delay-variant-embed

Analysis code for "Topological time-series analysis with delay-variant embedding" manuscript.

Preprint at https://arxiv.org/abs/1803.00208

Authors:

• Quoc Hoan Tran: [email protected]
• Yoshihiko Hasegawa: [email protected]

Hasegawa Lab, Department of Information and Communication Engineering, Graduate School of Information Science and Technology, The University of Tokyo

Compute three-dimensional persistence diagrams and persistence kernels for time-series data

Compile by Visual Studio 2015

Download ph-compute folder and launch DelayVariantTopo\TopolologyAnalysis.sln

Release/PersistenceRunner_D64.exe

Calculate persistence diagrams from point clouds.

Options:
    --nthreads : number of threads using for multi-processing (-1 for all possible threads)
    --modulus  : coefficient in the prime field Z/<p>Z to compute homology
    --maxdim   : maximum holes dimension to compute homology
    --thres    : maximum diameter to construct Rips complex
    --format   : format of the input (point-cloud, lower-distance, upper-distance, distance, dipha)
    --outdir   : directory for the output
    --input    : input file or file contains list of input files
    --multi    : compute single input file (0) or multi files in one input file  (1) 
    --help     : print usage option

Example: (see more at ph-compute\DelayVariantTopo\run-compute-persistent.bat)

Release\PersistentRunner_D64.exe --nthreads 16 --maxdim 1 --format point-cloud --outdir output --input data\pcl_1.txt --multi 0

Release\PersistentRunner_D64.exe --nthreads -1 --maxdim 1 --format point-cloud --outdir output --input data\pcl_list.txt --multi 1

Notice that the core C++ code for this module is derived from Ripser, which is also available under an MIT license and copyright to Ulrich Baeur.

Bauer, Ulrich. "Ripser: a lean C++ code for the computation of Vietoris–Rips persistence barcodes." 
Software available at https ://github. com/Ripser/ripser (2017).

Release/TimeSeriesRunner_D64.exe

Calculate 3-dimensional persistence diagrams for time-series data via delay-variant embedding.

Options:
    --nthreads : number of threads using for multi-processing (-1 for all possible threads)
    --emd      : embedded dimension for delay-variant embedding
    --modulus  : coefficient in the prime field Z/<p>Z to compute homology
    --maxdim   : maximum holes dimension to compute homology
    --thres    : maximum diameter to construct Rips complex
    --outdir   : directory for the output
    --input    : input time-series file or folder
    --multi    : compute single series (0) or multi series in one input file  (1) 
    --taumax   : compute up to maximum value of tau
    --npoints  : embed up to number of points, default=0, normal delay embedding
    --scale    : downsampling scale for time series, default=1
    --nskip    : skip a number of time series
    --help     : print usage option

Example of time-series data for input (csv format):

0.0099134,0.033429,-0.0057636,-0.029279,-0.052795,0.0099134,-0.021441,-0.029279,-0.060633,-0.091987
-0.013602,-0.060633,-0.013602,-0.07631,-0.060633,-0.12334,-0.084149,-0.068472,-0.037118,-0.07631
-0.060633,-0.12334,-0.060633,-0.091987,-0.068472,-0.10766,-0.099826,-0.14686,-0.029279,0.0099134

For multi mode (multi=1), the programm will process one line as one time series (see more at timeseries/ECGFiveDays/run-compute-delay-PH.bat).

Release/DiagramDistanceRunner_D64.exe

Calculate kernel for 3-dimensional persistence diagrams.

Options:
    --timehold : parameter sigmal in the kernel (=0 for optimal value)
    --timetau  : ratio of xi vs. sigmal in the kernel
    --left     : (left) input as list of barcodes
    --right    : (right) input as list of barcodes
    --dim      : dimension of holes to compute kernel
    --skipinf  : skip holes which have infinity death-scale (default=True)
    --infval   : replace infinity death-scales with a default value
    --thres    : threshold to skip holes with death-birth < thres (default=0 to use all holes)
    --output   : output filename for gram matrix
    --posfix   : posfix for output file
    --method   : method to compute kernel
                 0: L2_inner_multi_sse, 1: L2_squared_distance, 
                 2: Slice Wasserstein, 3:L2_inner_multi_nosse, 4:riemmannian_metric
    --theta_ndirs   : number of direction in wasserstein slice distance for theta
    --phi_ndirs     : number of direction in wasserstein slice distance for phi
    --alltau   : use all tau (True), or single tau (False)
    --opttau   : specify single tau (enable if alltau=0)
                 if opttau > 0  -> calculate single-delay kernel with tau=opttau
                 if opttau <= 0 -> calculate single-delay kernel with tau specified in barcode list file
    --help     : print usage option

Example of list of barcodes for input (see more at timeseries/ECGFiveDays/run-compute-kernel.bat):

ph(m=5,s=1)/delay_barcode_ECGFiveDays_time_series_0_dim_1.txt;tau=8
ph(m=5,s=1)/delay_barcode_ECGFiveDays_time_series_1_dim_1.txt;tau=9
ph(m=5,s=1)/delay_barcode_ECGFiveDays_time_series_2_dim_1.txt;tau=6
ph(m=5,s=1)/delay_barcode_ECGFiveDays_time_series_3_dim_1.txt;tau=9
ph(m=5,s=1)/delay_barcode_ECGFiveDays_time_series_4_dim_1.txt;tau=7
ph(m=5,s=1)/delay_barcode_ECGFiveDays_time_series_5_dim_1.txt;tau=9
ph(m=5,s=1)/delay_barcode_ECGFiveDays_time_series_6_dim_1.txt;tau=8
ph(m=5,s=1)/delay_barcode_ECGFiveDays_time_series_7_dim_1.txt;tau=16
ph(m=5,s=1)/delay_barcode_ECGFiveDays_time_series_8_dim_1.txt;tau=7
ph(m=5,s=1)/delay_barcode_ECGFiveDays_time_series_9_dim_1.txt;tau=3
ph(m=5,s=1)/delay_barcode_ECGFiveDays_time_series_10_dim_1.txt;tau=13