As the data resources grow, providing recommendations that best meet the demands has become a vital requirement in business and life to overcome the information overload problem. However, building a system suggesting relevant recommendations has always been a point of debate. One of the most cost-efficient techniques in terms of producing relevant recommendations at a low complexity is Product Quantization (PQ). PQ approaches have continued developing in recent years. This system's crucial challenge is improving product quantization performance in terms of recall measures without compromising its complexity. This makes the algorithm suitable for problems that require a greater number of potentially relevant items without disregarding others, at high-speed and low-cost to keep up with traffic. This is the case of online shops where the recommendations for the purpose are important, although customers can be susceptible to scoping other products. This research proposes a fuzzy approach to perform norm-based product quantization. Type-2 Fuzzy sets (T2FSs) define the codebook allowing sub-vectors (T2FSs) to be associated with more than one element of the codebook, and next, its norm calculus is resolved by means of integration. Our method finesses the recall measure up, making the algorithm suitable for problems that require querying at most possible potential relevant items without disregarding others. The proposed method outperforms all PQ approaches such as NEQ, PQ, and RQ up to +6%, +5%, and +8% by achieving a recall of 94%, 69%, 59% in Netflix, Audio, Cifar60k datasets, respectively. More and over, computing time and complexity nearly equals the most computationally efficient existing PQ method in the state-of-the-art.

Recently, CLIP has become an important model for aligning images and text in multi-modal contexts. However, researchers have identified limitations in the ability of CLIP's text and image encoders to extract detailed knowledge from pairs of captions and images. In response, this paper presents Knowledge-CLIP, an innovative approach designed to improve CLIP's performance by integrating a new knowledge distillation (KD) method based on Llama 2. Our approach focuses on three key objectives: Text Embedding Distillation, Concept Learning, and Contrastive Learning. First, Text Embedding Distillation involves training the Knowledge-CLIP text encoder to mirror the teacher model, Llama 2. Next, Concept Learning assigns a soft concept label to each caption-image pair by employing offline K-means clustering on text data from Llama 2, enabling Knowledge-CLIP to learn from these soft concept labels. Lastly, Contrastive Learning aligns the text and image embeddings. Our experimental findings show that the proposed model improves the performance of both text and image encoders.

The fairness of clustering algorithms has gained widespread attention across various areas, including machine learning, In this paper, we study fair $k$-means clustering in Euclidean space. Given a dataset comprising several groups, the fairness constraint requires that each cluster should contain a proportion of points from each group within specified lower and upper bounds. Due to these fairness constraints, determining the optimal locations of $k$ centers is a quite challenging task. We propose a novel ``Relax and Merge'' framework that returns a $(1+4\rho + O(\epsilon))$-approximate solution, where $\rho$ is the approximate ratio of an off-the-shelf vanilla $k$-means algorithm and $O(\epsilon)$ can be an arbitrarily small positive number. If equipped with a PTAS of $k$-means, our solution can achieve an approximation ratio of $(5+O(\epsilon))$ with only a slight violation of the fairness constraints, which improves the current state-of-the-art approximation guarantee. Furthermore, using our framework, we can also obtain a $(1+4\rho +O(\epsilon))$-approximate solution for the $k$-sparse Wasserstein Barycenter problem, which is a fundamental optimization problem in the field of optimal transport, and a $(2+6\rho)$-approximate solution for the strictly fair $k$-means clustering with no violation, both of which are better than the current state-of-the-art methods. In addition, the empirical results demonstrate that our proposed algorithm can significantly outperform baseline approaches in terms of clustering cost.

Clustering and outlier detection are two important tasks in data mining. Outliers frequently interfere with clustering algorithms to determine the similarity between objects, resulting in unreliable clustering results. Currently, only a few clustering algorithms (e.g., DBSCAN) have the ability to detect outliers to eliminate interference. For other clustering algorithms, it is tedious to introduce another outlier detection task to eliminate outliers before each clustering process. Obviously, how to equip more clustering algorithms with outlier detection ability is very meaningful. Although a common strategy allows clustering algorithms to detect outliers based on the distance between objects and clusters, it is contradictory to improving the performance of clustering algorithms on the datasets with outliers. In this paper, we propose a novel outlier detection approach, called ODAR, for clustering. ODAR maps outliers and normal objects into two separated clusters by feature transformation. As a result, any clustering algorithm can detect outliers by identifying clusters. Experiments show that ODAR is robust to diverse datasets. Compared with baseline methods, the clustering algorithms achieve the best on 7 out of 10 datasets with the help of ODAR, with at least 5% improvement in accuracy.

