper, we construct multimodal spectral geometry by finding a pair of closest commuting operators (CCO) to a given pair of Laplacians. The CCOs are jointly diagonalizable and hence have the same eigenbasis. Our construction naturally extends classical data analysis tools based on spectral geometry, such as diffusion maps and spectral clustering. We provide several synthetic and real examples of applications in dimensionality reduction, shape analysis, and clustering, demonstrating that our method better captures the inherent structure of multi-modal data

Stochastic Non-convex Ordinal Embedding with Stabilized Barzilai-Borwein Step Size

Learning representation from relative similarity comparisons, often called ordinal embedding, gains rising attention in recent years. Most of the existing methods are batch methods designed mainly based on the convex optimization, say, the projected gradient descent method. However, they are generally time-consuming due to that the singular value decomposition (SVD) is commonly adopted during the update, especially when the data size is very large. To overcome this challenge, we propose a stochastic algorithm called SVRG-SBB, which has the following features: (a) SVD-free via dropping convexity, with good scalability by the use of stochastic algorithm, i.e., stochastic variance reduced gradient (SVRG), and (b) adaptive step size choice via introducing a new stabilized Barzilai-Borwein (SBB) method as the original version for convex problems might fail for the considered stochastic \textit{non-convex} optimization problem. Moreover, we show that the proposed algorithm converges to a stationary point at a rate $\mathcal{O}(\frac{1}{T})$ in our setting, where $T$ is the number of total iterations. Numerous simulations and real-world data experiments are conducted to show the effectiveness of the proposed algorithm via comparing with the state-of-the-art methods, particularly, much lower computational cost with good prediction performance.Comment: 11 pages, 3 figures, 2 tables, accepted by AAAI201