The paper clusters sequences from unknown distributions using k-medoids.
problem Clustering sequences from unknown composite distributions.
method k-medoids algorithm for sequences with composite distributions.
result Error probability decreases exponentially with increasing sample size.
Many clustering algorithms exist that estimate a cluster centroid, such as K-means, K-medoids or mean-shift, but no algorithm seems to exist that clusters data by returning exactly K meaningful modes. We propose a natural definition of a K-modes objective function by combining the notions of density and cluster assignm…
BanditPAM clusters data faster than traditional methods.
problem Efficiently clustering large datasets with arbitrary distance metrics.
method Inspired by multi-armed bandits, reduces PAM complexity from O(n2) to O(nlogn). result Matches state-of-the-art clustering loss with up to 4x faster results and 200x fewer distance computations.
Determinantal consensus clustering improves clustering robustness.
problem Robustness of clustering algorithms.
method Use of determinantal point processes (DPP) for random restart of clustering algorithms.
result Determinantal consensus clustering outperforms classical algorithms.
Paper proposes SLINK clustering for nonparametric data sequences with improved consistency.
problem Nonparametric clustering of data sequences from unknown distributions.
method Exponentially consistent nonparametric SLINK clustering algorithm.
result SLINK clustering achieves exponential consistency under less strict conditions.
A new KM clustering algorithm reduces error and scales to large datasets.
problem Traditional KM error analyses suffer from generalization gaps and lack true error bounds.
method Formalized true K-Medoids error, decomposed into ME and MME, provided convergence result, proposed MCPAM algorithm.
result MCPAM achieves true error bounds and scales to 1 billion points.
EKM solves the K-medoids problem in polynomial time.
problem The K-medoids problem in data analysis. method EKM is a novel algorithm using transformational programming and combinatorial generation.
result EKM solves the K-medoids problem in worst-case $O\left(N^{K+1}
ight)$ time complexity. This paper introduces a noise-robust clustering method using distribution distances.
problem Reducing noise impact on clustering results.
method Introduces expectation distance (ED) for distribution clustering, extending K-means and K-medoids.
result Improved clustering accuracy and reduced computation time.
Improved k-medoids clustering with faster algorithms for big data.
problem High runtime cost of k-medoids clustering algorithms.
method Modifications to PAM, CLARA, and CLARANS algorithms to achieve O(k) runtime improvement.
result 458x and 1191x speedup in runtime for k=100,200 respectively.
Faster k-Medoids Clustering improves PAM, CLARA, CLARANS algorithms.
problem Efficiently clustering non-Euclidean data with high k.
method Modifications to PAM, CLARA, CLARANS algorithms to achieve O(k)-fold speedup.
result 200-fold speedup observed on real data with k=100.
New SVM feature selection methods improve wafer testing accuracy.
problem Need for improved SVM feature selection methods.
method Entropy measurement and K-medoid clustering for feature selection.
result One-class SVM's enhance wafer testing accuracy.
The paper proposes a new method to evaluate LLM agent responses using ECDF clustering.
problem The standard evaluation of LLM agent responses via majority voting obscures response quality and distribution.
method The paper introduces a novel evaluation framework based on ECDF of cosine similarities and clustering of ECDFs using distances and k-medoids algorithm. result ECDF clustering reveals interpretable group structures in LLM responses, offering insights into agent settings.
Paper uses autoencoders for time series clustering with energy data.
problem Challenges in time series clustering, especially with outliers.
method Combines convolutional autoencoder and k-medoids for clustering.
result Improves clustering robustness to outliers and finer clusters.
New method uses GNNs and node feature propagation for active learning in graph node classification.
problem Lack of labeled data for graph neural networks.
method Node feature propagation followed by K-Medoids clustering for instance selection.
result Proposed method significantly outperforms other methods on benchmark datasets.
For a certain class of distributions, we prove that the linear programming relaxation of k-medoids clustering---a variant of k-means clustering where means are replaced by exemplars from within the dataset---distinguishes points drawn from nonoverlapping balls with high probability once the number of points drawn a…
New theory for clustering in geometric and adaptive settings.
problem Clustering in non-Euclidean spaces and adaptive parameters.
method Asymptotic theory for k-means and related methods. result Strong consistency and asymptotic limit theorems for various clustering procedures.
