Optimal Time-Series Motifs

Motifs are the most repetitive/frequent patterns of a time-series. The discovery of motifs is crucial for practitioners in order to understand and interpret the phenomena occurring in sequential data. Currently, motifs are searched among series sub-sequences, aiming at selecting the most frequently occurring ones. Search-based methods, which try out series sub-sequence as motif candidates, are currently believed to be the best methods in finding the most frequent patterns. However, this paper proposes an entirely new perspective in finding motifs. We demonstrate that searching is non-optimal since the domain of motifs is restricted, and instead we propose a principled optimization approach able to find optimal motifs. We treat the occurrence frequency as a function and time-series motifs as its parameters, therefore we \textit{learn} the optimal motifs that maximize the frequency function. In contrast to searching, our method is able to discover the most repetitive patterns (hence optimal), even in cases where they do not explicitly occur as sub-sequences. Experiments on several real-life time-series datasets show that the motifs found by our method are highly more frequent than the ones found through searching, for exactly the same distance threshold.Comment: Submitted to KDD201

Mining Constrained Gradients

Many data analysis tasks can be viewed as search or mining in a multidimensional space (MDS). In such MDSs, dimensions capture potentially important factors for given applications, and cells represent combinations of values for the factors. To systematically analyze data in MDS, an interesting notion, called "cubegrade" was recently introduced by Imielinski et al. [14], which focuses on the notable changes in measures in MDS by comparing a cell (which we refer to as probe cell) with its gradient cells, namely, its ancestors, descendants, and siblings. We call such queries gradient analysis queries (GQs). Since an MDS can contain billions of cells, it is important to answer GQs efficiently. In this study, we focus on developing efficient methods for mining GQs constrained by certain (weakly) antimonotone constraints. Instead of conducting an independent gradient-cell search once per probe cell, which is inefficient due to much repeated work, we propose an efficient algorithm, LiveSet-Driven. This algorithm finds all good gradient-probe cell pairs in one search pass. It utilizes measure-value analysis and dimension-match analysis in a set-oriented manner, to achieve bidirectional pruning between the sets of hopeful probe cells and of hopeful gradient cells. Moreover, it adopts a hypertree structure and an H-cubing method to compress data and to maximize sharing of computation. Our performance study shows that this algorithm is efficient and scalable. In addition to data cubes, we extend our study to another important scenario: mining constrained gradients in transactional databases where each item is associated with some measures such as price. Such transactional databases can be viewed as sparse MDSs where items represent dimensions, although they have signi..

Visual Feature Fusion and its Application to Support Unsupervised Clustering Tasks

On visual analytics applications, the concept of putting the user on the loop refers to the ability to replace heuristics by user knowledge on machine learning and data mining tasks. On supervised tasks, the user engagement occurs via the manipulation of the training data. However, on unsupervised tasks, the user involvement is limited to changes in the algorithm parametrization or the input data representation, also known as features. Depending on the application domain, different types of features can be extracted from the raw data. Therefore, the result of unsupervised algorithms heavily depends on the type of employed feature. Since there is no perfect feature extractor, combining different features have been explored in a process called feature fusion. The feature fusion is straightforward when the machine learning or data mining task has a cost function. However, when such a function does not exist, user support for combination needs to be provided otherwise the process is impractical. In this paper, we present a novel feature fusion approach that uses small data samples to allows users not only to effortless control the combination of different feature sets but also to interpret the attained results. The effectiveness of our approach is confirmed by a comprehensive set of qualitative and quantitative tests, opening up different possibilities of user-guided analytical scenarios not covered yet. The ability of our approach to providing real-time feedback for the feature fusion is exploited on the context of unsupervised clustering techniques, where the composed groups reflect the semantics of the feature combination.Comment: 15 pages, 21 Figure

Theoretical foundations of emergent constraints: relationships between climate sensitivity and global temperature variability in conceptual models

There is as yet no theoretical framework to guide the search for emergent constraints. As a result, there are significant risks that indiscriminate data-mining of the multidimensional outputs from GCMs could lead to spurious correlations and less than robust constraints on future changes. To mitigate against this risk, Cox et al (hereafter CHW18) proposed a theory-motivated emergent constraint, using the one-box Hasselmann model to identify a linear relationship between ECS and a metric of global temperature variability involving both temperature standard deviation and autocorrelation ($\Psi$). A number of doubts have been raised about this approach, some concerning the theory and the application of the one-box model to understand relationships in complex GCMs which are known to have more than the single characteristic timescale. We illustrate theory driven testing of emergent constraints using this as an example, namely we demonstrate that the linear $\Psi$-ECS proportionality is not an artifact of the one-box model and rigorously features to a good approximation in more realistic, yet still analytically soluble conceptual models, namely the two-box and diffusion models. Each of the conceptual models predict different power spectra with only the diffusion model's pink spectrum being compatible with observations and the complex CMIP5 GCMs. We also show that the theoretically predicted $\Psi$-ECS relationship exists in the \texttt{piControl} as well as \texttt{historical} CMIP5 experiments and that the differing gradients of the proportionality are inversely related to the effective forcing in that experiment.Comment: 12 pages, 4 figures, accepted for publication in Dynamics and Statistics of the Climate System. V2 with rewritten abstract to conform to journal style and references no longer corrupte

Scalable Gaussian Processes for Characterizing Multidimensional Change Surfaces

We present a scalable Gaussian process model for identifying and characterizing smooth multidimensional changepoints, and automatically learning changes in expressive covariance structure. We use Random Kitchen Sink features to flexibly define a change surface in combination with expressive spectral mixture kernels to capture the complex statistical structure. Finally, through the use of novel methods for additive non-separable kernels, we can scale the model to large datasets. We demonstrate the model on numerical and real world data, including a large spatio-temporal disease dataset where we identify previously unknown heterogeneous changes in space and time.Comment: 18 pages, 8 figure

