Mining and Processing Biomedical Data

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Presentation transcript:

Mining and Processing Biomedical Data Dr. rer. nat. Krisztian Buza adiunkt naukowy Faculty of Mathematics, Informatics and Mechanics University of Warsaw, Poland chrisbuza@yahoo.com

Preprocessing Time Series

Time Series Sequence of numbers: 10, 12, 13 … Example: observation of the temperature 6:00 am – 10 ºC 7:00 am – 12 ºC 8:00 am – 13 ºC 9:00 am – 15 ºC ...

Multivariate Time Series Electrocardiograph (ECG) and Electroencephalograph (EEG) signals Several values (observations) at each point of time Excerpt from the publicly available EEG database at https://archive.ics.uci.edu/ml/datasets/EEG+Database Time point Senor 1 Sensor 2 Sensor 3 Sensor 4 Sensor 5 ... 1 -8.921 0.834 -19.847 8.148 -2.146 2 -8.433 3.276 -12.522 1.801 3 -2.574 5.717 1.149 -2.594 -1.658 4 5.239 7.67 14.821 -4.547 -0.682 5 11.587 9.623 20.681 -5.035 2.248 Image: http://en.wikipedia.org/wiki/File:EEG_cap.jpg

Nearest Neighbor Classification of Time Series How to compare two time series?

Nearest Neighbor Classification of Time Series How to compare two time series? Compare the values one by one: first time series: -1.34 -2 3.5 1.7 ... second time series: 0.32 -1.5 2.8 0.9 ...

Nearest Neighbor Classification of Time Series How to compare two time series? Compare the values one by one: first time series: -1.34 -2 3.5 1.7 ... second time series: 0.32 -1.5 2.8 0.9 ...

Nearest Neighbor Classification of Time Series How to compare two time series? Compare the values one by one: first time series: -1.34 -2 3.5 1.7 ... second time series: 0.32 -1.5 2.8 0.9 ...

Nearest Neighbor Classification of Time Series How to compare two time series? Compare the values one by one: first time series: -1.34 -2 3.5 1.7 ... second time series: 0.32 -1.5 2.8 0.9 ... Problems with this simple approach What if time series are of different length? Shiftings and elongations, i.e., patterns reflecting real-world phenomena may have various length and may begin at (slightly) different position of the time-series Noise

Preprocessing of Time Series Fourier transformation Aggregation of consequitve values Transformation to a symbolic representation Moving average Normalisation ...

Aggregation of consequtive values Time series: 1.0, 1.2, 1.3, 1.7, 1.7, 1.8, 1.8, 1.9, 1.9, 2.0, 2.1 2.2 … Aggregated time-series: 1.63 , 2.4 , ... (Average of the first 10 values) (Average of the next 10 values)

Aggregation of consequtive values Time series: 1.0, 1.2, 1.3, 1.7, 1.7, 1.8, 1.8, 1.9, 1.9, 2.0, 2.1 2.2 … Aggregated time-series: 1.63 , 2.4 , ... Symbolic representation B , C , ... (Average of the first 10 values) (Average of the next 10 values) 0..1 1..2 2..3 ... A B C

Moving Average Time series: Transformed time-series: 1.38 1.0, 1.2, 1.3, 1.7, 1.7, 1.8, 1.8, 1.9, 1.9, 2.0, 2.1 2.2 … Transformed time-series: 1.38 (Average of the first 5 values)

Moving Average Time series: Transformed time-series: 1.38, 1.54, 1.0, 1.2, 1.3, 1.7, 1.7, 1.8, 1.8, 1.9, 1.9, 2.0, 2.1 2.2 … Transformed time-series: 1.38, 1.54,

Moving Average Time series: Transformed time-series: 1.38, 1.54, ... 1.0, 1.2, 1.3, 1.7, 1.7, 1.8, 1.8, 1.9, 1.9, 2.0, 2.1 2.2 … Transformed time-series: 1.38, 1.54, ...

Normalisation Time series: 1.0, 1.2, 1.3, 1.7, 1.7, 1.8, 1.8, 1.9, 1.9, 2.0, 2.1 2.2 … Average of all the values: 3.2 Standard deviation of all the values: 1.5 Normalised time-series: -1.46, -1.33, -1.26 ... (1.0 – 3.2) / 1.5 = -1.46

Dynamic Time Warping (DTW)

Proximity measures for time series Similarity measures and distance measure Similarity measure High value → two time series are similar Low value → two time series are different Distance measure High value → two time series are different (dissimilar) Low value → two time series are similar Dynamic Time Warping (DTW) is a distance measure

Example x*: 0, 0, 0, 1, 3, 0, -2, -1, 0, 0, 0 x1: 0, 0, 2, 4, 1, -1, 0, 0, 0, 0, 0 x2: 0, 1, 2, 1, 0, 1, 2, 1, 0, 1, 2 x* x1 x2

Dynamic Time Warping

Dynamic Time Warping

Dynamic Time Warping

Dynamic Time Warping |3-1| + 1 = 3

Dynamic Time Warping For example, for this entry, we record that the yellow entry had the minimum out of the three entries that were considered while filling-in this entry.