TIME SERIES & MACHINE LEARNING

PHD Luis Miralles

INDEX:

1.- What are Time Series and its relation with Machine Learning?

2.- Time series supervised learning: Human activity recognition

3.- Time series unsupervised learning: Similarity measures

4.- Time series clustering

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1.- What are Time Series and its relation with

Machine Learning?

What are time series?

A series of values of a quantity obtained at successive times, often with equal

intervals between them.

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What are Time Series?

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Sampling techniques

Sampling is the process of transforming continuous data into discrete data. There

are basically two ways of sampling: one based on time (Riemann) and the other

based on the behaviour of the signals (Lebesgue).

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Time series sampling techniques

- Riemann sampling: Captures samples depending on the time.

- Lebesgue sampling: Captures samples depending on the variation of the

output signal.

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Riemann sampling

It is also known as Riemann sampling and it captures the information from the

continuous-signals at an equidistant time intervals (every second, every

minute,...). It is very simple to implement and that is why it has been used for

many years.

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Lebesgue sampling

● It is more effective but it is also more difficult to implement.

● Advantages: Increasing the battery life of the sensors, reducing network traffic

by decreasing the amount of information transferred and using fewer computer

resources.

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What is the relationship between Machine Learning

and Time Series?

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What is Machine Learning?

● Arthur Samuel (1959). Machine Learning: Field of study that gives computers

the ability to learn without being explicitly scheduled.

● Semi-automated extraction of knowledge from data

● Extract knowledge and insight from data. The computer extracts some

information from data using algorithms.

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Supervised vs Unsupervised learning

Machine Learning

Techniques

Supervised Learning

Unsupervised

Learning

Random Forest, Support Vector

Machine, Neural Networks, Naïve

Bayesian, K-nearest neighbors.

Hierarchical clustering, k-Means

clustering

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Supervised learning

Supervised Learning

Classification

Regression

The classification algorithms predict a

class/label based on the inputs.

The regression algorithms predict a quantity

based on the inputs.

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Unsupervised learning

Unsupervised

Learning

k-Means

Hierarchical clustering

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Reinforcement learning

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Cold start versus Warm start

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Basic Machine Learning Steps

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Step I:

Extract information

Step II:

Preprocessing: Clean

data, Missing values,

Feature selection

Step III:

Build model, Optimize

model

Step IV:

Implement data

Step III:

Plot results

Confusion matrix performance

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CM Binary class CM Multi-class

Cross validation technique to optimise models

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Machine Learning most used metrics

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2.- Time series classification and Human

activity recognition

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Time series Regression

Time series Regression

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Time series classification

Overview of the HAR process

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How to apply a time window to raw data

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1 1000

2000

1

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Methodology for HAR systems

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Why Deep Learning is so famous?

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IMU: Inertial measurement unit

An inertial measurement unit (IMU) is an electronic

device that measures and reports a body's specific

force, angular rate, and sometimes the magnetic field

surrounding the body, using a combination of

accelerometers and gyroscopes, sometimes also

magnetometers.

IMUs are typically used to manoeuvre aircraft,

including unmanned aerial vehicles (UAVs), among

many others, and spacecraft, including satellites and

landers.

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Feature selection saves time and improves accuracy

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Selecting features individually Selecting features by subsets

Filter vs Wrapper

PCA: Principal component analysis

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Feature selection in HAR

Feature extraction from the window

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Time

Frequency

Confusion matrix

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HAR: Accelerometer, magnetometer and Gyroscope

▪ The Accelerometer measures total acceleration on the vehicle, including the

static acceleration from gravity it would experience even when its not moving.

▪ The magnetometer measures the magnetic field around the robot, including the

static magnetic field pointing approximately north caused by the earth.

▪ The Gyroscope measures your instantaneous angular momentum around each

axis, basically how fast its rotating.

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Human activity recognition steps

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Evaluation

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Number of samples per activity

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Number of samples per user

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Values per axis for the walking activity

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3.- Time series similarity measures

Euclidean distance between ts1 and ts3 is smaller than ED between ts2 and ts3.

Euclidean distance is not the best similarity measure

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Similarity distance metrics I

● Euclidean distance

● Manhattan distance

● Minkowski distance

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Similarity distance metrics II

•Correlation distance

• Cov(X,Y) stands for covariance of X and Y

• degree to which two different variables are related

• Var(X) stands for variance of X

• measurement of a sample differ from their mean

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Similarity distance metrics III

• Variance

• Covariance

• Positive covariance

• two variables vary in the same way

• Negative covariance

• one variable might increase when the other decreases

• Covariance is only suitable for heterogeneous pairs 47

TS similarity measures ranking

Some papers focused on comparing the best dissimilarity

measures for time series. A remarkable one is that of Giusti,

R., & Batista, G. E. (2013) and its results is shown in Figure

1. Along this paper, all this measures are tested with a big

set of datasets.

In order to rank the best similarity measures 1-NN (Nearest

Neighbor) classification is used. 1-NN is a simple instance-

based classifier that depends heavily on the

similarity/dissimilarity measure employed. It is also

understood to be extremely competitive with more robust,

complex classification models.

