Fuzzy K-Means Clustering without Cluster Centroids

Fuzzy K-Means clustering is a critical technique in unsupervised data analysis. However, the performance of popular Fuzzy K-Means algorithms is sensitive to the selection of initial cluster centroids and is also affected by noise when updating mean cluster centroids. To address these challenges, this paper proposes a novel Fuzzy K-Means clustering algorithm that entirely eliminates the reliance on cluster centroids, obtaining membership matrices solely through distance matrix computation. This innovation enhances flexibility in distance measurement between sample points, thus improving the algorithm's performance and robustness. The paper also establishes theoretical connections between the proposed model and popular Fuzzy K-Means clustering techniques. Experimental results on several real datasets demonstrate the effectiveness of the algorithm.

Weighted Sparse Partial Least Squares for Joint Sample and Feature Selection

Sparse Partial Least Squares (sPLS) is a common dimensionality reduction technique for data fusion, which projects data samples from two views by seeking linear combinations with a small number of variables with the maximum variance. However, sPLS extracts the combinations between two data sets with all data samples so that it cannot detect latent subsets of samples. To extend the application of sPLS by identifying a specific subset of samples and remove outliers, we propose an $\ell_\infty/\ell_0$-norm constrained weighted sparse PLS ($\ell_\infty/\ell_0$-wsPLS) method for joint sample and feature selection, where the $\ell_\infty/\ell_0$-norm constrains are used to select a subset of samples. We prove that the $\ell_\infty/\ell_0$-norm constrains have the Kurdyka-\L{ojasiewicz}~property so that a globally convergent algorithm is developed to solve it. Moreover, multi-view data with a same set of samples can be available in various real problems. To this end, we extend the $\ell_\infty/\ell_0$-wsPLS model and propose two multi-view wsPLS models for multi-view data fusion. We develop an efficient iterative algorithm for each multi-view wsPLS model and show its convergence property. As well as numerical and biomedical data experiments demonstrate the efficiency of the proposed methods.

X-IQE: eXplainable Image Quality Evaluation for Text-to-Image Generation with Visual Large Language Models

This paper introduces a novel explainable image quality evaluation approach called X-IQE, which leverages visual large language models (LLMs) to evaluate text-to-image generation methods by generating textual explanations. X-IQE utilizes a hierarchical Chain of Thought (CoT) to enable MiniGPT-4 to produce self-consistent, unbiased texts that are highly correlated with human evaluation. It offers several advantages, including the ability to distinguish between real and generated images, evaluate text-image alignment, and assess image aesthetics without requiring model training or fine-tuning. X-IQE is more cost-effective and efficient compared to human evaluation, while significantly enhancing the transparency and explainability of deep image quality evaluation models. We validate the effectiveness of our method as a benchmark using images generated by prevalent diffusion models. X-IQE demonstrates similar performance to state-of-the-art (SOTA) evaluation methods on COCO Caption, while overcoming the limitations of previous evaluation models on DrawBench, particularly in handling ambiguous generation prompts and text recognition in generated images. Project website: https://github.com/Schuture/Benchmarking-Awesome-Diffusion-Models

Rethinking Two Consensuses of the Transferability in Deep Learning

Deep transfer learning (DTL) has formed a long-term quest toward enabling deep neural networks (DNNs) to reuse historical experiences as efficiently as humans. This ability is named knowledge transferability. A commonly used paradigm for DTL is firstly learning general knowledge (pre-training) and then reusing (fine-tuning) them for a specific target task. There are two consensuses of transferability of pre-trained DNNs: (1) a larger domain gap between pre-training and downstream data brings lower transferability; (2) the transferability gradually decreases from lower layers (near input) to higher layers (near output). However, these consensuses were basically drawn from the experiments based on natural images, which limits their scope of application. This work aims to study and complement them from a broader perspective by proposing a method to measure the transferability of pre-trained DNN parameters. Our experiments on twelve diverse image classification datasets get similar conclusions to the previous consensuses. More importantly, two new findings are presented, i.e., (1) in addition to the domain gap, a larger data amount and huge dataset diversity of downstream target task also prohibit the transferability; (2) although the lower layers learn basic image features, they are usually not the most transferable layers due to their domain sensitivity.

Learning to Optimize Permutation Flow Shop Scheduling via Graph-based Imitation Learning

The permutation flow shop scheduling (PFSS), aiming at finding the optimal permutation of jobs, is widely used in manufacturing systems. When solving the large-scale PFSS problems, traditional optimization algorithms such as heuristics could hardly meet the demands of both solution accuracy and computational efficiency. Thus learning-based methods have recently garnered more attention. Some work attempts to solve the problems by reinforcement learning methods, which suffer from slow convergence issues during training and are still not accurate enough regarding the solutions. To that end, we train the model via expert-driven imitation learning, which accelerates the convergence more stably and accurately. Moreover, in order to extract better feature representations of input jobs, we incorporate the graph structure as the encoder. The extensive experiments reveal that our proposed model obtains significant promotion and presents excellent generalizability in large-scale problems with up to 1000 jobs. Compared to the state-of-the-art reinforcement learning method, our model's network parameters are reduced to only 37\% of theirs, and the solution gap of our model towards the expert solutions decreases from 6.8\% to 1.3\% on average.

