{
"cells": [
{
"cell_type": "markdown",
"metadata": {
"id": "_fBSLMzIdTDw"
},
"source": [
"## **Тьюториал \"Параллельные алгоритмы поиска аномалий во временных рядах\" на всероссийской научной конференции с международным участием [«Параллельные вычислительные технологии (ПаВТ) 2026»](https://xn--80ae1bo.xn--p1ai/2026/)**"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "P5K3XSANfdZl"
},
"source": [
"### **Часть 1. Введение в задачу поиска аномалий**"
]
},
{
"cell_type": "markdown",
"source": [
"##### **Задание 1.** Подготовка GPU-среды выполнения"
],
"metadata": {
"id": "3p9I6kXGIw4R"
}
},
{
"cell_type": "markdown",
"source": [
"Перед началом прохождения практической части тьюториала выполните подключение Google Диск для сохранения материалов тьюториала и полученных результатов, а также клонируйте [GitHub-репозиторий с материалами](https://github.com/KraevaYA/pct-tutorial-2026). Репозиторий будет склонирован непосредственно на Google Диск, что обеспечит постоянное хранение всех материалов. При последующих запусках достаточно будет перейти в эту директорию. Далее установите все необходимые зависимости."
],
"metadata": {
"id": "B7taeJYRF01i"
}
},
{
"cell_type": "code",
"source": [
"from google.colab import drive\n",
"drive.mount('/content/drive')\n",
"\n",
"!git clone https://github.com/KraevaYA/pct-tutorial-2026.git /content/drive/MyDrive/pct-tutorial-2026\n",
"%cd /content/drive/MyDrive/pct-tutorial-2026\n",
"\n",
"!pip install -r requirements.txt -q"
],
"metadata": {
"id": "BzV4XkmxEaBe"
},
"execution_count": null,
"outputs": []
},
{
"cell_type": "markdown",
"source": [
"Выполните настройку Numba для работы с CUDA и проверьте доступность GPU. Для этого выполните следующие команды:\n",
"* `config.CUDA_ENABLE_PYNVJITLINK = 1`: включает поддержку Just-In-Time компиляции для GPU, необходимую для выполнения ядер CUDA в Numba.\n",
"* `!nvidia-smi`: выводит информацию об установленном графическом процессоре, версии драйверов и CUDA.\n",
"* `!nvcc --version`: отображает версию компилятора CUDA, что подтверждает корректность установки инструментов разработки."
],
"metadata": {
"id": "9ciLYILOI0AD"
}
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"id": "MJGVRKk702lA"
},
"outputs": [],
"source": [
"from numba import config\n",
"config.CUDA_ENABLE_PYNVJITLINK = 1"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"collapsed": true,
"id": "MWCkzigMeFhu",
"outputId": "9da8135a-2e75-4f43-fa71-1109e9fb9077"
},
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"Sun Apr 5 05:59:40 2026 \n",
"+-----------------------------------------------------------------------------------------+\n",
"| NVIDIA-SMI 580.82.07 Driver Version: 580.82.07 CUDA Version: 13.0 |\n",
"+-----------------------------------------+------------------------+----------------------+\n",
"| GPU Name Persistence-M | Bus-Id Disp.A | Volatile Uncorr. ECC |\n",
"| Fan Temp Perf Pwr:Usage/Cap | Memory-Usage | GPU-Util Compute M. |\n",
"| | | MIG M. |\n",
"|=========================================+========================+======================|\n",
"| 0 Tesla T4 Off | 00000000:00:04.0 Off | 0 |\n",
"| N/A 57C P8 10W / 70W | 0MiB / 15360MiB | 0% Default |\n",
"| | | N/A |\n",
"+-----------------------------------------+------------------------+----------------------+\n",
"\n",
"+-----------------------------------------------------------------------------------------+\n",
"| Processes: |\n",
"| GPU GI CI PID Type Process name GPU Memory |\n",
"| ID ID Usage |\n",
"|=========================================================================================|\n",
"| No running processes found |\n",
"+-----------------------------------------------------------------------------------------+\n"
]
}
],
"source": [
"!nvidia-smi"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "OBYjcuGPeHlg",
"outputId": "c078b025-5606-4a99-853b-e7e85fd55c02"
},
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"nvcc: NVIDIA (R) Cuda compiler driver\n",
"Copyright (c) 2005-2025 NVIDIA Corporation\n",
"Built on Fri_Feb_21_20:23:50_PST_2025\n",
"Cuda compilation tools, release 12.8, V12.8.93\n",
"Build cuda_12.8.r12.8/compiler.35583870_0\n"
]
}
],
"source": [
"!nvcc --version"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "JmHOPTvYfA7Q"
},
"source": [
"Импортируйте необходимые библиотеки и модули."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"id": "QuLhOS5veJ2Q",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 17
},
"outputId": "e76739d3-fc28-4e78-d6f9-8de839b0c96f"
},
"outputs": [
{
"output_type": "display_data",
"data": {
"text/html": [
" \n",
" "
]
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],
"source": [
"import numpy as np\n",
"import pandas as pd\n",
"\n",
"from anomaly_detection.plots import *\n",
"from anomaly_detection.algorithms.serial import STOMP\n",
"from anomaly_detection.metrics import get_metrics"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "upssgD79o7vF"
},
"source": [
"В данном тьюториале для выполнения частей 1 и 2 в качестве данных будет использоваться временной ряд [NYC_Taxi](https://doi.org/10.1109/ICMLA.2015.141), который показывает среднечасовое количество пассажировов такси в течение 75 дней осенью 2014 года.\n",
"\n",
"Исходные данные хранятся в csv-файле *nyc_taxi.csv*, расположенном в директории *./datasets*. В каждой строке файла содержится следующая информация, разделенная `;` :\n",
"* временная метка в формате %d.%m.%y %H:%M, где %d — день месяца, %m — месяц, %y — две последние цифры года, а %H:%M — часы в 24-часовом формате и минуты;\n",
"* количество пассажиров, которые воспользовались такси в течение 30 минут, отсчитываемых c соответствующей временной метки;\n",
"* метка, принимающая значение 0 или 1. Если метка равна 1, то это показывает о начале некоторого нетипичного события, приводящего к появлению аномалии в данных.\n",
"\n",
"Согласно разметке, в данных имеется две аномалии.\n",
"\n",
"##### **Задание 2.** Загрузка и визуализация ряда NYC Taxi\n",
"\n",
"Загрузите временной ряд NYC_Taxi из файла *nyc_taxi.csv*, расположенного в директории *./datasets*. Для этого воспользуйтесь функцией `read_csv()` из библиотеки *pandas*. Настройте считывание файла таким образом, чтобы первый столбец использовался в качестве индекса, а первая строка – в качестве названия столбцов. После успешного считывания с помощью функции `to_datetime()` из *pandas* преобразуйте столбец с временными метками в объекты datetime, указав необходимый формат %d.%m.%y %H:%M."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"id": "Q49GBcD3oyJP"
},
"outputs": [],
"source": [
"ts_path = './datasets/nyc_taxi.csv'\n",
"\n",
"# INSERT YOUR CODE\n",
"ts = pd.read_csv(ts_path, index_col=0, header=0)\n",
"ts.index = pd.to_datetime(ts.index, format='%d.%m.%y %H:%M')"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "p3lT0t8oo4Sz"
},
"source": [
"Для просмотра временного ряда NYC_Taxi постройте двумерный график. Для этого вызовите функцию `plot_ts()` из модуля *plots.py*, передав ей в качестве аргументов значения временного ряда `ts['value']`, название графика (например, 'Time series NYC_Taxi'), названия вертикальной и горизонтальной осей (например, 'Time' и 'Passenger number' соответственно)."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 417