In Location-Based Services (LBS), such as food delivery, a fundamental task is segmenting Areas of Interest (AOIs), aiming at partitioning the urban geographical spaces into non-overlapping regions. Traditional AOI segmentation algorithms primarily rely on road networks to partition urban areas. While promising in modeling the geo-semantics, road network-based models overlooked the service-semantic goals (e.g., workload equality) in LBS service. In this paper, we point out that the AOI segmentation problem can be naturally formulated as a Markov Decision Process (MDP), which gradually chooses a nearby AOI for each grid in the current AOI's border. Based on the MDP, we present the first attempt to generalize Deep Reinforcement Learning (DRL) for AOI segmentation, leading to a novel DRL-based framework called DRL4AOI. The DRL4AOI framework introduces different service-semantic goals in a flexible way by treating them as rewards that guide the AOI generation. To evaluate the effectiveness of DRL4AOI, we develop and release an AOI segmentation system. We also present a representative implementation of DRL4AOI - TrajRL4AOI - for AOI segmentation in the logistics service. It introduces a Double Deep Q-learning Network (DDQN) to gradually optimize the AOI generation for two specific semantic goals: i) trajectory modularity, i.e., maximize tightness of the trajectory connections within an AOI and the sparsity of connections between AOIs, ii) matchness with the road network, i.e., maximizing the matchness between AOIs and the road network. Quantitative and qualitative experiments conducted on synthetic and real-world data demonstrate the effectiveness and superiority of our method. The code and system is publicly available at https://github.com/Kogler7/AoiOpt.

Symmetric nonnegative matrix factorization (SymNMF) is a powerful tool for clustering, which typically uses the $k$-nearest neighbor ($k$-NN) method to construct similarity matrix. However, $k$-NN may mislead clustering since the neighbors may belong to different clusters, and its reliability generally decreases as $k$ grows. In this paper, we construct the similarity matrix as a weighted $k$-NN graph with learnable weight that reflects the reliability of each $k$-th NN. This approach reduces the search space of the similarity matrix learning to $n - 1$ dimension, as opposed to the $\mathcal{O}(n^2)$ dimension of existing methods, where $n$ represents the number of samples. Moreover, to obtain a discriminative similarity matrix, we introduce a dissimilarity matrix with a dual structure of the similarity matrix, and propose a new form of orthogonality regularization with discussions on its geometric interpretation and numerical stability. An efficient alternative optimization algorithm is designed to solve the proposed model, with theoretically guarantee that the variables converge to a stationary point that satisfies the KKT conditions. The advantage of the proposed model is demonstrated by the comparison with nine state-of-the-art clustering methods on eight datasets. The code is available at \url{https://github.com/lwl-learning/LSDGSymNMF}.

Predicting pedestrian crossing behavior is important for intelligent traffic systems to avoid pedestrian-vehicle collisions. Most existing pedestrian crossing behavior models are trained and evaluated on datasets collected from a single country, overlooking differences between countries. To address this gap, we compared pedestrian road-crossing behavior at unsignalized crossings in Germany and Japan. We presented four types of machine learning models to predict gap selection behavior, zebra crossing usage, and their trajectories using simulator data collected from both countries. When comparing the differences between countries, pedestrians from the study conducted in Japan are more cautious, selecting larger gaps compared to those in Germany. We evaluate and analyze model transferability. Our results show that neural networks outperform other machine learning models in predicting gap selection and zebra crossing usage, while random forest models perform best on trajectory prediction tasks, demonstrating strong performance and transferability. We develop a transferable model using an unsupervised clustering method, which improves prediction accuracy for gap selection and trajectory prediction. These findings provide a deeper understanding of pedestrian crossing behaviors in different countries and offer valuable insights into model transferability.

