For the past decades we have experienced an enormous expansion of the accumulated data that humanity produces. Daily a numerous number of smart devices, usually interconnected over internet, produce vast, real-values datasets. Time series representing datasets from completely irrelevant domains such as finance, weather, medical applications, traffic control etc. become more and more crucial in human day life. Analyzing and clustering these time series, or in general any kind of curves, could be critical for several human activities. In the current paper, the new Curves Clustering Using Common Patterns (3CP) methodology is introduced, which applies a repeated pattern detection algorithm in order to cluster sequences according to their shape and the similarities of common patterns between time series, data curves and eventually any kind of discrete sequences. For this purpose, the Longest Expected Repeated Pattern Reduced Suffix Array (LERP-RSA) data structure has been used in combination with the All Repeated Patterns Detection (ARPaD) algorithm in order to perform highly accurate and efficient detection of similarities among data curves that can be used for clustering purposes and which also provides additional flexibility and features.

The recent increase in the scale and complexity of software systems has introduced new challenges to the time series monitoring and anomaly detection process. A major drawback of existing anomaly detection methods is that they lack contextual information to help stakeholders identify the cause of anomalies. This problem, known as root cause detection, is particularly challenging to undertake in today's complex distributed software systems since the metrics under consideration generally have multiple internal and external dependencies. Significant manual analysis and strong domain expertise is required to isolate the correct cause of the problem. In this paper, we propose a method that isolates the root cause of an anomaly by analyzing the patterns in time series fluctuations. Our method considers the time series as observations from an underlying process passing through a sequence of discretized hidden states. The idea is to track the propagation of the effect when a given problem causes unaligned but homogeneous shifts of the underlying states. We evaluate our approach by finding the root cause of anomalies in Zillows clickstream data by identifying causal patterns among a set of observed fluctuations.

Counting the number of clusters, when these clusters overlap significantly is a challenging problem in machine learning. We argue that a purely mathematical quantum theory, formulated using the path integral technique, when applied to non-physics modeling leads to non-physics quantum theories that are statistical in nature. We show that a quantum theory can be a more robust statistical theory to separate data to count overlapping clusters. The theory is also confirmed from data simulations.This works identify how quantum theory can be effective in counting clusters and hope to inspire the field to further apply such techniques.

In recent years, the advances in single-cell RNA-seq techniques have enabled us to perform large-scale transcriptomic profiling at single-cell resolution in a high-throughput manner. Unsupervised learning such as data clustering has become the central component to identify and characterize novel cell types and gene expression patterns. In this study, we review the existing single-cell RNA-seq data clustering methods with critical insights into the related advantages and limitations. In addition, we also review the upstream single-cell RNA-seq data processing techniques such as quality control, normalization, and dimension reduction. We conduct performance comparison experiments to evaluate several popular single-cell RNA-seq clustering approaches on two single-cell transcriptomic datasets.

Marine buoys aid in the battle against Illegal, Unreported and Unregulated (IUU) fishing by detecting fishing vessels in their vicinity. Marine buoys, however, may be disrupted by natural causes and buoy vandalism. To minimize the effects of buoy disruption on a buoy network, we propose a more robust buoy placement using dropout k-means and dropout k-median. We apply dropout k-means and dropout k-median to determine locations for deploying marine buoys in the Gabonese waters near West Africa. We simulated the passage of ships using historical Automatic Identification System (AIS) data, then compared the ship detection probability of dropout k-means to classic k-means and dropout k-median to classic k-median, taking into account that the current sensor detection radius is 10km. With 5 buoys, the buoy arrangement computed by classic k-means, dropout k-means, classic k-median and dropout k-median have ship detection probabilities of 38%, 45%, 48% and 52%.

Motivated by the concept of network motifs we construct certain clustering methods (functors) which are parametrized by a given collection of motifs (or representers).

We introduce Grinch, a new algorithm for large-scale, non-greedy hierarchical clustering with general linkage functions that compute arbitrary similarity between two point sets. The key components of Grinch are its rotate and graft subroutines that efficiently reconfigure the hierarchy as new points arrive, supporting discovery of clusters with complex structure. Grinch is motivated by a new notion of separability for clustering with linkage functions: we prove that when the model is consistent with a ground-truth clustering, Grinch is guaranteed to produce a cluster tree containing the ground-truth, independent of data arrival order. Our empirical results on benchmark and author coreference datasets (with standard and learned linkage functions) show that Grinch is more accurate than other scalable methods, and orders of magnitude faster than hierarchical agglomerative clustering.

The idea of Innovation Search was proposed as a data clustering method in which the directions of innovation were utilized to compute the adjacency matrix and it was shown that Innovation Pursuit can notably outperform the self representation based subspace clustering methods. In this paper, we present a new discovery that the directions of innovation can be used to design a provable and strong robust (to outlier) PCA method. The proposed approach, dubbed iSearch, uses the direction search optimization problem to compute an optimal direction corresponding to each data point. iSearch utilizes the directions of innovation to measure the innovation of the data points and it identifies the outliers as the most innovative data points. Analytical performance guarantees are derived for the proposed robust PCA method under different models for the distribution of the outliers including randomly distributed outliers, clustered outliers, and linearly dependent outliers. In addition, we study the problem of outlier detection in a union of subspaces and it is shown that iSearch provably recovers the span of the inliers when the inliers lie in a union of subspaces. Moreover, we present theoretical studies which show that the proposed measure of innovation remains stable in the presence of noise and the performance of iSearch is robust to noisy data. In the challenging scenarios in which the outliers are close to each other or they are close to the span of the inliers, iSearch is shown to remarkably outperform most of the existing methods. The presented method shows that the directions of innovation are useful representation of the data which can be used to perform both data clustering and outlier detection.

Prior work inspired by compression algorithms has described how the Burrows Wheeler Transform can be used to create a distance measure for bioinformatics problems. We describe issues with this approach that were not widely known, and introduce our new Burrows Wheeler Markov Distance (BWMD) as an alternative. The BWMD avoids the shortcomings of earlier efforts, and allows us to tackle problems in variable length DNA sequence clustering. BWMD is also more adaptable to other domains, which we demonstrate on malware classification tasks. Unlike other compression-based distance metrics known to us, BWMD works by embedding sequences into a fixed-length feature vector. This allows us to provide significantly improved clustering performance on larger malware corpora, a weakness of prior methods.

We present an approach for end-to-end learning that allows one to jointly learn a feature representation from unlabeled data (with or without labeled data) and predict labels for unlabeled data. The feature representation is assumed to be specified in a differentiable programming framework, that is, as a parameterized mapping amenable to automatic differentiation. The proposed approach can be used with any amount of labeled and unlabeled data, gracefully adjusting to the amount of supervision. We provide experimental results illustrating the effectiveness of the approach.