We propose an algorithmic approach for synthesizing linear hybrid automata from time-series data. Unlike existing approaches, our approach provides a whole family of models. Each model in the family is guaranteed to capture the input data up to a precision error {\epsilon}, in the following sense: For each time series, the model contains an execution that is {\epsilon}-close to the data points. Our construction allows to effectively choose a model from this family with minimal precision error {\epsilon}. We demonstrate the algorithm's efficiency and its ability to find precise models in two case studies.

Abstract: In this study, a novel method for the construction of a driving cycle based on Mean Shift clustering is proposed to solve the problems existing in the traditional micro-trips method. Firstly, 1701 kinematic segments are obtained by processing and dividing the driving data in real road conditions. Secondly, 12 kinematic parameters are calculated for each segment, and the dimensionality of parameters is reduced through principal component analysis (PCA). Three principal components are chosen to classify all cycles into three types by the Mean Shift algorithm. Finally, according to the principle of minimum deviation, representative micro-trips are selected from each type of cycle to complete the construction of the final driving cycle.

We propose a novel method for building fuzzy clusters of large data sets, using a smoothing numerical approach. The usual sum-of-squares criterion is relaxed so the search for good fuzzy partitions is made on a continuous space, rather than a combinatorial space as in classical methods \cite{Hartigan}. The smoothing allows a conversion from a strongly non-differentiable problem into differentiable subproblems of optimization without constraints of low dimension, by using a differentiable function of infinite class. For the implementation of the algorithm we used the statistical software $R$ and the results obtained were compared to the traditional fuzzy $C$--means method, proposed by Bezdek.

We present a large-scale comparative study of self-supervised speech representation (S3R)-based voice conversion (VC). In the context of recognition-synthesis VC, S3Rs are attractive owing to their potential to replace expensive supervised representations such as phonetic posteriorgrams (PPGs), which are commonly adopted by state-of-the-art VC systems. Using S3PRL-VC, an open-source VC software we previously developed, we provide a series of in-depth objective and subjective analyses under three VC settings: intra-/cross-lingual any-to-one (A2O) and any-to-any (A2A) VC, using the voice conversion challenge 2020 (VCC2020) dataset. We investigated S3R-based VC in various aspects, including model type, multilinguality, and supervision. We also studied the effect of a post-discretization process with k-means clustering and showed how it improves in the A2A setting. Finally, the comparison with state-of-the-art VC systems demonstrates the competitiveness of S3R-based VC and also sheds light on the possible improving directions.

We propose Few-Example Clustering (FEC), a In this paper, we propose Few-Example Clustering (FEC), a novel algorithm that performs contrastive learning novel clustering algorithm based on the hypothesis that the to cluster few examples. Our method is composed contrastive learner with the ground-truth cluster assignment of the following three steps: (1) generation of candidate is trained faster than the others. This hypothesis is built on cluster assignments, (2) contrastive learning the phenomenon that deep neural networks initially learn for each cluster assignment, and (3) selection patterns from the training examples. FEC is composed of of the best candidate. Based on the hypothesis the following three steps (see Figure 1): (1) generation of that the contrastive learner with the ground-truth candidate cluster assignments, (2) contrastive learning for cluster assignment is trained faster than the others, each cluster assignment, and (3) selection of the best candidate.

When designing clustering algorithms, the choice of initial centers is crucial for the quality of the learned clusters. In this paper, we develop a new initialization scheme, called HST initialization, for the $k$-median problem in the general metric space (e.g., discrete space induced by graphs), based on the construction of metric embedding tree structure of the data. From the tree, we propose a novel and efficient search algorithm, for good initial centers that can be used subsequently for the local search algorithm. Our proposed HST initialization can produce initial centers achieving lower errors than those from another popular initialization method, $k$-median++, with comparable efficiency. The HST initialization can also be extended to the setting of differential privacy (DP) to generate private initial centers. We show that the error from applying DP local search followed by our private HST initialization improves previous results on the approximation error, and approaches the lower bound within a small factor. Experiments justify the theory and demonstrate the effectiveness of our proposed method. Our approach can also be extended to the $k$-means problem.

In this paper, we proposed a new clustering-based active learning framework, namely Active Learning using a Clustering-based Sampling (ALCS), to address the shortage of labeled data. ALCS employs a density-based clustering approach to explore the cluster structure from the data without requiring exhaustive parameter tuning. A bi-cluster boundary-based sample query procedure is introduced to improve the learning performance for classifying highly overlapped classes. Additionally, we developed an effective diversity exploration strategy to address the redundancy among queried samples.

Multiple kernel clustering (MKC) is committed to achieving optimal information fusion from a set of base kernels. Constructing precise and local kernel matrices is proved to be of vital significance in applications since the unreliable distant-distance similarity estimation would degrade clustering per-formance. Although existing localized MKC algorithms exhibit improved performance compared to globally-designed competi-tors, most of them widely adopt KNN mechanism to localize kernel matrix by accounting for {\tau} -nearest neighbors. However, such a coarse manner follows an unreasonable strategy that the ranking importance of different neighbors is equal, which is impractical in applications. To alleviate such problems, this paper proposes a novel local sample-weighted multiple kernel clustering (LSWMKC) model. We first construct a consensus discriminative affinity graph in kernel space, revealing the latent local structures. Further, an optimal neighborhood kernel for the learned affinity graph is output with naturally sparse property and clear block diagonal structure. Moreover, LSWMKC im-plicitly optimizes adaptive weights on different neighbors with corresponding samples. Experimental results demonstrate that our LSWMKC possesses better local manifold representation and outperforms existing kernel or graph-based clustering algo-rithms. The source code of LSWMKC can be publicly accessed from https://github.com/liliangnudt/LSWMKC.

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In many reacting flow systems, the thermo-chemical state-space is known or assumed to evolve close to a low-dimensional manifold (LDM). Various approaches are available to obtain those manifolds and subsequently express the original high-dimensional space with fewer parameterizing variables. Principal component analysis (PCA) is one of the dimensionality reduction methods that can be used to obtain LDMs. PCA does not make prior assumptions about the parameterizing variables and retrieves them empirically from the training data. In this paper, we show that PCA applied in local clusters of data (local PCA) is capable of detecting the intrinsic parameterization of the thermo-chemical state-space. We first demonstrate that utilizing three common combustion models of varying complexity: the Burke-Schumann model, the chemical equilibrium model and the homogeneous reactor. Parameterization of these models is known a priori which allows for benchmarking with the local PCA approach. We further extend the application of local PCA to a more challenging case of a turbulent non-premixed $n$-heptane/air jet flame for which the parameterization is no longer obvious. Our results suggest that meaningful parameterization can be obtained also for more complex datasets. We show that local PCA finds variables that can be linked to local stoichiometry, reaction progress and soot formation processes.