Change Surfaces for Expressive Multidimensional Changepoints and Counterfactual Prediction

Identifying changes in model parameters is fundamental in machine learning and statistics. However, standard changepoint models are limited in expressiveness, often addressing unidimensional problems and assuming instantaneous changes. We introduce change surfaces as a multidimensional and highly expressive generalization of changepoints. We provide a model-agnostic formalization of change surfaces, illustrating how they can provide variable, heterogeneous, and non-monotonic rates of change across multiple dimensions. Additionally, we show how change surfaces can be used for counterfactual prediction. As a concrete instantiation of the change surface framework, we develop Gaussian Process Change Surfaces (GPCS). We demonstrate counterfactual prediction with Bayesian posterior mean and credible sets, as well as massive scalability by introducing novel methods for additive non-separable kernels. Using two large spatio-temporal datasets we employ GPCS to discover and characterize complex changes that can provide scientific and policy relevant insights. Specifically, we analyze twentieth century measles incidence across the United States and discover previously unknown heterogeneous changes after the introduction of the measles vaccine. Additionally, we apply the model to requests for lead testing kits in New York City, discovering distinct spatial and demographic patterns

RetainVis: Visual Analytics with Interpretable and Interactive Recurrent Neural Networks on Electronic Medical Records

We have recently seen many successful applications of recurrent neural networks (RNNs) on electronic medical records (EMRs), which contain histories of patients' diagnoses, medications, and other various events, in order to predict the current and future states of patients. Despite the strong performance of RNNs, it is often challenging for users to understand why the model makes a particular prediction. Such black-box nature of RNNs can impede its wide adoption in clinical practice. Furthermore, we have no established methods to interactively leverage users' domain expertise and prior knowledge as inputs for steering the model. Therefore, our design study aims to provide a visual analytics solution to increase interpretability and interactivity of RNNs via a joint effort of medical experts, artificial intelligence scientists, and visual analytics researchers. Following the iterative design process between the experts, we design, implement, and evaluate a visual analytics tool called RetainVis, which couples a newly improved, interpretable and interactive RNN-based model called RetainEX and visualizations for users' exploration of EMR data in the context of prediction tasks. Our study shows the effective use of RetainVis for gaining insights into how individual medical codes contribute to making risk predictions, using EMRs of patients with heart failure and cataract symptoms. Our study also demonstrates how we made substantial changes to the state-of-the-art RNN model called RETAIN in order to make use of temporal information and increase interactivity. This study will provide a useful guideline for researchers that aim to design an interpretable and interactive visual analytics tool for RNNs.Comment: Accepted at IEEE VIS 2018. To appear in IEEE Transactions on Visualization and Computer Graphics in January 201

From BOP to BOSS and Beyond: Time Series Classification with Dictionary Based Classifiers

A family of algorithms for time series classification (TSC) involve running a sliding window across each series, discretising the window to form a word, forming a histogram of word counts over the dictionary, then constructing a classifier on the histograms. A recent evaluation of two of this type of algorithm, Bag of Patterns (BOP) and Bag of Symbolic Fourier Approximation Symbols (BOSS) found a significant difference in accuracy between these seemingly similar algorithms. We investigate this phenomenon by deconstructing the classifiers and measuring the relative importance of the four key components between BOP and BOSS. We find that whilst ensembling is a key component for both algorithms, the effect of the other components is mixed and more complex. We conclude that BOSS represents the state of the art for dictionary based TSC. Both BOP and BOSS can be classed as bag of words approaches. These are particularly popular in Computer Vision for tasks such as image classification. Converting approaches from vision requires careful engineering. We adapt three techniques used in Computer Vision for TSC: Scale Invariant Feature Transform; Spatial Pyramids; and Histrogram Intersection. We find that using Spatial Pyramids in conjunction with BOSS (SP) produces a significantly more accurate classifier. SP is significantly more accurate than standard benchmarks and the original BOSS algorithm. It is not significantly worse than the best shapelet based approach, and is only outperformed by HIVE-COTE, an ensemble that includes BOSS as a constituent module

A Moving Least Squares Based Approach for Contour Visualization of Multi-Dimensional Data

Analysis of high dimensional data is a common task. Often, small multiples are used to visualize 1 or 2 dimensions at a time, such as in a scatterplot matrix. Associating data points between different views can be difficult though, as the points are not fixed. Other times, dimensional reduction techniques are employed to summarize the whole dataset in one image, but individual dimensions are lost in this view. In this paper, we present a means of augmenting a dimensional reduction plot with isocontours to reintroduce the original dimensions. By applying this to each dimension in the original data, we create multiple views where the points are consistent, which facilitates their comparison. Our approach employs a combination of a novel, graph-based projection technique with a GPU accelerated implementation of moving least squares to interpolate space between the points. We also present evaluations of this approach both with a case study and with a user study

Visual Analytics and Human Involvement in Machine Learning

The rapidly developing AI systems and applications still require human involvement in practically all parts of the analytics process. Human decisions are largely based on visualizations, providing data scientists details of data properties and the results of analytical procedures. Different visualizations are used in the different steps of the Machine Learning (ML) process. The decision which visualization to use depends on factors, such as the data domain, the data model and the step in the ML process. In this chapter, we describe the seven steps in the ML process and review different visualization techniques that are relevant for the different steps for different types of data, models and purposes