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"id": "gtEhko3BoyMI",
"outputId": "409b30bd-bad2-432d-b7e4-c760c11f4965"
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23718,
22936,
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23387,
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"text": "Time",
"font": {
"size": 22,
"color": "black"
}
},
"tickfont": {
"size": 18,
"color": "black"
},
"showgrid": false,
"linecolor": "#000",
"ticks": "outside",
"tickformat": "%Y-%m-%d %H:%M",
"linewidth": 2,
"tickwidth": 2
},
"yaxis": {
"title": {
"text": "Passenger number",
"font": {
"size": 22,
"color": "black"
}
},
"tickfont": {
"size": 18,
"color": "black"
},
"showgrid": false,
"linecolor": "#000",
"ticks": "outside",
"zeroline": false,
"linewidth": 2,
"tickwidth": 2
},
"title": {
"text": "Time series NYC_Taxi",
"font": {
"size": 24,
"color": "black"
}
},
"legend": {
"font": {
"size": 20,
"color": "black"
}
},
"plot_bgcolor": "rgba(0,0,0,0)",
"paper_bgcolor": "rgba(0,0,0,0)",
"width": 1500,
"height": 400
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"config": {
"plotlyServerURL": "https://plot.ly"
}
},
"text/html": [
""
]
},
"metadata": {}
}
],
"source": [
"# INSERT YOUR CODE\n",
"plot_ts(ts['value'], title=\"Time series NYC_Taxi\", x_label=\"Time\", y_label=\"Passenger number\")"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "e_gEUywylZV6"
},
"source": [
"Одним из вариантов решения задачи поиска диссонансов во временной ряде является вычисление матричного профиля ряда.\n",
"\n",
"**Матричным профилем ряда $T$** для длины подпоследовательности $m$ называется ряд $MP$, $i$-м элементом которого является расстояние между $i$-й подпоследовательностью ряда, имеющей длину $m$, и ее ближайшим соседом той же длины $m$:\n",
"\\begin{equation}\n",
" MP = \\{\\text{Dist}(T_{i,\\,m}, T_{j,\\,m})\\}_{i=1}^{n-m+1},\n",
" \\\\\n",
" {где} \\quad T_{j,\\,m}=\\arg \\min_{1\\leqslant q\\leqslant n-m+1} \\text{Dist}(T_{i,\\,m}, T_{q,\\,m}), \\quad |i-q| > m.\n",
"\\end{equation}\n",
"\n",
"Матричный профиль дает аналитику понимание свойств подпоследовательностей временного ряда через степень сходства этих подпоследовательностей со своими ближайшими соседями. Так, например, *локальные максимумы* матричного ряда соответствуют *аномалиям* (диссонансам) ряда.\n",
"\n",
"##### **Задание 3.** Поиск top-$k$ диссонансов\n",
"\n",
"Для поиска top-$k$ диссонансов на основе матричного профиля выполните следующие действия:\n",
"* Создайте экземпляр класса `STOMP`, передав в конструктор длину диссонанса `m` и количество диссонансов `top_k`, которые необходимо найти.\n",
"* Вызовите метод `predict()` у созданного экземпляра, передав ему значения временного ряда `ts['value'].values`.\n",
"\n",
"В качестве значений задайте `m = 96` и `top_k = 5`.\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true,
"id": "VKevcNh9j432"
},
"outputs": [],
"source": [
"# INSERT YOUR CODE\n",
"m = 96\n",
"top_k = 5\n",
"discords = {}\n",
"\n",
"stomp = STOMP(m, top_k=top_k)\n",
"discords = stomp.predict(ts['value'].values)"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "vlyXBwHooN6p"
},
"source": [
"В результате выполнения метода `predict()` будет возвращен словарь, содержащий следующее:\n",
"* `m` – длины найденных диссонансов;\n",
"* `indices` — индексы диссонансов (порядковые номера подпоследовательностей-диссонансов во временном ряде);\n",
"* `distances` — расстояния от диссонансов до их ближайших соседей;\n",
"* `nn_indices` — индексы ближайших соседей для каждого диссонанса;\n",
"* `mp` — матричный профиль ряда.\n",
"\n",
"Чтобы убедиться в этом, выполните вывод полученных результатов."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "SLIg7bs6_ilD",
"outputId": "23961296-b0ce-4f60-ae96-4782236eca5f"
},
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"{'m': [96, 96, 96, 96, 96],\n",
" 'indices': [np.int64(2689),\n",
" np.int64(2789),\n",
" np.int64(1452),\n",
" np.int64(531),\n",
" np.int64(3452)],\n",
" 'distances': [np.float64(5.862946432964089),\n",
" np.float64(4.618772721966986),\n",
" np.float64(4.241043745808476),\n",
" np.float64(2.3301960358957237),\n",
" np.float64(1.916386927268015)],\n",
" 'nn_indices': [484, 912, 1788, 867, 3116],\n",
" 'mp': array([0.69943062, 0.70114158, 0.70503142, ..., 0.93276591, 0.94483392,\n",
" 0.96234584])}"
]
},
"metadata": {},
"execution_count": 9
}
],
"source": [
"# INSERT YOUR CODE\n",
"discords"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "yeeKWysMj4JG"
},
"source": [
"Выполните визуализацию найденных top-$k$ диссонансов с помощью функции `plot_discords()` из модуля *plots.py*, передав временной ряд `ts`, результат выполнения алгоритма поиска диссонансов, полученный на предыдущем шаге, `discords` и флаг `is_detailed = True`, включающий детальный режим визуализации. При установке этого аргумента на графике будут дополнительно отображены верно найденные диссонансы (True Positive, TP), ложные срабатывания (False Positive, FP), пропущенные аномалии (False Negative, FN)."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 542
},
"id": "ZCnwl6HhkDwo",
"outputId": "c094c643-89b5-4c9e-833f-e39c969b2c43"
},
"outputs": [
{
"output_type": "display_data",
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21761,
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15670,
18411,
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"source": [
"# INSERT YOUR CODE\n",
"plot_discords(ts, discords, is_detailed=True)"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "nuDwgwULrRob"
},
"source": [
"**Выводы:**\n",
"\n",
"На верхнем графике представлен исходный временной ряд с отмеченными диссонансами, найденными алгоритмом. В среднем графике показан матричный профиль, содержащий расстояния от каждой подпоследовательности ряда до их ближайших соседей. Нижний график отображает истинную разметку, которая указывает на наличие двух аномалий в моменты времени 01.11.2014 19:00 и 27.11.2014 15:30. Эти аномалии объясняются двумя событиями в США:\n",
"1. переходом с летнего на зимнее время, осуществляемым ежегодно в первое воскресенье ноября и выпавшим в 2014 году на 2 ноября;\n",
"2. Днем благодарения, празднование которого ежегодно проводится в четвертый четверг ноября, и выпавшим в 2014 году на 27 ноября.\n",
"\n",
"Можно видеть, что алгоритм находит все истинные диссонансы, однако среди предсказанных диссонансов есть и три ложно-положительных, появившиеся в моменты времени 12.10.2014 01:30, 28.11.2014 02:30 и 11.12.2014 22:00. Несмотря на то, что данные диссонансы отмечены как FP, обнаружение их алгоритмом не является безосновательным:\n",
"* диссонанс (12.10.2014 01:30) можно связать с праздником Днем Колумба, отмечаемым ежегодно 12 октября в честь прибытия Х. Колумба в Америку 12 октября 1492;\n",
"* диссонанс (28.11.2014 02:30) можно связать с «Черной пятницей», днем массовых распродаж.\n",
"\n",
"Диссонанс 11.12.2014 22:00 остается необъясненным — возможно, ажиотаж перед рождественским праздником?\n",
"\n",
"Таким образом, можно сделать вывод о том, что алгоритм позволяет находить диссонансы, которые зрительно нельзя обнаружить."
