Recommender systems have become an essential tool for providers and users of online services and goods, especially with the increased use of the Internet to access information and purchase products and services. This work proposes a novel recommendation method based on complex networks generated by a similarity-popularity model to predict ones. We first construct a model of a network having users and items as nodes from observed ratings and then use it to predict unseen ratings. The prospect of producing accurate rating predictions using a similarity-popularity model with hidden metric spaces and dot-product similarity is explored. The proposed approach is implemented and experimentally compared against baseline and state-of-the-art recommendation methods on 21 datasets from various domains. The experimental results demonstrate that the proposed method produces accurate predictions and outperforms existing methods. We also show that the proposed approach produces superior results in low dimensions, proving its effectiveness for data visualization and exploration.

From optimal transport to robust dimensionality reduction, a plethora of machine learning applications can be cast into the min-max optimization problems over Riemannian manifolds. Though many min-max algorithms have been analyzed in the Euclidean setting, it has proved elusive to translate these results to the Riemannian case. Zhang et al. [2022] have recently shown that geodesic convex concave Riemannian problems always admit saddle-point solutions. Inspired by this result, we study whether a performance gap between Riemannian and optimal Euclidean space convex-concave algorithms is necessary. We answer this question in the negative-we prove that the Riemannian corrected extragradient (RCEG) method achieves last-iterate convergence at a linear rate in the geodesically strongly-convex-concave case, matching the Euclidean result. Our results also extend to the stochastic or non-smooth case where RCEG and Riemanian gradient ascent descent (RGDA) achieve near-optimal convergence rates up to factors depending on curvature of the manifold.

In this paper, we study contrastive learning from an optimization perspective, aiming to analyze and address a fundamental issue of existing contrastive learning methods that either rely on a large batch size or a large dictionary of feature vectors. We consider a global objective for contrastive learning, which contrasts each positive pair with all negative pairs for an anchor point. From the optimization perspective, we explain why existing methods such as SimCLR require a large batch size in order to achieve a satisfactory result. In order to remove such requirement, we propose a memory-efficient Stochastic Optimization algorithm for solving the Global objective of Contrastive Learning of Representations, named SogCLR. We show that its optimization error is negligible under a reasonable condition after a sufficient number of iterations or is diminishing for a slightly different global contrastive objective. Empirically, we demonstrate that SogCLR with small batch size (e.g., 256) can achieve similar performance as SimCLR with large batch size (e.g., 8192) on self-supervised learning task on ImageNet-1K. We also attempt to show that the proposed optimization technique is generic and can be applied to solving other contrastive losses, e.g., two-way contrastive losses for bimodal contrastive learning. The proposed method is implemented in our open-sourced library LibAUC (www.libauc.org).

Image retrieval has become an increasingly appealing technique with broad multimedia application prospects, where deep hashing serves as the dominant branch towards low storage and efficient retrieval. In this paper, we carried out in-depth investigations on metric learning in deep hashing for establishing a powerful metric space in multi-label scenarios, where the pair loss suffers high computational overhead and converge difficulty, while the proxy loss is theoretically incapable of expressing the profound label dependencies and exhibits conflicts in the constructed hypersphere space. To address the problems, we propose a novel metric learning framework with Hybrid Proxy-Pair Loss (HyP$^2$ Loss) that constructs an expressive metric space with efficient training complexity w.r.t. the whole dataset. The proposed HyP$^2$ Loss focuses on optimizing the hypersphere space by learnable proxies and excavating data-to-data correlations of irrelevant pairs, which integrates sufficient data correspondence of pair-based methods and high-efficiency of proxy-based methods. Extensive experiments on four standard multi-label benchmarks justify the proposed method outperforms the state-of-the-art, is robust among different hash bits and achieves significant performance gains with a faster, more stable convergence speed. Our code is available at https://github.com/JerryXu0129/HyP2-Loss.

Indexing is an effective way to support efficient query processing in large databases. Recently the concept of learned index, which replaces or complements traditional index structures with machine learning models, has been actively explored to reduce storage and search costs. However, accurate and efficient similarity query processing in high-dimensional metric spaces remains to be an open challenge. In this paper, we propose a novel indexing approach called LIMS that uses data clustering, pivot-based data transformation techniques and learned indexes to support efficient similarity query processing in metric spaces. In LIMS, the underlying data is partitioned into clusters such that each cluster follows a relatively uniform data distribution. Data redistribution is achieved by utilizing a small number of pivots for each cluster. Similar data are mapped into compact regions and the mapped values are totally ordinal. Machine learning models are developed to approximate the position of each data record on disk. Efficient algorithms are designed for processing range queries and nearest neighbor queries based on LIMS, and for index maintenance with dynamic updates. Extensive experiments on real-world and synthetic datasets demonstrate the superiority of LIMS compared with traditional indexes and state-of-the-art learned indexes.

