In functional programming, a fold is a higher-order function, also known as reduce and accumulate, whose purpose is to reduce a given data structure, typically a sequence of elements, into a single value. For example, a reduction could return an average value for a series of numbers, calculating a summation, maximum value, or minimum value. The fold function takes an initial value, commonly called the accumulator, which is used as a container for intermediate results. Then, the second argument it takes is a binary expression that acts as a reduction function to apply against each element in the sequence to finally return the new value for the accumulator. In general, reduction works as follows.

The best-known optimization clustering algorithm is k-means clustering. Unlike hierarchical clustering methods that require processing time proportional to the square or cube of the number of observations, the time required by the k-means algorithm is proportional to the number of observations. This means that k-means clustering can be used on larger data sets. In fact, k-means clustering is inappropriate for small ( 100 observations) data sets. If the data set is small, the k-means solution becomes sensitive to the order in which the observations appear (the order effect).

The commonly accepted definition of a community is that nodes tend to be more densely connected within a community than with the rest of the graph. Communities are often hidden in practice and recovering the community structure directly from the graph is a key step in the analysis of these datasets. Spectral algorithms are popular methods for detecting communities [26], that consist in two phases. First, a spectral embedding is built, where then nodes of the graph are projected onto some low dimensional space generated by well-chosen eigenvectors of some matrix related to the graph (e.g., the adjacency matrix or a Laplacian matrix). Then, a clustering algorithm (e.g.,k -means ork -median) is applied to then embedded vectors to obtain a partition of the nodes into communities.

Preserving the privacy of individuals by protecting their sensitive attributes is an important consideration during microdata release. However, it is equally important to preserve the quality or utility of the data for at least some targeted workloads. We propose a novel framework for privacy preservation based on the k-anonymity model that is ideally suited for workloads that require preserving the probability distribution of the quasi-identifier variables in the data. Our framework combines the principles of distribution-preserving quantization and k-member clustering, and we specialize it to two variants that respectively use intra-cluster and Gaussian dithering of cluster centers to achieve distribution preservation. We perform theoretical analysis of the proposed schemes in terms of distribution preservation, and describe their utility in workloads such as covariate shift and transfer learning where such a property is necessary. Using extensive experiments on real-world Medical Expenditure Panel Survey data, we demonstrate the merits of our algorithms over standard k-anonymization for a hallmark health care application where an insurance company wishes to understand the risk in entering a new market. Furthermore, by empirically quantifying the reidentification risk, we also show that the proposed approaches indeed maintain k-anonymity.

Many real world tasks such as reasoning and physical interaction require identification and manipulation of conceptual entities. A first step towards solving these tasks is the automated discovery of distributed symbol-like representations. In this paper, we explicitly formalize this problem as inference in a spatial mixture model where each component is parametrized by a neural network. Based on the Expectation Maximization framework we then derive a differentiable clustering method that simultaneously learns how to group and represent individual entities. We evaluate our method on the (sequential) perceptual grouping task and find that it is able to accurately recover the constituent objects. We demonstrate that the learned representations are useful for next-step prediction.

Molecular simulations produce very high-dimensional data-sets with millions of data points. As analysis methods are often unable to cope with so many dimensions, it is common to use dimensionality reduction and clustering methods to reach a reduced representation of the data. Yet these methods often fail to capture the most important features necessary for the construction of a Markov model. Here we demonstrate the results of various dimensionality reduction methods on two simulation data-sets, one of protein folding and another of protein-ligand binding. The methods tested include a k-means clustering variant, a non-linear auto encoder, principal component analysis and tICA. The dimension-reduced data is then used to estimate the implied timescales of the slowest process by a Markov state model analysis to assess the quality of the projection. The projected dimensions learned from the data are visualized to demonstrate which conformations the various methods choose to represent the molecular process.

Hypergraph partitioning is an important problem in machine learning, computer vision and network analytics. A widely used method for hypergraph partitioning relies on minimizing a normalized sum of the costs of partitioning hyperedges across clusters. Algorithmic solutions based on this approach assume that different partitions of a hyperedge incur the same cost. However, this assumption fails to leverage the fact that different subsets of vertices within the same hyperedge may have different structural importance. We hence propose a new hypergraph clustering technique, termed inhomogeneous hypergraph partitioning, which assigns different costs to different hyperedge cuts. We prove that inhomogeneous partitioning produces a quadratic approximation to the optimal solution if the inhomogeneous costs satisfy submodularity constraints. Moreover, we demonstrate that inhomogenous partitioning offers significant performance improvements in applications such as structure learning of rankings, subspace segmentation and motif clustering.

The Κ-means clustering algorithm uses iterative refinement to produce a final result. The algorithm inputs are the number of clusters Κ and the data set. The data set is a collection of features for each data point. The algorithm starts with initial estimates for the Κ centroids, which can either be randomly generated or randomly selected from the dataset. Each centroid defines one of the clusters.

Here at New Relic, we collect 1.37 billion data points per minute. A vast amount of the data we collect, analyze, and display for our customers is stored as time series. In an effort to build relationships between applications and other entities, such as servers and containers, for new, intelligent products like New Relic Radar, we're constantly exploring faster and more efficient methods of grouping time series data. Given the amount of data we collect, faster clustering times are crucial. A popular method of grouping data is k-means clustering.

Process mining is a research field focused on the analysis of event data with the aim of extracting insights related to dynamic behavior. Applying process mining techniques on data from smart home environments has the potential to provide valuable insights into (un)healthy habits and to contribute to ambient assisted living solutions. Finding the right event labels to enable the application of process mining techniques is however far from trivial, as simply using the triggering sensor as the label for sensor events results in uninformative models that allow for too much behavior (i.e., the models are overgeneralizing). Refinements of sensor level event labels suggested by domain experts have been shown to enable discovery of more precise and insightful process models. However, there exists no automated approach to generate refinements of event labels in the context of process mining. In this paper we propose a framework for the automated generation of label refinements based on the time attribute of events, allowing us to distinguish behaviourally different instances of the same event type based on their time attribute. We show on a case study with real-life smart home event data that using automatically generated refined labels in process discovery, we can find more specific, and therefore more insightful, process models. We observe that one label refinement could have an effect on the usefulness of other label refinements when used together. Therefore, we explore four strategies to generate useful combinations of multiple label refinements and evaluate those on three real-life smart home event logs.