]
},
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"cell_type": "markdown",
"metadata": {
"id": "oGtbvM4QeZcs"
},
"source": [
"### **Часть 2. Поиск диссонансов фиксированной длины**"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "Zz6YKgVnMysZ"
},
"source": [
"#### Последовательный алгоритм DRAG (Discord Range Aware Gathering)\n",
"\n",
"Однако сложность вычисления матричного профиля высока и составляет $O(n^2)$, где $n$ — длина ряда, что в случае больших временных рядов приводит к низкому быстродействию. Существуют более эффективные алгоритмы поиска диссонансов во временных рядах. К таким алгоритмам относят алгоритм [DRAG](https://doi.org/10.1109/ICDM.2007.61). DRAG основан на понятии диапазонного диссонанса. Под **диапазонным диссонансом** понимается подпоследовательность ряда длины $m$, ближайший сосед которой находится на расстоянии не менее наперед заданного порога $r$. Алгоритм DRAG включает две фазы: отбор и очистка кандидатов, на которых выполняется поиск потенциальных диссонансов и отбрасывание ложноположительных экземпляров соответственно.\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "bNlIEp6KPYMR"
},
"source": [
"##### **Задание 4.** Алгоритм DRAG (CPU)\n",
"\n",
"Выполните поиск диапазонных диссонансов во временном ряде NYC_Taxi с помощью алгоритма DRAG. Для этого создайте экземпляр класса `DRAG`, передав в конструктор следующие параметры:\n",
"* `m = 96` — длина диссонанса;\n",
"* `r = 1.85` — пороговое расстояние до ближайшего соседа.\n",
"\n",
"Затем вызовите метод `predict()` у созданного экземпляра, передав ему значения временного ряда `ts['value'].values.astype('float64')`."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 17
},
"id": "rd2ThdVMLK1K",
"outputId": "1e89443b-9365-4819-cc5c-1f0a4a6f11c9",
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"output_type": "display_data",
"data": {
"text/html": [
" \n",
" "
]
},
"metadata": {}
}
],
"source": [
"from anomaly_detection.algorithms.serial import DRAG\n",
"from anomaly_detection.experiments import Experiment"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"id": "_ObjyGY9SXK1"
},
"outputs": [],
"source": [
"# INSERT YOUR CODE\n",
"m = 96\n",
"r = 1.85\n",
"\n",
"drag = DRAG(m, r)\n",
"drag_discords = drag.predict(ts['value'].values.astype('float64'))"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "RL0ZboftSc7n"
},
"source": [
"В результате метод `predict()` вернет найденные диапазонные диссонансы. Далее выполните вывод полученных результатов."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"collapsed": true,
"id": "84d-V84RTpxr",
"outputId": "fedf7440-efa0-4a89-ab57-ad4c37ff1012"
},
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"{'m': [96, 96, 96, 96, 96],\n",
" 'indices': [np.int64(2689),\n",
" np.int64(2789),\n",
" np.int64(1452),\n",
" np.int64(531),\n",
" np.int64(3452)],\n",
" 'distances': [np.float64(5.8629464329641365),\n",
" np.float64(4.6187727219669785),\n",
" np.float64(4.241043745808521),\n",
" np.float64(2.330196035895792),\n",
" np.float64(1.9163869272679481)],\n",
" 'mp': array([-inf, -inf, -inf, ..., -inf, -inf, -inf])}"
]
},
"metadata": {},
"execution_count": 13
}
],
"source": [
"# INSERT YOUR CODE\n",
"drag_discords"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "sSfcWLrNku0w"
},
"source": [
"Постройте графики, визуализирующие найденные алгоритмом DRAG диссонансы, с помощью функции `plot_discords()` из модуля *plots.py*."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 542
},
"collapsed": true,
"id": "czobkvVlY59a",
"outputId": "7b00e5ed-99f3-4812-f835-807321245b47"
},
"outputs": [
{
"output_type": "display_data",
"data": {
"application/vnd.plotly.v1+json": {
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4152,
3319,
2432,
1968,
1769,
2018,
1933,
2240,
4305,
6719,
11392,
14960,
18975,
19602,
19572,
18772,
17757,
16706,
16601,
15673,
16929,
17435,
16953,
16417,
17022,
17540,
18417,
18698,
16193,
14544,
13864,
17041,
20434,
23029,
23711,
24817,
24933,
24002,
23651,
23764,
23224,
22020,
22214,
21446,
15974,
12484,
9130,
6693,
5333,
3820,
3065,
2511,
2299,
2318,
2125,
2484,
4358,
6790,
11660,
15780,
19516,
20307,
19954,
18254,
18010,
17206,
17213,
16691,
18259,
18151,
17555,
16944,
17728,
18074,
18993,
18695,
17191,
15023,
14164,
17004,
20361,
23633,
24661,
25754,
25671,
25156,
24961,
24938,
24851,
24683,
23411,
20599,
17147,
13602,
10452,
7836,
6040,
4981,
3613,
2923,
2632,
2912,
2577,
2921,
4679,
6693,
12140,
15534,
19974,
20533,
19988,
19239,
18788,
17934,
18048,
17415,
18292,
18506,
18180,
17401,
18973,
19361,
19722,
19572,
17500,
15213,
14457,
17736,
21319,
23270,
24892,
26555,
26743,
26376,
26311,
26179,
26774,
26449,
25459,
23927,
21851,
18756,
14990,
13865,
10263,
7873,
6480,
5094,
4217,
4289,
3640,
3376,
5145,
7144,
11739,
15197,
19716,
20851,
20463,
19658,
19287,
17986,
17776,
17735,
18716,
19032,
17702,
17023,
18352,
19791,
20131,
18645,
16572,
14736,
13731,
17166,
20392,
22838,
23791,
25914,
26355,
25656,
25449,
25448,
25823,
25813,
26407,
26898,
26587,
25257,
23717,
22541,
19773,
19652,
16294,
13968,
12000,
10432,
6402,
4443,
3481,
3971,
5191,
6434,
8435,
10255,
13847,
14970,
18403,
19338,
21107,
20821,
21854,
21813,
22250,
21450,
21271,
20595,
20863,
20262,
21024,
19141,
17903,
19903,
22820,
24243,
25880,
26756,
26593,
25248,
23934,
23401,
24145,
25308,
26284,
27136,
27099,
26610,
25400,
23992,
22359,
21054,
18812,
16584,
14204,
11990,
7092,
4311,
3844,
3796,
4755,
4491,
5559,
6959,
9127,
11015,
13961,
15445,
17923,
18438,
19592,
19733,
19766,
19809,
19242,
18990,
18676,
18037,
16660,
15948,
15261,
17141,
19085,
20188,
20512,
20723,
20415,
19483,
19008,
17958,
18341,
18181,
17069,
15057,
13867,
11544,
9016,
6739,
5420,
4584,
3787,
3018,
2667,
2981,
2756,
2712,
3798,
5117,
7727,
9655,
12109,
13484,
15506,
15325,
15924,
14830,
14907,
14796,
15699,
15705,
15880,
15693,
16643,
16929,
17698,
17429,
17248,
16219,
15918,
17780,
19414,
21594,
24915,
24556,
22341,
22343,
21619,
21315,
19821,
17669,
15504,
14525,
10738,
8908,
6593,
5560,
4014,
3046,
2349,
1876,
1691,
1941,
1850,
2318,
4337,
6669,
11585,
15170,
19136,
20085,
19758,
18842,
18530,
16617,
17458,
16359,
17483,
17600,
17552,
17058,
17658,
18319,
18818,
18735,
17254,
15022,
14365,
16300,
19687,
22620,
23309,
23636,
23752,
23095,
23108,
23221,
23581,
22249,
19533,
17226,
13935,
11429,
8486,
6484,
5093,
4018,
3218,
2536,
2219,
2171,
2268,
2437,
4569,
6862,
11924,
15860,
19821,
20508,
20540,
19590,
18480,
17330,
18508,
17354,
18552,
18241,
18475,
17939,
18398,
18875,
19559,
19133,
16816,
14757,
14470,
17800,
21127,
22269,
22819,
23582,
26273,
25338,
24021,
26163,
23839,
22608,
24886,
20128,
16180,
13302,
10509,
8241,
5536,
4664,
3460,
2799,
2730,
2801,
2511,
2670,
4767,
7096,
12556,
16431,
21581,
21355,
21573,
20390,
20452,
19678,
18801,
17223,
18249,
17691,
17052,
16783,
18392,
18593,
19364,
19176,
16795,
15293,
14922,
17899,
21758,
24169,
24615,
26370,
26990,
26168,
25449,
25994,
27115,
26191,
25146,
24371,
23771,
19268,
15623,
12595,
10224,
7941,
6678,
5182,
4502,
4316,
3512,
3174,
4771,
6557,
11929,
14950,
19835,
20149,
19998,
19310,
18601,
17567,
17890,
17470,
18557,
18944,
17922,
17627,
18361,
19557,
19811,
19277,
16741,
14948,
14244,
17563,
21246,
23115,
24785,
26396,
26837,
26621,
26144,
26019,
26816,
26701,
26519,
26740,
26173,
25059,
24437,
22718,
20700,
19623,
16675,
14447,
12377,
10609,
6436,
4562,
3783,
3923,
5060,
5992,
8639,
10309,
13563,
14136,
16945,
17004,
19045,
19859,
21198,
21550,
21583,
21455,
21869,
21426,
21650,
21611,
20904,
18820,
17255,
19029,
22812,
24455,
26373,
27460,
27222,
25204,
24329,
24526,
25203,
25975,
27073,
27881,
