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diff --git a/src/python/doc/perslay_params.md b/src/python/doc/perslay_params.md new file mode 100644 index 00000000..58537939 --- /dev/null +++ b/src/python/doc/perslay_params.md @@ -0,0 +1,95 @@ +PersLay parameters +------------------ + +In the following description of PersLay parameters, each parameter, or dictionary key, that contains `_init` in its name is optimized and learned by PersLay during training. If you do not want to optimize the vectorization, set the keys **train_vect** and **train_weight** to False. + +* The following keys are mandatory: + + layer + Either "PermutationEquivariant", "Image", "Landscape", "BettiCurve", "Entropy", "Exponential", "Rational" or "RationalHat". Type of the PersLay layer. "Image" is for `persistence images <https://arxiv.org/abs/1507.06217>`_, "Landscape" is for `persistence landscapes <http://www.jmlr.org/papers/volume16/bubenik15a/bubenik15a.pdf>`_, "Exponential", "Rational" and "RationalHat" are for `structure elements <http://jmlr.org/beta/papers/v20/18-358.html>`_, "PermutationEquivariant" is for the original DeepSet layer, defined in `this article <https://arxiv.org/abs/1703.06114>`_, "BettiCurve" is for `Betti curves <https://www.jstage.jst.go.jp/article/tjsai/32/3/32_D-G72/_pdf>`_ and "Entropy" is for `entropy <https://arxiv.org/abs/1803.08304>`_. + + perm_op + Either "sum", "mean", "max", "topk". Permutation invariant operation. + + keep + Number of top values to keep. Used only if **perm_op** is "topk". + + pweight + Either "power", "grid", "gmix" or None. Weight function to be applied on persistence diagram points. If "power", this function is a (trainable) coefficient times the distances to the diagonal of the points to a certain power. If "grid", this function is piecewise-constant and defined with pixel values of a grid. If "gmix", this function is defined as a mixture of Gaussians. If None, no weighting is applied. + + final_model + A Tensorflow / Keras model used to postprocess the persistence diagrams in each channel. Use "identity" if you don't want to postprocess. +* Depending on what **pweight** is, the following additional keys are requested: + + if **pweight** is "power": + - pweight_init + Initializer of the coefficient of the power weight function. It can be either a single value, or a random initializer from tensorflow, such as tensorflow.random_uniform_initializer(0., 1.). + - pweight_power + Integer used for exponentiating the distances to the diagonal of the persistence diagram points. + + if **pweight** is "grid": + - pweight_size + Grid size of the grid weight function. It is a tuple of integer values, such as (10,10). + - pweight_bnds + Grid boundaries of the grid weight function. It is a tuple containing two tuples, each containing the minimum and maximum values of each axis of the plane. Example: ((-0.01, 1.01), (-0.01, 1.01)). + - pweight_init + Initializer for the pixel values of the grid weight function. It can be either a numpy array of values, or a random initializer from tensorflow, such as tensorflow.random_uniform_initializer(0., 1.). + + if **pweight** is "gmix": + - pweight_num + Number of Gaussian functions of the mixture of Gaussians weight function. + - pweight_init + Initializer of the means and variances of the mixture of Gaussians weight function. It can be either a numpy array of values, or a random initializer from tensorflow, such as tensorflow.random_uniform_initializer(0., 1.). +* Depending on what **layer** is, the following additional keys are requested: + + if **layer** is "PermutationEquivariant": + - lpeq + Sequence of permutation equivariant operations, as defined in [the DeepSet article](). It is a list of tuples of the form (*dim*, *operation*). Each tuple defines a permutation equivariant function of dimension *dim* and second permutation operation *operation* (string, either "max", "min", "sum" or None). Second permutation operation is optional and is not applied if *operation* is set to None. Example: [(150, "max"), (75, None)]. + - lweight_init + Initializer for the weight matrices of the permutation equivariant operations. It can be either a numpy array of values, or a random initializer from tensorflow, such as tensorflow.random_uniform_initializer(0., 