Figure 1: Best Dissimilarity measures for Time series

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TRAINING SET

TESTING SET

K-NN algorithm

How can we calculate how good a new TSM is?

Time series most used similarity measures

● Most used similarity measures are Euclidean, DTW, Pearson, Spearman, and Cosine.

Minkowski, Mahalanobis and Manhattan distance are also very well-known measures.

● Some other interesting methods can be LCSS (Longest Common SubSequence) and the

EDR techniques (Edit distance with Real Penalty and Edit Distance on Real sequences).

● EDR has been shown to be robust in the presence of noise, time shifts, and data scaling

Morse, M. D., & Patel, J. M. (2007, June).

● SAX is a novel algorithm which due to its outstanding performance can be interesting to

test. Lin, J. et al. (2007).

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1.- Shape-based distances 2.- Feature-based distances

1.1.- Lock-step measures (Partial) Autocorrelation based

Lp distances Fourier Decomposition based

DISSIM TQuest

Short Time Series Distance (STS) Wavelet Decomposition based

Cross-correlation based (Integrated) Periodogram based

Pearson correlation based SAX representation based

CORT distance Spectral Density-based

1.2.- Elastic measures 3.- Structure-based distances

Frechet distance 3.1- Model-based

Dynamic Time Warping (DTW) Piccolo distance

Keogh_LB for DTW Maharaj distance

Edit Distance for Real Sequences (EDR) Cepstral based distances

Edit Distance with Real Penalty (ERP) 3.2.- Compression based

Longest Common Subsequence (LCSS) Compression based distances

Complexity invariant distance

Permutation distribution based distance

4.- Prediction based

Non-Parametric Forecast based

Time series similarity measures classification

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Dynamic Time Warping

Sakoe, Hiroaki, and Seibi Chiba. "Dynamic programming algorithm optimization for spoken word recognition." IEEE

transactions on acoustics, speech, and signal processing 26.1 (1978): 43-49. (5000 citations)

Dynamic time warping (DTW) is a well-known technique to find an optimal alignment

between two given (time-dependent) sequences under certain restrictions

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What is DTW versus Euclidean Distance?

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Dynamic Time Warping

Advantages

● The DTW distance takes into account (part of) the local temporal

correlations.

● No system identification step is needed.

● Lower bounds on the distance are reasonably efficient.

● This measure allows to calculate distances between time series

of different lengths.

Disadvantages

● There is no clear link between this distance measure and the

generating system.

● The DTW distance as such is expensive to calculate.

● This measure does not take the input into account.

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Symbolic Aggregate Approximation (SAX)

● SAX is the first symbolic representation for time series that allows for

dimensionality reduction and indexing with a lower-bounding distance measure.

In classic data mining tasks such as clustering, classification, index, etc.

● SAX is as good as well-known representations such as Discrete Wavelet

Transform (DWT) and Discrete Fourier Transform (DFT), while requiring less

storage space.

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Symbolic Aggregate Approximation (SAX)

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4.- Clustering approach

What is clustering?

Cluster analysis or clustering is the task of grouping a set of objects in such a way that objects in the same group (called a cluster) are more similar (in some sense or another) to each other than to those in other groups (clusters).

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• A clustering problem can be viewed as unsupervised classification.

• Clustering is appropriate when there is no a priori knowledge about the data.

• Finding the class labels and the number of classes directly from the data (in contrast to classification).

• More informally, finding natural groupings among objects.

When do we have to apply clustering?

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Organizing data into classes such that there is:● High intra-class similarity● Low inter-class similarity

Intraclass and interclass similarity

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Types of clustering:

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School EmployeesSimpson's Family MalesFemales

Clustering is subjective

What is a natural grouping among these objects?

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But at the same time... we can detect similarity.

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Two Types of Clustering

Hierarchical

• Partitional algorithms: Construct various partitions and then evaluate them by some criterion (we will see an example called BIRCH)• Hierarchical algorithms: Create a hierarchical decomposition of the set of objects using some criterion.

Partitional

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Hierarchical Clustering

• Produces a set of nested clusters organized as a hierarchical tree

• Can be visualized as a dendrogram, which is a tree-like diagram that records the sequences of merges or splits.

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Hierarchical Clustering

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Hierarchical clustering

• Advantages• They have good visualization

• Gives similarity distances between clusters

•Disadvantages• Not great performance

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Partitional algorithms (K-means):

The objective of K-means is simple: group similar data points together and discover underlying patterns. To achieve this objective, K-means looks for a fixed number (k) of clusters in a dataset.

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k-means

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Algorithm k-means

1. Decide on a value for k.

2. Initialize the k cluster centers (randomly, if necessary).

3. Decide the class memberships of the N objects by assigning them to the nearest cluster center.

4. Re-estimate the k cluster centers, by assuming the memberships found above are correct.

5. If none of the N objects changed membership in the last iteration, exit. Otherwise goto 3.

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Comments on the K-Means Method

Pros:• Relatively efficient• Often terminates at a local optimum.

Cons:• No applicable to categorical data• Need to specify the number of clusters• Unable to handle noisy data and outliers

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Time series k-means

Time series dendogram

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TIME SERIES & MACHINE LEARNING

PHD Luis Miralles