MetaLR: Layer-wise Learning Rate based on Meta-Learning for Adaptively Fine-tuning Medical Pre-trained Models

When applying transfer learning for medical image analysis, downstream tasks often have significant gaps with the pre-training tasks. Previous methods mainly focus on improving the transferabilities of the pre-trained models to bridge the gaps. In fact, model fine-tuning can also play a very important role in tackling this problem. A conventional fine-tuning method is updating all deep neural networks (DNNs) layers by a single learning rate (LR), which ignores the unique transferabilities of different layers. In this work, we explore the behaviors of different layers in the fine-tuning stage. More precisely, we first hypothesize that lower-level layers are more domain-specific while higher-level layers are more task-specific, which is verified by a simple bi-directional fine-tuning scheme. It is harder for the pre-trained specific layers to transfer to new tasks than general layers. On this basis, to make different layers better co-adapt to the downstream tasks according to their transferabilities, a meta-learning-based LR learner, namely MetaLR, is proposed to assign LRs for each layer automatically. Extensive experiments on various medical applications (i.e., POCUS, BUSI, Chest X-ray, and LiTS) well confirm our hypothesis and show the superior performance of the proposed methods to previous state-of-the-art fine-tuning methods.

Towards Class-Specific Unit

Class selectivity is an attribute of a unit in deep neural networks, which characterizes the discriminative ability of units to a specific class. Intuitively, decisions made by several highly selective units are more interpretable since it is easier to be traced back to the origin while that made by complex combinations of lowly selective units are more difficult to interpret. In this work, we develop a novel way to directly train highly selective units, through which we are able to examine the performance of a network that only rely on highly selective units. Specifically, we train the network such that all the units in the penultimate layer only response to one specific class, which we named as class-specific unit. By innovatively formulating the problem using mutual information, we find that in such a case, the output of the model has a special form that all the probabilities over non-target classes are uniformly distributed. We then propose a minimax loss based on a game theoretic framework to achieve the goal. Nash equilibria are proved to exist and the outcome is consistent with our regularization objective. Experimental results show that the model trained with the proposed objective outperforms models trained with baseline objective among all the tasks we test. Our results shed light on the role of class-specific units by indicating that they can be directly used for decisions without relying on low selective units.

Regularized Singular Value Decomposition and Application to Recommender System

Singular value decomposition (SVD) is the mathematical basis of principal component analysis (PCA). Together, SVD and PCA are one of the most widely used mathematical formalism/decomposition in machine learning, data mining, pattern recognition, artificial intelligence, computer vision, signal processing, etc. In recent applications, regularization becomes an increasing trend. In this paper, we present a regularized SVD (RSVD), present an efficient computational algorithm, and provide several theoretical analysis. We show that although RSVD is non-convex, it has a closed-form global optimal solution. Finally, we apply RSVD to the application of recommender system and experimental result show that RSVD outperforms SVD significantly.

Minimal Support Vector Machine

Support Vector Machine (SVM) is an efficient classification approach, which finds a hyperplane to separate data from different classes. This hyperplane is determined by support vectors. In existing SVM formulations, the objective function uses L2 norm or L1 norm on slack variables. The number of support vectors is a measure of generalization errors. In this work, we propose a Minimal SVM, which uses L0.5 norm on slack variables. The result model further reduces the number of support vectors and increases the classification performance.

Outlier Regularization for Vector Data and L21 Norm Robustness

In many real-world applications, data usually contain outliers. One popular approach is to use L2,1 norm function as a robust error/loss function. However, the robustness of L2,1 norm function is not well understood so far. In this paper, we propose a new Vector Outlier Regularization (VOR) framework to understand and analyze the robustness of L2,1 norm function. Our VOR function defines a data point to be outlier if it is outside a threshold with respect to a theoretical prediction, and regularize it-pull it back to the threshold line. We then prove that L2,1 function is the limiting case of this VOR with the usual least square/L2 error function as the threshold shrinks to zero. One interesting property of VOR is that how far an outlier lies away from its theoretically predicted value does not affect the final regularization and analysis results. This VOR property unmasks one of the most peculiar property of L2,1 norm function: The effects of outliers seem to be independent of how outlying they are-if an outlier is moved further away from the intrinsic manifold/subspace, the final analysis results do not change. VOR provides a new way to understand and analyze the robustness of L2,1 norm function. Applying VOR to matrix factorization leads to a new VORPCA model. We give a comprehensive comparison with trace-norm based L21-norm PCA to demonstrate the advantages of VORPCA.