28626,
28093,
26200,
25610,
23483,
21850,
19297,
16574,
14355,
12112,
7284,
4845,
3667,
3718,
4573,
5167,
6844,
7279,
9761,
11712,
14210,
15394,
18387,
19168,
20891,
21806,
22188,
22153,
21713,
21838,
21082,
20448,
20113,
18645,
17210,
18326,
20498,
20924,
21579,
22026,
22197,
19709,
18780,
18060,
17973,
16572,
14957,
12461,
10448,
8295,
6837,
4747,
3283,
2904,
2345,
1917,
1783,
2174,
2157,
2989,
4841,
7228,
11726,
14557,
17848,
18436,
18059,
18028,
17353,
16350,
16376,
16099,
16817,
16898,
16809,
16199,
16758,
17679,
18148,
18644,
17183,
16196,
15534,
18451,
20950,
23192,
24655,
24094,
23285,
22083,
21485,
21579,
21118,
20204,
16909,
13785,
11695,
9214,
6931,
5413,
4130,
3276,
2475,
2080,
1917,
2123,
1984,
2458,
4338,
6470,
11775,
15088,
19429,
20482,
19886,
19170,
18277,
17064,
16386,
16633,
17681,
18233,
17996,
16695,
16912,
18124,
18411,
19013,
17590,
15673,
14923,
17981,
21208,
23458,
24028,
24934,
25135,
24613,
24617,
25841,
24141,
23069,
21243,
18077,
15745,
12115,
9035,
7015,
5113,
4220,
3331,
2870,
2516,
2656,
2336,
2494,
5081,
8091,
13037,
16579,
19657,
20914,
20612,
20015,
19001,
17533,
17877,
16470,
18266,
17992,
17419,
16775,
17378,
18067,
19841,
18552,
16825,
14712,
14439,
17305,
20949,
22182,
23886,
25234,
24731,
25195,
25551,
26110,
24842,
23178,
23408,
21749,
17918,
13496,
10416,
8090,
5946,
4330,
3282,
2732,
2524,
2700,
2290,
2743,
4732,
7570,
12751,
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20268,
21992,
21301,
20526,
19251,
18228,
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19645,
20453,
19400,
18448,
18199,
18845,
18973,
17968,
15112,
13580,
12751,
15901,
19774,
21960,
23790,
24998,
25414,
26075,
25616,
25916,
25589,
25041,
24891,
23888,
22464,
19061,
16689,
13006,
9512,
7745,
6037,
5194,
4419,
4267,
3366,
3096,
4532,
6877,
11826,
15333,
19013,
20131,
19779,
19227,
18824,
17705,
18111,
17408,
18509,
18510,
17910,
17690,
18149,
19632,
19426,
18760,
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15083,
14553,
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20911,
22958,
25257,
26659,
27104,
26439,
25840,
25694,
26093,
26821,
26870,
26889,
27283,
25739,
23889,
22278,
20337,
19179,
16566,
14146,
12015,
10285,
6316,
4106,
3465,
3657,
4756,
6003,
7853,
9091,
12209,
13433,
16768,
16390,
18666,
19740,
21266,
21452,
21613,
21773,
21440,
20362,
20601,
20989,
20210,
18243,
16875,
19078,
22244,
23703,
25544,
27125,
26539,
24964,
23665,
23200,
24238,
25202,
26140,
27417,
27692,
26866,
26254,
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22425,
20865,
18801,
16066,
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4661,
3656,
3780,
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4530,
6287,
7318,
9260,
10911,
14136,
15466,
18611,
18437,
20375,
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21283,
20200,
20135,
20306,
20404,
19931,
19772,
18406,
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17972,
19563,
20106,
20449,
19860,
19343,
18128,
17298,
16004,
16422,
14618,
13017,
11532,
10089,
8326,
6579,
4385,
3470,
2854,
2128,
1785,
1707,
2138,
2406,
2847,
4951,
7094,
11090,
14205,
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16086,
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16614,
16155,
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17617,
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20618,
22703,
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21778,
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15613,
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5589,
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4581,
6612,
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19422,
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16744,
17075,
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17421,
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17443,
17890,
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15175,
13958,
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19615,
22196,
22906,
23482,
23088,
23728,
23210,
23685,
23843,
22597,
20923,
19229,
15963,
12292,
9190,
6864,
5693,
4499,
3304,
2560,
2485,
2560,
2248,
2389,
4313,
6649,
11289,
15103,
19437,
19443,
19707,
18912,
18203,
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16837,
16075,
17160,
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17940,
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23582,
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25299,
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18631,
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5251,
3714,
3232,
3057,
3005,
2506,
2821,
5287,
7427,
12248,
15618,
19528,
19813,
19680,
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17899,
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18094,
18575,
18022,
17359,
18035,
18733,
19410,
18991,
16749,
14604,
13367,
16382,
19879,
21735,
23802,
24832,
24964,
25791,
25810,
25816,
25849,
24877,
25072,
24763,
22241,
19957,
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9119,
7589,
6221,
4936,
4796,
3555,
3337,
4665,
7084,
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20430,
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16981,
15045,
13978,
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20025,
21438,
23813,
25517,
25493,
25475,
26996,
27015,
27264,
26977,
26343,
26333,
26524,
25425,
24937,
24946,
23736,
23245,
21459,
19849,
17679,
15018,
10600,
7758,
5907,
5743,
6223,
6386,
9098,
9864,
12903,
14185,
18584,
19066,
22683,
23292,
24154,
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26625,
25584,
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22199,
20008,
18443,
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23719,
25241,
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28398,
27426,
26537,
25980,
24601,
24838,
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26567,
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25110,
23109,
39197,
35212,
13259,
12250,
10013,
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6375,
4532,
5116,
5232,
4542,
5298,
5155,
6029,
6280,
8771,
10151,
12501,
13990,
16534,
17133,
18775,
18985,
19911,
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19524,
19640,
18364,
17940,
17949,
17288,
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17522,
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20291,
21649,
22839,
21772,
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19774,
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17764,
17334,
15431,
12958,
10224,
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6045,
4413,
3235,
2688,
1983,
1756,
1683,
2140,
2288,
2948,
4813,
8044,
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14627,
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6005,
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2526,
2112,
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4413,
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22924,
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16314,
13917,
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21762,
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23705,
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23789,
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25613,
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11746,
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4008,
3263,
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4813,
7519,
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19945,
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16030,
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21778,