3D situational awareness is critical for any autonomous system. However, when operating underwater, environmental conditions often dictate the use of acoustic sensors. These acoustic sensors are plagued by high noise and a lack of 3D information in sonar imagery, motivating the use of an orthogonal pair of imaging sonars to recover 3D perceptual data. Thus far, mapping systems in this area only use a subset of the available data at discrete timesteps and rely on object-level prior information in the environment to develop high-coverage 3D maps. Moreover, simple repeating objects must be present to build high-coverage maps. In this work, we propose a submap-based mapping system integrated with a simultaneous localization and mapping (SLAM) system to produce dense, 3D maps of complex unknown environments with varying densities of simple repeating objects. We compare this submapping approach to our previous works in this area, analyzing simple and highly complex environments, such as submerged aircraft. We analyze the tradeoffs between a submapping-based approach and our previous work leveraging simple repeating objects. We show where each method is well-motivated and where they fall short. Importantly, our proposed use of submapping achieves an advance in underwater situational awareness with wide aperture multi-beam imaging sonar, moving toward generalized large-scale dense 3D mapping capability for fully unknown complex environments.

The $\ell_2^2$ min-sum $k$-clustering problem is to partition an input set into clusters $C_1,\ldots,C_k$ to minimize $\sum_{i=1}^k\sum_{p,q\in C_i}\|p-q\|_2^2$. Although $\ell_2^2$ min-sum $k$-clustering is NP-hard, it is not known whether it is NP-hard to approximate $\ell_2^2$ min-sum $k$-clustering beyond a certain factor. In this paper, we give the first hardness-of-approximation result for the $\ell_2^2$ min-sum $k$-clustering problem. We show that it is NP-hard to approximate the objective to a factor better than $1.056$ and moreover, assuming a balanced variant of the Johnson Coverage Hypothesis, it is NP-hard to approximate the objective to a factor better than 1.327. We then complement our hardness result by giving the first $(1+\varepsilon)$-coreset construction for $\ell_2^2$ min-sum $k$-clustering. Our coreset uses $\mathcal{O}\left(k^{\varepsilon^{-4}}\right)$ space and can be leveraged to achieve a polynomial-time approximation scheme with runtime $nd\cdot f(k,\varepsilon^{-1})$, where $d$ is the underlying dimension of the input dataset and $f$ is a fixed function. Finally, we consider a learning-augmented setting, where the algorithm has access to an oracle that outputs a label $i\in[k]$ for input point, thereby implicitly partitioning the input dataset into $k$ clusters that induce an approximately optimal solution, up to some amount of adversarial error $\alpha\in\left[0,\frac{1}{2}\right)$. We give a polynomial-time algorithm that outputs a $\frac{1+\gamma\alpha}{(1-\alpha)^2}$-approximation to $\ell_2^2$ min-sum $k$-clustering, for a fixed constant $\gamma>0$.

Given points from an arbitrary metric space and a sequence of point updates sent by an adversary, what is the minimum recourse per update (i.e., the minimum number of changes needed to the set of centers after an update), in order to maintain a constant-factor approximation to a $k$-clustering problem? This question has received attention in recent years under the name consistent clustering. Previous works by Lattanzi and Vassilvitskii [ICLM '17] and Fichtenberger, Lattanzi, Norouzi-Fard, and Svensson [SODA '21] studied $k$-clustering objectives, including the $k$-center and the $k$-median objectives, under only point insertions. In this paper we study the $k$-center objective in the fully dynamic setting, where the update is either a point insertion or a point deletion. Before our work, {\L}\k{a}cki, Haeupler, Grunau, Rozho\v{n}, and Jayaram [SODA '24] gave a deterministic fully dynamic constant-factor approximation algorithm for the $k$-center objective with worst-case recourse of $2$ per update. In this work, we prove that the $k$-center clustering problem admits optimal recourse bounds by developing a deterministic fully dynamic constant-factor approximation algorithm with worst-case recourse of $1$ per update. Moreover our algorithm performs simple choices based on light data structures, and thus is arguably more direct and faster than the previous one which uses a sophisticated combinatorial structure. Additionally, we develop a new deterministic decremental algorithm and a new deterministic incremental algorithm, both of which maintain a $6$-approximate $k$-center solution with worst-case recourse of $1$ per update. Our incremental algorithm improves over the $8$-approximation algorithm by Charikar, Chekuri, Feder, and Motwani [STOC '97]. Finally, we remark that since all three of our algorithms are deterministic, they work against an adaptive adversary.