Adaptive sampling improves finding good local optima in combinatorial optimization.
problem Finding good local optima in NP-hard combinatorial optimization problems.
method Derive a robust learning algorithm to adapt sampling distributions towards good local optima.
result Adaptive sampling outperforms related methods in recovering locally maximal cliques and k-medoid clustering.
Develops a faster soybean genome clustering method combining spectral and vector quantization.
problem Clustering soybean whole genome sequences efficiently.
method Combines Spectral Clustering and Vector Quantization for computational efficiency.
result Significantly outperforms existing methods in cluster quality and time complexity.
We quantify the amount of information filtered by different hierarchical clustering methods on correlations between stock returns comparing it with the underlying industrial activity structure. Specifically, we apply, for the first time to financial data, a novel hierarchical clustering approach, the Directed Bubble Hi…
Neural clustering learns time series affinity from statistical features.
problem Challenging time series clustering with unknown cluster shapes and structures.
method Amortized neural inference using statistical features.
result Competitive clustering accuracy without manual specification of cluster shapes.
Graph clustering improved using Boltzmann machine heuristics.
problem Graph clustering to form densely connected clusters.
method Two mathematical programming formulations, two variations of Boltzmann machine heuristic.
result Boltzmann machine provides superior solutions and faster computation times.
In this paper, we propose a technique for time series clustering using community detection in complex networks. Firstly, we present a method to transform a set of time series into a network using different distance functions, where each time series is represented by a vertex and the most similar ones are connected. The…
Starting from a dataset with input/output time series generated by multiple deterministic linear dynamical systems, this paper tackles the problem of automatically clustering these time series. We propose an extension to the so-called Martin cepstral distance, that allows to efficiently cluster these time series, and a…
We present a new algorithm, trimed, for obtaining the medoid of a set, that is the element of the set which minimises the mean distance to all other elements. The algorithm is shown to have, under certain assumptions, expected run time O(N^(3/2)) in R^d where N is the set size, making it the first sub-quadratic exact m…
In this paper, we firstly give a brief introduction of expectation maximization (EM) algorithm, and then discuss the initial value sensitivity of expectation maximization algorithm. Subsequently, we give a short proof of EM's convergence. Then, we implement experiments with the expectation maximization algorithm (We im…
Machine learning optimizes box selection for efficient warehouse operations.
problem Optimizing the selection of shipping boxes for thousands of products.
method Formulated as a clustering problem, parameters estimated via analytics.
result Improves box utilization rate by over 10%.
Quantum machine learning improves satellite image alignment.
problem Align satellite images taken at different times and angles.
method Quantum machine learning techniques for feature extraction and matching.
result Quantum methods show potential for future improvements.
A new method reduces high-dimensional parameter spaces for faster numerical tasks.
problem Efficiently reducing high-dimensional parameter spaces for numerical tasks.
method Local Active Subspaces (LAS) combining active subspaces with clustering techniques.
result Significant speed-up in numerical tasks through efficient dimension reduction.
ProtoBandit uses bandits to find prototypes efficiently.
problem Finding a compact set of prototypes from a large dataset.
method Stochastic greedy search and multi-armed bandits.
result ProtoBandit reduces similarity comparisons to O(k3∣S∣), independent of target set size. A new evolutionary algorithm improves k-means clustering by recombining the entire population.
problem Optimizing the k-means clustering problem, especially in non-convex cases.
method Recombinator-k-means uses stochastic recombination with a reweighting mechanism.
result Recombinator-k-means outperforms standard genetic algorithms in optimization objective.
Diffusion maps are a nonlinear manifold learning technique based on harmonic analysis of a diffusion process over the data. Out-of-sample extensions with computational complexity O(N), where N is the number of points comprising the manifold, frustrate applications to online learning applications requiring…
k-GANs uses an ensemble of GANs with semi-discrete OT for better modeling.
problem Mode collapse in GANs.
method Semi-discrete optimal transport for training an ensemble of GANs.
result k-GANs consistently outperforms baseline GANs in experiments.