24460,
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27335,
26727,
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20748,
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14431,
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5942,
4063,
3498,
3726,
5242,
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13050,
13820,
17437,
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19999,
22047,
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1853,
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20734,
17540,
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10511,
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4622,
3785,
2970,
2332,
2166,
2179,
2040,
2278,
3860,
5517,
9569,
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15966,
15584,
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13003,
12213,
15103,
18301,
20626,
22533,
22905,
22181,
21899,
21789,
22253,
22515,
21410,
19812,
17135,
13567,
10829,
7850,
6572,
4748,
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3833,
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19843,
19031,
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18516,
17635,
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19090,
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18412,
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22745,
24219,
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23727,
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21926,
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17742,
21769,
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26029,
27266,
26817,
25049,
23713,
23324,
23970,
26325,
26139,
27312,
28114,
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22665,
21069,
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16590,
14414,
12228,
7230,
4624,
3594,
3332,
4083,
4416,
5214,
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21847,
21695,
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19230,
19883,
19768,
18931,
17936,
16360,
16885,
16000,
14902,
13707,
13406,
12021,
11115,
8317,
5887,
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3425,
2961,
2328,
2020,
1764,
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18436,
16099,
14985,
11612,
9828,
7529,
6162,
4296,
3090,
2366,
2094,
1831,
1987,
1936,
2346,
4328,
6935,
12642,
16037,
20032,
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20127,
19075,
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17581,
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17870,
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24831,
25564,
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24501,
24316,
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14466,
10771,
8100,
5976,
5000,
3727,
2984,
2584,
2591,
2253,
2489,
4419,
7014,
12470,
16549,
19879,
20437,
19549,
18639,
18683,
18486,
18014,
16720,
18570,
18309,
17294,
16699,
17819,
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21215,
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24623,
24564,
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23638,
21861,
21500,
19838,
16307,
12324,
10006,
8077,
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5091,
4247,
4440,
3089,
2930,
4782,
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20053,
20654,
21158,
19863,
18775,
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17986,
19070,
18901,
17585,
17309,
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18788,
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15945,
14181,
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22514,
24457,
26156,
26677,
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26370,
26344,
26736,
27093,
27569,
27064,
26220,
24289,
22849,
20731,
19081,
16573,
14188,
12213,
10145,
5902,
3983,
3556,
3651,
5153,
5379,
7174,
9070,
12114,
13665,
17463,
17209,
20299,
20255,
22981,
23368,
23444,
22610,
22258,
21160,
22960,
23007,
21145,
18440,
16028,
19101,
22361,
24256,
26410,
27377,
26255,
23977,
23565,
22703,
23078,
25755,
27028,
28126,
28472,
27424,
25493,
24876,
22639,
21013,
19100,
16662,
14489,
12023,
7069,
4453,
3483,
3479,
3968,
4092,
5877,
6845,
8283,
10231,
13189,
14458,
17284,
17800,
19509,
20547,
20211,
20041,
19619,
19947,
19844,
19088,
19237,
18316,
16996,
18134,
19633,
20204,
19810,
17925,
16938,
15096,
15539,
14806,
15035,
13285,
12090,
10552,
9136,
8106,
7020,
5562,
3917,
3592,
2637,
2031,
1900,
2172,
2008,
2546,
4409,
7269,
11863,
14244,
17238,
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17940,
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15319,
15867,
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16292,
16317,
16104,
16967,
17035,
17976,
18230,
16521,
14887,
13707,
16596,
18683,
20289,
21377,
21962,
21126,
20531,
19217,
19353,
19109,
18814,
17036,
14147,
11595,
10091,
7575,
5977,
4705,
3796,
2894,
2471,
2115,
2474,
2285,
2538,
4380,
6537,
11238,
14764,
18187,
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19188,
18398,
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16899,
17137,
16203,
17742,
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17866,
17548,
18306,
18577,
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18691,
15729,
13396,
11923,
14463,
17026,
19078,
20439,
20776,
20941,
20209,
19987,
19952,
19234,
18455,
18097,
17461,
16002,
13400,
10978,
8613,
6446,
5205,
4118,
3510,
3249,
3698,
3584,
3622,
4987,
7213,
10827,
14141,
16965,
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20227,
19602,
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19572,
18925,
17545,
15465,
14104,
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20113,
21015,
21580,
22501,
21159,
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18046,
18300,
18538,
17170,
17081,
15613,
13718,
13522,
11323,
10315,
8870,
8150,
7209,
6018,
5819,
5291,
4127,
3540,
3715,
4613,
5500,
5955,
6512,
7076,
7813,
8365,
9013,
9695,
11389,
12701,
13400,
13282,
13542,
13538,
13663,
13980,
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14614,
15255,
13560,
13120,
13273,
13334,
12930,
13683,
13682,
14106,
14088,
14417,
15187,
15280,
15654,
13989,
12592,
11811,
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7791,
6862,
5644,
4639,
3673,
2945,
2875,
2883,
2165,
1902,
2226,
2870,
4313,
4936,
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8850,
9864,
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11900,
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14045,
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20519,
20626,
21227,
22716,
21044,
18862,
18821,
18485,
18416,
19806,
19671,
19234,
17725,
16089,
14561,
13292,
12000,
10967,
9747,
8556,
8342,
7178,
4441,
2747,
2489,
2283,
3109,
3380,
4628,
5291,
7405,
9044,
11193,
12541,
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15551,
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18680,
19621,
19830,
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21554,
22678,
24055,
23418,
20196,
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19566,
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20686,
21659,
21154,
21170,
20149,
18555,
17768,
15608,
14966,
13074,
11332,
9965,
9167,
5520,
3812,
3123,
3103,
3777,
3699,
4968,
5630,
7422,
9123,
10981,
12227,
15247,
14970,
16912,
17420,
18336,
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18946,
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17670,
17941,
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16867,
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14083,
13714,
12119,
9904,
8970,
7706,
5494,
4249,
2891,
2632,
2192,
1648,
1639,
1913,
2142,
2909,
4587,
