Measuring the diversity of recommendations: a preference-aware approach for evaluating and adjusting

• 概
• RMSDE
• 代码

Meymandpour R. and Davis J. G. Measuring the diversity of recommendations: a preference-aware approach for evaluating and adjusting diversity. Knowledge and Information Systems, vol. 62, pp. 787-811, 2020.

概

本文介绍了一种强调 '一致性' 的多样性指标.

RMSDE

• 以往的多样性指标往往是:
  \[\text{Diveristy}(I) = \frac{2}{n \times (n - 1)} \sum_{\forall i \in I}\sum_{j\not=i \in I} \text{Dissimilarity}(i, j), \]
  其中 \(n\) 为 推荐列表 \(I\) 的大小. \(\text{Dissimilarity}(i, j) \in [0, 1]\) 衡量了两个 item 间的不相似度.
  o
• 本文提出的 RMSDE 如下:
  \[\text{RMSDE} = \sqrt{\frac{1}{|T|}\sum_{u \in T} (\text{Diversity}(I(u)) - \text{Diversity}(R(u)))^2}. \]
  其中 \(I(u)\) 是用户 \(u\) 之前历史交互过的 items, \(R(u)\) 是我们接下来推荐的 items. RMSDE 越小说明推荐列表的 diversity 和用户实际的偏好越一致. 该指标的意义在于刻画了不同用户的多样性的需求, 很自然地, 并非所有的用户都是那么愿意探索的.

代码

from typing import Callable, Iterable

import numpy as np


def diversity(items: np.ndarray, sim_mat: np.ndarray):
    x, y = np.meshgrid(items, items)
    x = np.ravel(x)
    y = np.ravel(y)
    indices = np.stack((x, y), axis=1)
    diversity = 1 - sim_mat[indices]
    return np.mean(diversity)


def MSDE(previous: Iterable[np.ndarray], predicts: Iterable[np.ndarray], sim_mat: np.ndarray):
    r"""
    Parameters:
    -----------
    previous: Iterable[np.ndarray]
        Historical interactions.
    predicts: Iterable[np.ndarray]
        Predicted interactions.
    sim_mat: np.ndarray, (M, M)
        Matrix for similarity.
    """
    def calc_sde(prev, pred):
        div_prev = diversity(prev, sim_mat)
        div_pred = diversity(pred, sim_mat)
        return (div_prev - div_pred) ** 2
    results = list(map(calc_sde, previous, predicts))
    return np.mean(results)