Paper develops malware detection methods using Hamming distance.
problem Detecting and preventing spread of Android malware.
method Four detection methods using Hamming distance for similarity.
result Accuracy rates of proposed algorithms are more than 90%.
Convex clustering can only learn convex clusters, with significant gaps between clusters.
problem Understanding the limitations and capabilities of convex clustering.
method Analyzing convex clustering solutions, proving properties, and characterizing clusters.
result Convex clustering can only learn convex clusters with significant gaps between clusters.
Proposes a method to predict cluster number and cluster representatives using cluster stability analysis.
problem Determining the number of clusters in a dataset.
method Analyzes cluster stability using Monte-Carlo simulation to predict cluster number and find cluster representatives.
result Significant improvement in predicting cluster numbers and cluster composition in large datasets.
Paper compares clusterability measures for data mining.
problem Selecting appropriate clusterability measures for data.
method Extensive comparison of clusterability measures.
result Guidelines for selecting suitable measures for clustering.
Proposes a new clustering method based on expectiles for non-spherical clusters.
problem Inability of K-means to handle non-spherical clusters. method Uses expectiles to define cluster centers and searches for clusters via a greedy algorithm.
result Outperforms K-means and spectral clustering on asymmetric shaped clusters. CCMM efficiently solves large-scale convex clustering problems.
problem Scalability and hierarchical structure in convex clustering.
method Majorization-minimization algorithm with cluster fusions and efficient updating.
result CCMM achieves efficient solutions for large datasets.
This paper reviews weighted clustering ensemble methods.
problem Improving clustering results from individual methods.
method Different types of weights and approaches to determining weight values.
result Unified framework for selecting appropriate weighting mechanisms.
Discussing issues in robust clustering, especially with Gaussian models.
problem Handling outliers and ambiguity in clustering groups.
method Focus on Gaussian mixture model, examining formal definitions, interactions, and tuning decisions.
result Outliers can confuse clustering groups and existing stability measures fail with them.
New indices for determining cluster compactness and separability.
problem Challenges in identifying true clusters in data sets.
method Developed absolute cluster indices to measure compactness and separability.
result Demonstrated improved performance compared to existing indices.
Mode clustering is a nonparametric method for clustering that defines clusters using the basins of attraction of a density estimator's modes. We provide several enhancements to mode clustering: (i) a soft variant of cluster assignment, (ii) a measure of connectivity between clusters, (iii) a technique for choosing the …
In this paper, a similarity-driven cluster merging method is proposed for unsuper-vised fuzzy clustering. The cluster merging method is used to resolve the problem of cluster validation. Starting with an overspecified number of clusters in the data, pairs of similar clusters are merged based on the proposed similarity-…
This paper introduces a persistence metric to compare clustering solutions with different numbers of clusters.
problem Determining the true number of clusters in a dataset when prior knowledge is lacking.
method The paper introduces a persistence metric based on the maximum over two-norms of all cluster-covariance matrices.
result The persistence metric accurately identifies clustering solutions with the true number of clusters.
In many practical applications of clustering, the objects to be clustered evolve over time, and a clustering result is desired at each time step. In such applications, evolutionary clustering typically outperforms traditional static clustering by producing clustering results that reflect long-term trends while being ro…
Study examines how cluster number affects short-text clustering, introducing a stability metric.
problem Challenges in finding meaningful clusters in short-text data.
method Introduces a stability metric to determine cluster robustness and visualizes cluster subdivisions.
result Choosing a cluster number involves balancing informativeness and complexity, not seeking a single 'optimal' solution.
Convex clustering, a convex relaxation of k-means clustering and hierarchical clustering, has drawn recent attentions since it nicely addresses the instability issue of traditional nonconvex clustering methods. Although its computational and statistical properties have been recently studied, the performance of convex c…
Cluster LOCO: A model-agnostic feature importance score for interpreting cluster outputs
problem Interpreting and auditing cluster outputs
method Cluster LOCO (Leave-One-Covariate-Out)
result More reliably recovers informative features than existing methods