7235,
11448,
14106,
17184,
18306,
18746,
17914,
16699,
15681,
15210,
14532,
15985,
16226,
16000,
15641,
16373,
16830,
17470,
18131,
16870,
15192,
14453,
17382,
19815,
21750,
22217,
21813,
21536,
22541,
21329,
20165,
19498,
19355,
16691,
14387,
12101,
9805,
7121,
5019,
3822,
3268,
2261,
1853,
1722,
2077,
1988,
2296,
4537,
6661,
11901,
15501,
19573,
20896,
21051,
19670,
18654,
17108,
17553,
16232,
17534,
17697,
19165,
18916,
19543,
18570,
19043,
18343,
16666,
14050,
12845,
16111,
19112,
21205,
22337,
23340,
23082,
23718,
22936,
23466,
23387,
22893,
20923,
18684,
14962,
12558,
8876,
6626,
4926,
4046,
3168,
2692,
2237,
2384,
2109,
2403,
4250,
6529,
12185,
16016,
19504,
20925,
20891,
20047,
19138,
18431,
16960,
16426,
18092,
19190,
18957,
18288,
18843,
19003,
18193,
17260,
15103,
12941,
11797,
15545,
17938,
20693,
21585,
21689,
21995,
22096,
22115,
21860,
22041,
21680,
21378,
20295,
18176,
14846,
11480,
8939,
6679,
5175,
3800,
3135,
2671,
2843,
2476,
2670,
4521,
6841,
12178,
15916,
19872,
20957,
20358,
19717,
18943,
18082,
18560,
17316,
18817,
18439,
17771,
17214,
17836,
18676,
19241,
19068,
16567,
14529,
12862,
16086,
19221,
21408,
23385,
23604,
23384,
23209,
22592,
23164,
23638,
23192,
22417,
22630,
21278,
19300,
16241,
12966,
10322,
8160,
6611,
5410,
4453,
4287,
3250,
3396,
4846,
7090,
11832,
15506,
20211,
21053,
20635,
20128,
18838,
17936,
18210,
17653,
18847,
18814,
17478,
18029,
18953,
19684,
19747,
18464,
16396,
14436,
13461,
17047,
20614,
23322,
25791,
26650,
26971,
26688,
25508,
26284,
26978,
26983,
25438,
24914,
24165,
22925,
22187,
21493,
19021,
18009,
15786,
13114,
10541,
9296,
5388,
3578,
3205,
3427,
4666,
5262,
7841,
8786,
11893,
12849,
16411,
16917,
19706,
22924,
26224,
25548,
24376,
24464,
23825,
24235,
24001,
23877,
21761,
18277,
15670,
18411,
21332,
23306,
24856,
25798,
25274,
25158,
24164,
23771,
24363,
25705,
26429,
27272,
27636,
26695,
25626,
24285,
22249,
20741,
18554,
15770,
13976,
11368,
6531,
3929,
3236,
3177,
3757,
4042,
5401,
6483,
9264,
11497,
14585,
16159,
20205,
21146,
22387,
23081,
23163,
22660,
22127,
22237,
22193,
21252,
20818,
19110,
17255,
18368,
20327,
21411,
21379,
21735,
20031,
18305,
17961,
17334,
17401,
17020,
14661,
12367,
10891,
8141,
6411,
4762,
3616,
3130,
2273,
2031,
1788,
2203,
2270,
2727,
4686,
6827,
11984,
14644,
18338,
19590,
19762,
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18754,
17736,
17624,
16856,
18005,
18028,
17733,
17678,
18275,
18070,
19038,
18998,
16932,
15201,
14426,
16942,
19768,
21911,
22917,
23371,
23343,
22358,
22302,
22712,
22329,
21979,
19387,
17494,
13745,
11339,
8699,
6796,
5236,
3800,
3042,
2532,
2258,
2212,
2135,
2592,
4617,
8006,
13619,
16700,
19651,
20630,
21217,
19857,
18753,
17813,
17833,
17164,
18181,
17482,
15676,
16018,
17066,
17654,
17696,
16781,
14189,
12461,
12252,
15431,
18137,
20649,
21989,
22350,
22177,
22991,
22128,
23207,
23091,
22616,
21118,
19301,
16789,
14252,
10138,
7847,
5782,
4951,
3696,
2833,
2375,
2533,
2423,
2512,
4337,
6721,
11812,
16054,
19337,
21348,
21167,
20051,
18809,
17812,
17889,
17482,
18775,
18351,
17604,
17729,
17499,
17558,
18070,
17422,
14666,
12252,
11174,
13853,
16962,
19708,
20764,
21802,
22239,
22169,
23923,
24403,
24211,
23439,
23394,
21701,
19727,
17270,
13379,
10314,
7470,
6039,
4322,
3461,
2872,
2854,
2422,
2578,
4513,
6672,
12358,
15790,
19441,
20920,
20665,
19708,
20066,
18424,
18403,
17621,
18994,
18845,
17937,
17974,
18671,
19082,
20224,
18966,
16165,
14013,
12246,
15021,
18834,
21115,
22746,
23679,
23992,
23597,
23581,
24093,
24130,
24027,
23575,
22502,
22049,
20667,
19265,
16192,
12814,
10410,
8218,
6335,
5377,
4659,
3597,
3208,
4698,
6900,
12308,
15444,
19511,
20489,
20834,
19854,
18687,
18014,
18564,
18237,
18916,
18244,
16850,
17845,
18162,
19043,
19128,
18287,
15667,
13938,
12626,
15807,
19375,
21905,
24008,
25410,
25568,
24888,
25190,
25350,
25927,
26737,
26771,
26180,
25739,
24743,
24285,
22826,
21266,
19907,
17053,
14423,
12363,
10600,
6501,
4211,
3425,
3475,
5132,
4986,
7716,
8873,
12361,
13217,
17706,
19199,
21605,
22106,
23452,
24095,
24114,
24368,
23648,
22929,
22531,
21489,
19081,
15734,
13140,
15041,
17961,
20757,
22233,
23550,
24311,
24320,
23465,
24125,
24696,
24848,
25952,
26481,
26376,
26065,
25745,
24053,
22288,
21263,
18637,
16106,
13609,
11786,
6978,
4468,
3728,
3611,
3909,
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"##### **Задание 5.** Исследование влияния порога\n",
"\n",
"Проведите эксперимент по исследованию влияния порога $r$ на точность алгоритма DRAG, а также на количество найденных кандидатов и диссонансов на фазах отбора и очистки.\n",
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"\\begin{equation}\n",
" Precision = \\frac{TP}{TP+FP}; \\quad Recall=\\frac{TP}{TP+FN}; \\quad F1=2\\cdot\\frac{Precision\\cdot Recall}{Precision+Recall}, \\;\\; где\n",
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"Для проведение эксперимента создайте экземпляр класса `Experiment`, передав ему следующие параметры:\n",
"* `cpu_alg = DRAG` — используемый алгоритм;\n",
"* `fixed_params = {'m': 96}` — фиксированная длина диссонанса;\n",
"* `arying_params = {'r': np.arange(0.5, 5, 0.5)}` — порог $r$ от 0.5 до 5 с шагом 0.5;\n",
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"Запустите эксперимент методом `run()`, передав значения временного ряда и аннотацию истинных аномалий. Визуализируйте результаты с помощью метода `plot()`."
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CPU: Linux-6.6.113+-x86_64-with-glibc2.35",
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"exp1 = Experiment(cpu_alg=DRAG,\n",
" fixed_params={'m': 96},\n",
" varying_params={'r': np.arange(0.5, 5, 0.5)},\n",
" metrics=['phase_stats', 'accuracy'])\n",
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"**Выводы:**\n",
"\n",
"На первом графике представлена зависимость количества кандидатов (фаза отбора) и диссонансов (фаза очистки) от значения порога $r$. Видно, что при увеличении значения порога $r$, количество найденных кандидатов и диссонансов на фазах алгоритма DRAG уменьшается.\n",
"\n",
"На втором графике отображены метрики качества $Precision$, $Recall$ и $F1$ в зависимости от $r$. Можно заметить, что при слишком маленьких значениях порога $r$ (при $r=0.5$, $r=1.0$, $r=1.5$) алгоритм DRAG находит как истинные диссонансы (соответствующие указанным выше событиям в США), так и ложноположительные. Этот факт доказывается низкими показателями $Precision$ по сравнению с большими значениями $r$. Таким образом, чем меньше $r$, тем больше ложных диссонансов и тем меньше становится метрика $Precision$ (приближается к нулю).\n",
"\n",
"При слишком больших значениях порога $r$ (при $r=4.5$) алгоритм DRAG не находит все истинные диссонансы в исходном ряде. Наблюдается падение метрики $Recall$ в два раза относительно значений при меньших $r$.\n",
"\n",
"Тем самым, результат алгоритма DRAG критически зависит от подбора порога $r$. Неудачно подобранный порог может привести к избыточному количеству ложноположительных диссонансов, либо к пропуску истинных аномалий."
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"cell_type": "markdown",
"metadata": {
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"source": [
"Выполните визуализацию результатов работы алгоритма DRAG для трех различных значений порога $r$: маленького, оптимального и большого (например,\n",
"`r=1`, `r=3` и `r=4.5`). Для каждого значения создайте экземпляр класса `DRAG` с соответствующим параметром `r` (при фиксированном `m=96`), выполните поиск диссонансов методом `predict()`, затем постройте график с помощью функции `plot_discords()`из модуля `plots.py`."
