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| 1 | +Diffusion |
| 2 | +========= |
| 3 | +The methods in this modules manage the treatment of the different score diffusion methods applied of/from an path set of |
| 4 | +labels/scores of/on a certain network (as a graph format or a graph kernel matrix stemming from a graph). |
| 5 | + |
| 6 | +Diffusion methods procedures provided in this package differ on: |
| 7 | +(a) How to distinguish positives, negatives and unlabelled examples. |
| 8 | +(b) Their statistical normalisation. |
| 9 | + |
| 10 | +Input scores can be specified in three formats: |
| 11 | +1. A named numeric vector, whereas if several of these vectors that share the node names need to be smoothed. |
| 12 | +2. A column-wise matrix. However, if the unlabelled entities are not the same from one case to another. |
| 13 | +2. A named list of such score matrices can be passed to this function. The path format will be kept in the output. |
| 14 | + |
| 15 | +If the path labels are not quantitative, i.e. positive(1), negative(0) and possibly unlabelled, all the scores raw, gm, |
| 16 | +ml, z, mc, ber_s, ber_p can be used. |
| 17 | + |
| 18 | +Methods |
| 19 | +------- |
| 20 | + |
| 21 | +Methods without statistical normalisation |
| 22 | +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
| 23 | +- **raw**: positive nodes introduce unitary flow {y_raw[i] = 1} to the network, whereas either negative and unlabelled |
| 24 | + nodes introduce null diffusion {y_raw[j] = 0}. [Vandin, 2011]. They are computed as: f_{raw} = K · y_{raw}. Where K is |
| 25 | + a graph kernel, see :doc:`kernel <kernel>`. These scores treat negative and unlabelled nodes equivalently. |
| 26 | + |
| 27 | +- **ml**: Same as raw, but negative nodes introduce a negative unit of flow. Therefore not equivalent to unlabelled |
| 28 | + nodes. [Zoidi, 2015] |
| 29 | + |
| 30 | +- **gl**: Same as ml, but the unlabelled nodes are assigned a (generally non-null) bias term based on the total number |
| 31 | + of positives, negatives and unlabelled nodes [Mostafavi, 2008]. |
| 32 | + |
| 33 | +- **ber_s**: A quantification of the relative change in the node score before and after the network smoothing. The score |
| 34 | + for a particular node i can be written as f_{ber_s}[i] = f_{raw}[i] / (y_{raw}[i] + eps). Where eps is a parameter |
| 35 | + controlling the importance of the relative change. |
| 36 | + |
| 37 | +Methods with statistical normalisation |
| 38 | +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
| 39 | +- **z**: a parametric alternative to the raw score of node is subtracted its mean value and divided by its standard |
| 40 | + deviation. Differential trait of this package. The statistical moments have a closed analytical form and are inspired |
| 41 | + in [Harchaoui, 2013]. |
| 42 | + |
| 43 | +- **mc**: the score of node code {i} is based on its empirical p-value, computed by permuting the path {n.perm} times. |
| 44 | + It is roughly the proportion of path permutations that led to a diffusion score as high or higher than the original |
| 45 | + diffusion score. |
| 46 | + |
| 47 | +- **ber_p**: A used in [Bersanelli, 2016], this score combines raw and mc, in order to take into account both the |
| 48 | + magnitude of the {raw} scores and the effect of the network topology: this is a quantification of the relative change |
| 49 | + in the node score before and after the network smoothing. |
| 50 | + |
| 51 | +Summary Table |
| 52 | +------------- |
| 53 | +| Scores | y+ | y- | yn | Normalized | Stochastic | Quantitative | Reference |
| 54 | +Unnormalized |
| 55 | +| raw | 1 | 0 | 0 | No | No | Yes | Vandin (2010) | |
| 56 | +
|
| 57 | +| ml | 1 | -1 | 0 | No | No | No | Tsuda (2010) | |
| 58 | +
|
| 59 | +| gm | 1 | -1 | k | No | No | No | Mostafavi (2008) | |
| 60 | +
|
| 61 | +| ber_s | 1 | 0 | 0 | No | No | Yes | Bersanelli (2016)| |
| 62 | +
|
| 63 | +Normalized |
| 64 | + |
| 65 | +| ber_p | 1 | 0 | 0* | Yes | Yes | Yes | Bersanelli (2016)| |
| 66 | +
|
| 67 | +| mc | 1 | 0 | 0* | Yes | Yes | Yes | Bersanelli (2016)| |
| 68 | +
|
| 69 | +| z | 1 | 0 | 0* | Yes | No | Yes | Harchaoui (2013) | |
| 70 | +
|
| 71 | + |
| 72 | +.. automodule:: diffupy.diffusion |
| 73 | + :members: |
| 74 | + |
| 75 | +.. automodule:: diffupy.diffusion_raw |
| 76 | + :members: |
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