1.). + - lbias_init + Initializer for the biases of the permutation equivariant operations. It can be either a numpy array of values, or a random initializer from tensorflow, such as tensorflow.random_uniform_initializer(0., 1.). + - lgamma_init + Initializer for the Gamma matrices of the permutation equivariant operations. It can be either a numpy array of values, or a random initializer from tensorflow, such as tensorflow.random_uniform_initializer(0., 1.). + + if **layer** is "Image": + - image_size + Persistence image size. It is a tuple of integer values, such as (10,10). + - image_bnds + Persistence image boundaries. It is a tuple containing two tuples, each containing the minimum and maximum values of each axis of the plane. Example: ((-0.01, 1.01), (-0.01, 1.01)). + - lvariance_init + Initializer for the bandwidths of the Gaussian functions centered on the persistence image pixels. It can be either a single value, or a random initializer from tensorflow, such as tensorflow.random_uniform_initializer(0., 3.). + + if **layer** is "Landscape": + - lsample_num + Number of samples of the diagonal that will be evaluated on the persistence landscapes. + - lsample_init + Initializer of the samples of the diagonal. It can be either a numpy array of values, or a random initializer from tensorflow, such as tensorflow.random_uniform_initializer(0., 1.). + + if **layer** is "BettiCurve": + - lsample_num + Number of samples of the diagonal that will be evaluated on the Betti curves. + - lsample_init + Initializer of the samples of the diagonal. It can be either a numpy array of values, or a random initializer from tensorflow, such as tensorflow.random_uniform_initializer(0., 1.). + - theta + Sigmoid parameter used for approximating the piecewise constant functions associated to the persistence diagram points. + + if **layer** is "Entropy": + - lsample_num + Number of samples on the diagonal that will be evaluated on the persistence entropies. + - lsample_init + Initializer of the samples of the diagonal. It can be either a numpy array of values, or a random initializer from tensorflow, such as tensorflow.random_uniform_initializer(0., 1.). + - theta + Sigmoid parameter used for approximating the piecewise constant functions associated to the persistence diagram points. + + if **layer** is "Exponential": + - lnum + Number of exponential structure elements that will be evaluated on the persistence diagram points. + - lmean_init + Initializer of the means of the exponential structure elements. It can be either a numpy array of values, or a random initializer from tensorflow, such as tensorflow.random_uniform_initializer(0., 1.). + - lvariance_init + Initializer of the bandwidths of the exponential structure elements. It can be either a numpy array of values, or a random initializer from tensorflow, such as tensorflow.random_uniform_initializer(3., 3.). + + if **layer** is "Rational": + - lnum + Number of rational structure elements that will be evaluated on the persistence diagram points. + - lmean_init + Initializer of the means of the rational structure elements. It can be either a numpy array of values, or a random initializer from tensorflow, such as tensorflow.random_uniform_initializer(0., 1.). + - lvariance_init + Initializer of the bandwidths of the rational structure elements. It can be either a numpy array of values, or a random initializer from tensorflow, such as tensorflow.random_uniform_initializer(3., 3.). + - lalpha_init + Initializer of the exponents of the rational structure elements. It can be either a numpy array of values, or a random initializer from tensorflow, such as tensorflow.random_uniform_initializer(3., 3.). + + if **layer** is "RationalHat": + - lnum + Number of rational hat structure elements that will be evaluated on the persistence diagram points. + - lmean_init + Initializer of the means of the rational hat structure elements. It can be either a numpy array of values, or a random initializer from tensorflow, such as tensorflow.random_uniform_initializer(0., 1.). + - lr_init + Initializer of the threshold of the rational hat structure elements. It can be either a numpy array of values, or a random initializer from tensorflow, such as tensorflow.random_uniform_initializer(3., 3.). + - q + Norm parameter. |