]
},
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"id": "pYKVzKBQdPak",
"outputId": "cffe217c-55af-45a1-c04a-2b129d3f86a4"
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"for r in r_list:\n",
" drag = DRAG(m, r)\n",
" drag_discords = drag.predict(ts['value'].values.astype('float64'))\n",
" plot_discords(ts, drag_discords, is_detailed=True)"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "35ZR2bg5eSPJ"
},
"source": [
"#### Параллельный алгоритм PD3 (Parallel DRAG-based Discord Discovery)\n",
"\n",
"Параллельный алгоритм [PD3](https://doi.org/10.1134/S1054661823020062) для GPU основан на последовательном алгоритме [DRAG](https://doi.org/10.1109/ICDM.2007.61) Янкова и др. В отличие от исходного алгоритма, PD3 использует квадрат нормализованного евклидова расстояния в качестве метрики для ускорения вычислений. Кроме того, в алгоритм PD3 добавлена фаза предобработки, заключающаяся в параллельном вычислении средних значений и стандартных отклонений всех подпоследовательностей временного ряда. Результаты затем используются на фазах отбора и очистки кандидатов для вычисления расстояний между подпоследовательностями временного ряда. Каждая из этих фаз алгоритма распараллеливается отдельно на основе концепции параллелизма по данным и использования векторных структур данных."
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "ZfrPM7eROYjT"
},
"source": [
"##### **Задание 6.** Алгоритм PD3 (GPU)\n",
"\n",
"Выполните поиск диапазонных диссонансов во временном ряде NYC_Taxi с помощью алгоритма PD3. Для этого создайте экземпляр класса `PD3` из модуля *pd3.py*, передав в конструктор параметры `m = 96` и `r = 1.85` (аналогично алгоритму DRAG). Затем вызовите метод `predict()`, передав ему значения временного ряда `ts['value'].values.astype('float64')`."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"id": "D8hZTsErJmHJ"
},
"outputs": [],
"source": [
"from anomaly_detection.algorithms.parallel import PD3"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"collapsed": true,
"id": "oN2xv1-9JKlo",
"outputId": "5899770a-e6a0-4b7d-ee73-00ce19102866"
},
"outputs": [
{
"output_type": "stream",
"name": "stderr",
"text": [
"/usr/local/lib/python3.12/dist-packages/numba_cuda/numba/cuda/dispatcher.py:696: NumbaPerformanceWarning:\n",
"\n",
"Grid size 29 will likely result in GPU under-utilization due to low occupancy.\n",
"\n",
"/usr/local/lib/python3.12/dist-packages/numba_cuda/numba/cuda/dispatcher.py:696: NumbaPerformanceWarning:\n",
"\n",
"Grid size 7 will likely result in GPU under-utilization due to low occupancy.\n",
"\n",
"/usr/local/lib/python3.12/dist-packages/numba_cuda/numba/cuda/dispatcher.py:696: NumbaPerformanceWarning:\n",
"\n",
"Grid size 29 will likely result in GPU under-utilization due to low occupancy.\n",
"\n",
"/usr/local/lib/python3.12/dist-packages/numba_cuda/numba/cuda/dispatcher.py:696: NumbaPerformanceWarning:\n",
"\n",
"Grid size 7 will likely result in GPU under-utilization due to low occupancy.\n",
"\n"
]
}
],
"source": [
"# INSERT YOUR CODE\n",
"r = 1.85\n",
"m = 96\n",
"\n",
"pd3 = PD3(m, r)\n",
"pd3_discords = pd3.predict(ts['value'].values.astype('float64'))"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "-CbRcDKknly-"
},
"source": [
"Далее выведите полученные результаты на экран и выполните визуализацию найденных с помощью PD3 диссонансов с помощью функции `plot_discords()`."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "Y26XKijVecG_",
"outputId": "3fe5d01a-1cca-4e6e-cea8-2981db11fec0"
},
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"{'m': [96, 96, 96, 96, 96],\n",
" 'indices': [np.int64(2689),\n",
" np.int64(2789),\n",
" np.int64(1452),\n",
" np.int64(531),\n",
" np.int64(3452)],\n",
" 'distances': array([5.86298424, 4.61877001, 4.24106759, 2.33015487, 1.93751064]),\n",
" 'mp': array([-inf, -inf, -inf, ..., -inf, -inf, -inf], dtype=float32)}"
]
},
"metadata": {},
"execution_count": 19
}
],
"source": [
"pd3_discords"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 542
},
"id": "rriPap12nl7S",
"outputId": "61afaba6-a68f-4abb-eb27-d563707ee85d",
"collapsed": true
},
"outputs": [
{
"output_type": "display_data",
"data": {
"application/vnd.plotly.v1+json": {
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19841,
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18973,
17968,
15112,
13580,
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15901,
19774,
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23790,
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25916,
25589,
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22464,
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17705,
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19426,
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12015,
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6316,
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3465,
3657,
4756,
6003,
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9091,
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13433,
16768,
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19740,
21266,
21452,
21613,
21773,
21440,
20362,
20601,
20989,
20210,
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16875,
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25544,
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26539,
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23665,
23200,
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9260,
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19772,
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19563,
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16422,
14618,
13017,
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18022,
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20008,
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6280,
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12501,
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18364,
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17949,
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19774,
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3235,
2688,
1983,
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4813,
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23098,
23154,
22688,
22047,
21283,
21070,
19910,
20541,
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10667,
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6005,
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2526,
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4413,
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17318,
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17973,
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18445,
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22626,
22924,
22853,
22393,
23088,
22431,
22239,
19918,
17675,
14953,
12025,
8767,
6670,
5197,
4289,
3186,
2747,
2257,
2397,
2205,
2625,
4404,
7007,
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19651,
20630,
21217,
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CPU: Linux-6.6.113+-x86_64-with-glibc2.35,
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"source": [
"exp2 = Experiment(cpu_alg=DRAG, gpu_alg=PD3,\n",
" fixed_params={'m': 96},\n",
" varying_params={'r': np.arange(0.5, 5, 0.5)},\n",
" metrics=['time', 'speedup', 'phase_stats'])\n",
"results_exp2 = exp2.run(ts['value'].values.astype('float64'))\n",
"exp2.plot()"
]
},
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"metadata": {
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"source": [
"**Выводы:**\n",
"\n",
"Можно видеть, что параллельный алгоритм PD3 опережает последовательную версию DRAG как минимум на один порядок. При этом при увеличении параметра $r$ время выполнения обоих алгоритмов уменьшается. Это можно объяснить тем, что при увеличении порога отбрасывается больше кандидатов, что, в свою очередь, приводит к уменьшению времени, затрачиваемому на фазу очистки, и выполняется, в целом, меньше операций для вычисления расстояний между подпоследовательностями ряда."
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "Dah8dPfXeiLG"
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"source": [
"### **Часть 3. Поиск диссонансов произвольной длины**"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "GM3324k5QCky"
},
"source": [
"Несмотря на то, что алгоритмы DRAG и PD3 позволяют находить диапазонные диссонансы, они имеют два главных недостатка. Во-первых, необходимо вручную подбирать значение порога $r$. Во-вторых, необходимо задавать точную длину искомых диссонансов. На практике это может доставить трудности даже эксперту\n",
"в предметной области.\n",
"\n",
"Следовательно, возникает потребность в алгоритмах, способных выполнять поиск диссонансов для всех длин из заданного диапазона с возможностью адаптивного подбора порога. Для решения этой задачи были разработаны алгоритм MERLIN и его параллельная версия PALMAD, которые устраняют указанные ограничения."