In this work, we present formulations for regularized Kullback-Leibler and R\'enyi divergences via the Alpha Log-Determinant (Log-Det) divergences between positive Hilbert-Schmidt operators on Hilbert spaces in two different settings, namely (i) covariance operators and Gaussian measures defined on reproducing kernel Hilbert spaces (RKHS); and (ii) Gaussian processes with squared integrable sample paths. For characteristic kernels, the first setting leads to divergences between arbitrary Borel probability measures on a complete, separable metric space. We show that the Alpha Log-Det divergences are continuous in the Hilbert-Schmidt norm, which enables us to apply laws of large numbers for Hilbert space-valued random variables. As a consequence of this, we show that, in both settings, the infinite-dimensional divergences can be consistently and efficiently estimated from their finite-dimensional versions, using finite-dimensional Gram matrices/Gaussian measures and finite sample data, with {\it dimension-independent} sample complexities in all cases. RKHS methodology plays a central role in the theoretical analysis in both settings. The mathematical formulation is illustrated by numerical experiments.

Music is a mysterious language that conveys feeling and thoughts via different tones and timbre. For better understanding of timbre in music, we chose music data of 6 representative instruments, analysed their timbre features and classified them. Instead of the current trend of Neural Network for black-box classification, our project is based on a combination of MFCC and LPC, and augmented with a 6-dimensional feature vector designed by ourselves from observation and attempts. In our white-box model, we observed significant patterns of sound that distinguish different timbres, and discovered some connection between objective data and subjective senses. With a totally 32-dimensional feature vector and a naive all-pairs SVM, we achieved improved classification accuracy compared to a single tool. We also attempted to analyze music pieces downloaded from the Internet, found out different performance on different instruments, explored the reasons and suggested possible ways to improve the performance.

We consider the problem of convex function chasing with black-box advice, where an online decision-maker aims to minimize the total cost of making and switching between decisions in a normed vector space, aided by black-box advice such as the decisions of a machine-learned algorithm. The decision-maker seeks cost comparable to the advice when it performs well, known as $\textit{consistency}$, while also ensuring worst-case $\textit{robustness}$ even when the advice is adversarial. We first consider the common paradigm of algorithms that switch between the decisions of the advice and a competitive algorithm, showing that no algorithm in this class can improve upon 3-consistency while staying robust. We then propose two novel algorithms that bypass this limitation by exploiting the problem's convexity. The first, INTERP, achieves $(\sqrt{2}+\epsilon)$-consistency and $\mathcal{O}(\frac{C}{\epsilon^2})$-robustness for any $\epsilon > 0$, where $C$ is the competitive ratio of an algorithm for convex function chasing or a subclass thereof. The second, BDINTERP, achieves $(1+\epsilon)$-consistency and $\mathcal{O}(\frac{CD}{\epsilon})$-robustness when the problem has bounded diameter $D$. Further, we show that BDINTERP achieves near-optimal consistency-robustness trade-off for the special case where cost functions are $\alpha$-polyhedral.

We propose the SAMU-XLSR: Semantically-Aligned Multimodal Utterance-level Cross-Lingual Speech Representation learning framework. Unlike previous works on speech representation learning, which learns multilingual contextual speech embedding at the resolution of an acoustic frame (10-20ms), this work focuses on learning multimodal (speech-text) multilingual speech embedding at the resolution of a sentence (5-10s) such that the embedding vector space is semantically aligned across different languages. We combine state-of-the-art multilingual acoustic frame-level speech representation learning model XLS-R with the Language Agnostic BERT Sentence Embedding (LaBSE) model to create an utterance-level multimodal multilingual speech encoder SAMU-XLSR. Although we train SAMU-XLSR with only multilingual transcribed speech data, cross-lingual speech-text and speech-speech associations emerge in its learned representation space. To substantiate our claims, we use SAMU-XLSR speech encoder in combination with a pre-trained LaBSE text sentence encoder for cross-lingual speech-to-text translation retrieval, and SAMU-XLSR alone for cross-lingual speech-to-speech translation retrieval. We highlight these applications by performing several cross-lingual text and speech translation retrieval tasks across several datasets.

In human contact, emotion is very crucial. Attributes like words, voice intonation, facial expressions, and kinesics can all be used to portray one's feelings. However, brain-computer interface (BCI) devices have not yet reached the level required for emotion interpretation. With the rapid development of machine learning algorithms, dry electrode techniques, and different real-world applications of the brain-computer interface for normal individuals, emotion categorization from EEG data has recently gotten a lot of attention. Electroencephalogram (EEG) signals are a critical resource for these systems. The primary benefit of employing EEG signals is that they reflect true emotion and are easily resolved by computer systems. In this work, EEG signals associated with good, neutral, and negative emotions were identified using channel selection preprocessing. However, researchers had a limited grasp of the specifics of the link between various emotional states until now. To identify EEG signals, we used discrete wavelet transform and machine learning techniques such as recurrent neural network (RNN) and k-nearest neighbor (kNN) algorithm. Initially, the classifier methods were utilized for channel selection. As a result, final feature vectors were created by integrating the features of EEG segments from these channels. Using the RNN and kNN algorithms, the final feature vectors with connected positive, neutral, and negative emotions were categorized independently. The classification performance of both techniques is computed and compared. Using RNN and kNN, the average overall accuracies were 94.844 % and 93.438 %, respectively.