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Mar 14

Stable Vectorization of Multiparameter Persistent Homology using Signed Barcodes as Measures

Persistent homology (PH) provides topological descriptors for geometric data, such as weighted graphs, which are interpretable, stable to perturbations, and invariant under, e.g., relabeling. Most applications of PH focus on the one-parameter case -- where the descriptors summarize the changes in topology of data as it is filtered by a single quantity of interest -- and there is now a wide array of methods enabling the use of one-parameter PH descriptors in data science, which rely on the stable vectorization of these descriptors as elements of a Hilbert space. Although the multiparameter PH (MPH) of data that is filtered by several quantities of interest encodes much richer information than its one-parameter counterpart, the scarceness of stability results for MPH descriptors has so far limited the available options for the stable vectorization of MPH. In this paper, we aim to bring together the best of both worlds by showing how the interpretation of signed barcodes -- a recent family of MPH descriptors -- as signed measures leads to natural extensions of vectorization strategies from one parameter to multiple parameters. The resulting feature vectors are easy to define and to compute, and provably stable. While, as a proof of concept, we focus on simple choices of signed barcodes and vectorizations, we already see notable performance improvements when comparing our feature vectors to state-of-the-art topology-based methods on various types of data.

Differentiability and Optimization of Multiparameter Persistent Homology

Real-valued functions on geometric data -- such as node attributes on a graph -- can be optimized using descriptors from persistent homology, allowing the user to incorporate topological terms in the loss function. When optimizing a single real-valued function (the one-parameter setting), there is a canonical choice of descriptor for persistent homology: the barcode. The operation mapping a real-valued function to its barcode is differentiable almost everywhere, and the convergence of gradient descent for losses using barcodes is relatively well understood. When optimizing a vector-valued function (the multiparameter setting), there is no unique choice of descriptor for multiparameter persistent homology, and many distinct descriptors have been proposed. This calls for the development of a general framework for differentiability and optimization that applies to a wide range of multiparameter homological descriptors. In this article, we develop such a framework and show that it encompasses well-known descriptors of different flavors, such as signed barcodes and the multiparameter persistence landscape. We complement the theory with numerical experiments supporting the idea that optimizing multiparameter homological descriptors can lead to improved performances compared to optimizing one-parameter descriptors, even when using the simplest and most efficiently computable multiparameter descriptors.

CNN based Cuneiform Sign Detection Learned from Annotated 3D Renderings and Mapped Photographs with Illumination Augmentation

Motivated by the challenges of the Digital Ancient Near Eastern Studies (DANES) community, we develop digital tools for processing cuneiform script being a 3D script imprinted into clay tablets used for more than three millennia and at least eight major languages. It consists of thousands of characters that have changed over time and space. Photographs are the most common representations usable for machine learning, while ink drawings are prone to interpretation. Best suited 3D datasets that are becoming available. We created and used the HeiCuBeDa and MaiCuBeDa datasets, which consist of around 500 annotated tablets. For our novel OCR-like approach to mixed image data, we provide an additional mapping tool for transferring annotations between 3D renderings and photographs. Our sign localization uses a RepPoints detector to predict the locations of characters as bounding boxes. We use image data from GigaMesh's MSII (curvature, see https://gigamesh.eu) based rendering, Phong-shaded 3D models, and photographs as well as illumination augmentation. The results show that using rendered 3D images for sign detection performs better than other work on photographs. In addition, our approach gives reasonably good results for photographs only, while it is best used for mixed datasets. More importantly, the Phong renderings, and especially the MSII renderings, improve the results on photographs, which is the largest dataset on a global scale.

Improving Continuous Sign Language Recognition with Cross-Lingual Signs

This work dedicates to continuous sign language recognition (CSLR), which is a weakly supervised task dealing with the recognition of continuous signs from videos, without any prior knowledge about the temporal boundaries between consecutive signs. Data scarcity heavily impedes the progress of CSLR. Existing approaches typically train CSLR models on a monolingual corpus, which is orders of magnitude smaller than that of speech recognition. In this work, we explore the feasibility of utilizing multilingual sign language corpora to facilitate monolingual CSLR. Our work is built upon the observation of cross-lingual signs, which originate from different sign languages but have similar visual signals (e.g., hand shape and motion). The underlying idea of our approach is to identify the cross-lingual signs in one sign language and properly leverage them as auxiliary training data to improve the recognition capability of another. To achieve the goal, we first build two sign language dictionaries containing isolated signs that appear in two datasets. Then we identify the sign-to-sign mappings between two sign languages via a well-optimized isolated sign language recognition model. At last, we train a CSLR model on the combination of the target data with original labels and the auxiliary data with mapped labels. Experimentally, our approach achieves state-of-the-art performance on two widely-used CSLR datasets: Phoenix-2014 and Phoenix-2014T.

CiCo: Domain-Aware Sign Language Retrieval via Cross-Lingual Contrastive Learning

This work focuses on sign language retrieval-a recently proposed task for sign language understanding. Sign language retrieval consists of two sub-tasks: text-to-sign-video (T2V) retrieval and sign-video-to-text (V2T) retrieval. Different from traditional video-text retrieval, sign language videos, not only contain visual signals but also carry abundant semantic meanings by themselves due to the fact that sign languages are also natural languages. Considering this character, we formulate sign language retrieval as a cross-lingual retrieval problem as well as a video-text retrieval task. Concretely, we take into account the linguistic properties of both sign languages and natural languages, and simultaneously identify the fine-grained cross-lingual (i.e., sign-to-word) mappings while contrasting the texts and the sign videos in a joint embedding space. This process is termed as cross-lingual contrastive learning. Another challenge is raised by the data scarcity issue-sign language datasets are orders of magnitude smaller in scale than that of speech recognition. We alleviate this issue by adopting a domain-agnostic sign encoder pre-trained on large-scale sign videos into the target domain via pseudo-labeling. Our framework, termed as domain-aware sign language retrieval via Cross-lingual Contrastive learning or CiCo for short, outperforms the pioneering method by large margins on various datasets, e.g., +22.4 T2V and +28.0 V2T R@1 improvements on How2Sign dataset, and +13.7 T2V and +17.1 V2T R@1 improvements on PHOENIX-2014T dataset. Code and models are available at: https://github.com/FangyunWei/SLRT.