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "tUbque-7el-Z"
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"source": [
"#### Последовательный алгоритм MERLIN\n",
"\n",
" Идея последовательного алгоритма [MERLIN](https://doi.org/10.1109/ICDM50108.2020.00147) заключается в многократном вызове алгоритма DRAG и адаптивном подборе параметра $r$ для каждой длины диссонанса $m$ из заданного диапазона $minL...maxL$. Подбор порога $r$ выполняется следующим образом:\n",
"1. для $m = minL$ значение порога устанавливается как $r=2\\sqrt{minL}$, поскольку это максимально возможное расстояние между любой парой подпоследовательностей длины $minL$;\n",
"2. для $m \\in [minL+1; minL+5)$ порог равен $r = 0.99 \\cdot nnDist_{m-1}$, где $nnDist_{m-1}$ – расстояние от диссонанса, полученного на предыдущем шаге, до его ближайшего соседа за вычетом небольшой величины в 1%;\n",
"2. для $m \\in [minL+5; maxL]$ порог равен $r = \\mu - 2\\sigma$, где $\\mu$ и $\\sigma$ вычисляются на основе расстояний от диссонансов до их ближайших соседей пяти предыдущих длин как:\n",
"\\begin{equation}\n",
"\\mu \\leftarrow \\mathrm{Mean}(\\{ nnDist_k\\}^{m - 5}_{k=m - 1}); \\quad\n",
" \\sigma \\leftarrow \\mathrm{StdDev}(\\{ nnDist_k\\}^{m - 5}_{k=m - 1}).\n",
"\\end{equation}\n"
]
},
{
"cell_type": "markdown",
"source": [
"Для выполнения части 3 тьюториала в качестве данных будет использоваться временной ряд PolyTER, который содержит показания беспроводного датчика температуры, снимавшиеся в течение 2018 года в одной из лекционных аудиторий кампуса Южно-Уральского государственного университета (ЮУрГУ) с периодичностью один раз в час. Свое название ряд получил от SCADA-системы PolyTER, установленной в ЮУрГУ. Эта система управляет теплоснабжением зданий университетского кампуса на основе анализа показаний проводных и беспроводных датчиков, установленных в помещениях ЮУрГУ.\n",
"\n",
"\n",
"Исходные данные хранятся в csv-файле *PolyTER_sensor_data_346.csv*, расположенном в директории *./datasets*. В каждой строке файла содержится следующая информация, разделенная ';' :\n",
"* временная метка в формате `%Y-%m-%d %H:%M:S%`, где `%Y` – год, `%m` – месяц, `%d` – день месяца, а `%H:%M:%S` – часы в 24-часовом формате, минуты и секунды;\n",
"* температура воздуха в аудитории.\n",
"\n",
"Разметка в данных отсутствует."
],
"metadata": {
"id": "EfDg05vLrjVX"
}
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"id": "IJcU29tZuYtp"
},
"outputs": [],
"source": [
"from anomaly_detection.algorithms.serial import MERLIN\n",
"from anomaly_detection.utils import select_topk_interest_discords, read_json_file"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "RrEvIsTS1NVn"
},
"source": [
"##### **Задание 8.** Загрузка и визуализация ряда PolyTER\n",
"\n",
"Загрузите временной ряд PolyTER из файла *./datasets/PolyTER_sensor_data_346.csv*. Для этого воспользуйтесь функцией `read_csv()` из библиотеки *pandas*. Настройте считывание файла таким образом, чтобы первый столбец использовался в качестве индекса, а первая строка – в качестве названия столбцов. После успешного считывания с помощью функции `to_datetime()` из *pandas* преобразуйте столбец с временными метками в объекты datetime, указав необходимый формат `%Y-%m-%d %H:%M:%S`. Далее выполните визуализацию ряда с помощью функции `plot_ts()` (как в задании 2 из части 1)."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"id": "67aASrmg1Mb3",
"collapsed": true
},
"outputs": [],
"source": [
"ts_path = './datasets/PolyTER_sensor_data_346.csv'\n",
"\n",
"# INSERT YOUR CODE\n",
"ts = pd.read_csv(ts_path, index_col=0, header=0)\n",
"ts.index = pd.to_datetime(ts.index, format='%Y-%m-%d %H:%M:%S')"
]
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"##### **Задание 9.** Алгоритм MERLIN (CPU)\n",
"\n",
"Выполните поиск top-$k$ диссонансов во временном ряде PolyTER с помощью алгоритма MERLIN. Для этого создайте экземпляр класса `MERLIN`, передав в конструктор левую границу диапазона длин диссонансов $minL$, правую границу $maxL$ и количество диссонансов $topK$. Затем вызовите метод `predict()`, передав ему значения временного ряда.\n",
"\n",
"Значения параметров алгоритма следующие:\n",
"* `minL = 60` — левая граница диапазона длин (2.5 суток);\n",
"* `maxL = 144` — правая граница диапазона длин (6 суток);\n",
"* `topK = 10` — количество искомых диссонансов каждой длины.\n",
"\n",
"**Важно!** Алгоритм MERLIN выполняется на временном ряде PolyTER значительно дольше допустимого времени работы тьюториала, поэтому запуск алгоритма на занятии не предусмотрен. Вместо этого используйте заранее сохраненные результаты, импортировав их из JSON-файла *./results/MERLIN_PolyTER_m_60_144_topK_10.json* с помощью функции `read_json_file()`, передав путь до этого файла."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
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"id": "TC7lToOwhq-Y"
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"source": [
"# INSERT YOUR CODE\n",
"#minL = 60\n",
"#maxL = 144\n",
"#topK = 10\n",
"\n",
"#merlin = MERLIN(minL, maxL, topK=topK)\n",
"#merlin_discords = merlin.predict(ts['value'].values.astype('float64'))\n",
"\n",
"merlin_discords = read_json_file('./results/MERLIN_PolyTER_m_60_144_topK_10.json')"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "yVh5YDlTuitI"
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"source": [
"Далее выполните поиск top-$k$ интересных диссонансов, незавимо от их длин. Будем считать, что диссонансы наиболее интересны и полезны те, которые обладают наибольшей степенью аномальности среди всех найденных на предыдущем шаге. Степень аномальности диссонанса вычисляется путем нормирования расстояния от диссонанса до его ближайшего соседа с помощью множителя $\\frac{1}{2m}$:\n",
"\\begin{equation}\n",
"score(m, i) = \\frac{T_{i, m}.nnDist}{2m}, \\quad score(m,i) \\in [0,1].\n",
"\\end{equation}\n",
"\n",
"Для получения top-$k$ интересных диссонансов вызовите функцию `select_topk_interest_discords()` из модуля *utils.py* и передайте в качестве аргументов полученные алгоритмом MERLIN результаты `merlin_discords` и количество интересных диссонансов `topK_interest = 10`."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"id": "f3kRa8JjdeT2"
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"outputs": [],
"source": [
"# INSERT YOUR CODE\n",
"topK_interest = 10\n",
"merlin_interest_discords = select_topk_interest_discords(merlin_discords, topK_interest)"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "pZxoggeI6D7n"
},
"source": [
"Выполните визуализацию найденных top-$k$ интересных диссонансов с помощью функции `plot_discords()` из *plots.py*, для которой установите флаг `is_detailed = False`, отключающий детальный режим визуализации (из-за отсутствия аннотации аномалий).\n"
]
},
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},
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"showgrid": false,
"linecolor": "#000",
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"linewidth": 2,
"tickwidth": 2
},
"xaxis2": {
"anchor": "y2",
"domain": [
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"linecolor": "#000",
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"font": {
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"color": "black"
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},
"plot_bgcolor": "rgba(0,0,0,0)",
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"source": [
"# INSERT YOUR CODE\n",
"plot_discords(ts['value'], merlin_interest_discords, False)"
]
},
{
"cell_type": "markdown",
"source": [
"**Вывод:**\n",
"\n",
"На основе визуализации top-10 диссонансов, найденных алгоритмом MERLIN во временном ряде PolyTER, можно дать следующую содержательную интерпретацию каждому из них.\n",
"\n",
"| Категория | Диссонансы | Описание |\n",
"|-----------|:------------:|:-----------:|\n",
"| **Неисправность датчика** | top‑1 (31 августа - 4 сентябрь),
top‑2 (20-26 октября),
top‑6 (30 июня – 6 июля) | Датчик выдает одинаковые показания
в течение соответствующего периода времени. |\n",
"| **Проветривание (открытые окна)** | top‑3 (1-7 декабря),
top‑5 (14-20 марта),
top‑9 (10-16 сентября),
top‑10 (4-10 февраля) | Резкие отклонения температуры,
вызванные естественной вентиляцией аудитории. |\n",
"| **Выходные дни** | top‑4 (14-20 ноября),
top‑7 (15-20 декабря),