Analyzing Time-Series Data. Presentation by Colin Shea-Blymyer
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1 Analyzing Time-Series Data Presentation by Colin Shea-Blymyer
2 Outline 1. Time Series Chains a. Motivation b. Problem c. Concepts d. Approach e. Results f. Conclusion 2. Analyzing Epidemics - FUNNEL a. Motivation b. Problem c. Models d. Algorithms e. Results f. Conclusion
3 Matrix Profile VII: Time Series Chains: A New Primitive for Time Series Data Mining Yan Zhu, Makoto Imamura, Daniel Nikovski, Eamonn Keogh Some content adapted from a presentation given at ICDM 2018
4 Motivation A major retailer wants to know how consumers shopping habits have changed. Given the number of times the retailer s name has been queried on Google, develop a model for the trend of the data. Data is obviously periodic, but this periodic behavior evolves. Model can be used to understand, and to forecast. Google query volume for Kohl s
5 Problem Given one example time series, No domain knowledge, Find a representation of the system s evolution Using a scalable algorithm.
6 Concepts - Matrix Profile (MP) Data structure that stores the distance from each subsequence of length m in a time series to its nearest neighbor.
7 Concepts - Motifs If a matrix profile s window size is 2... These clusters are motifs. Motif Region in time series with low matrix profile values.
8 Concepts - Chains Related to motifs - Chains integrate directionality Like a motif, but evolves over time Directionality is related to time
9 Approach - Overview 1. Compute left and right nearest neighbor a. Based off STOMP algorithm b. O(n 2 ) time, O(n) space 2. Find cains a. Find Anchored chains - O(n) time b. Find Unanchored chain - O(n) time
10 Approach - Example Matrix Profile window of m=1 Chain requires consecutive links to be connected by a loop. The all chain set is the set of chains that are not included in larger chains. All numbers are included exactly once.
11 Results 4 empirical evaluations - Blood flow, penguin dives, walking, and Blood Flow Penguin Dives Walking Web Queries 1 Robustness test Embed chains in synthetic data Increase noise and see if patterns are recovered
12 Results - Kohl s Understanding - links on chain show growing importance of Cyber Monday Forecasting - link analysis on these chains (RMSE = 0.17)
13 Conclusion Summary Independent of domain knowledge Requires only one example of the data Very fast One parameter - MP window size Robust to noise Future Work You reasoned it out beautifully, it is so long a chain, and yet every link rings true. -Sir Arthur Conan Doyle: Adventures of Sherlock Holmes More applications Multidimensional time series Different distance measure Something other than time series?
14 FUNNEL: Automatic Mining of Spatially Coevolving Epidemics Yasuko Matsubara, Yasushi Sakurai, Willem G. van Panhuis, Christos Faloutsos Some content adapted from a presentation given at SIGKDD 2014
15 Motivation Given a large data set of many diseases, in many locations, over a long period of time Discover 5 key properties of epidemics using an algorithm that is Fully automatic, Efficient, And generalizable across many types of epidemic.
16 Problem Project Tycho 50 locations (states) 56 diseases Weekly number of infected from 1888 to 2013 Forms a 3 rd order tensor Develop a model that summarizes each disease by: P1 - Periodicity P2 - Disease reduction effects P3 - Locality effects P4 - External shock effects P5 - Mistakes and incorrect values
17 Models - Single Epidemic FUNNEL-BASE b={n,β 0,δ,γ,Pa,Ps} FUNNEL-R FUNNEL-RE (t) - Strength of infection N: Population δ: Healing rate γ: Forgetting rate P a : Amplitude of fluctuation (peak season value) P s : Phase shift of seasonal cycle
18 Models - Multi-Evolving Epidemics
19 Algorithms - FUNNELFIT 1) Find external shocks and mistakes through Model Description Cost 2) Fit model parameters through Multi-Layer Optimization Global Fit Local Fit Levenberg-Marquardt (LM), aka the damped least-squares method - a least-squares curve fitting algorithm that uses both the Gauss-Newton method, and gradient descent - is used to minimize the cost function.
20 Results
21 Conclusion Finds the 5 properties of epidemics Execution time scales linearly to data size Can be applied to computer viruses as well Model is often 5x more accurate than competing algorithms
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