Mapping vs EDA
Disclaimer: No I do not own any of the characters of Numb3rs. I just borrow them for fun.
Once again, the two brothers realise that they are not so different after all. But of course, Alan already knew that. COMPLETE.
This idea came to me after watching Trust metric. It's not quite the kind of thing I would usually write but I thought it would be a good exercise.
Reference to Assassin, Dark matter, Backscatter, the Janus list and Trust metric.
Charlie let out a sigh of relief when he drove his car into the driveway of the Craftsman house. He glanced tiredly at the clock on his dashboard: 3.10 am.
"God, I'm glad to be home. It took so much longer than I thought," he complained to Amita who was sitting next to him. They had spent the last past two days attending a seminar in Santa Barbara and had decided to go back to Pasadena instead of spending another night at the hotel.
"Don's here," Amita noticed, trying to stifle a yawn.
The black SUV was parked in front of the entrance and the lights were on in the living-room. Charlie stopped his car next to the suburban.
"Don't tell me he's still working at this time of the night? The guy never rests!" Charlie exclaimed as he turned the engine off.
Amita raised an eyebrow and glanced sideway with a little smirk. "Look who's talking. How many times have you fallen asleep on your computer or in the garage?" she commented as she unbuckled her belt and opened her door.
"Not the same," Charlie grumbled and got out of the Prius.
"No? Well you'll have to explain the difference one day."
They both headed to the porch and entered the house.
Charlie expected to find his brother watching a match of some kind on TV or reading a file but the room seemed empty despite the lights on: no noise, no movement. The couple walked into the living room and froze. The first thing they saw was about fifty files scattered everywhere on the floor. Pushing Amita behind him in a protective way, the professor moved carefully further into the room and froze again. A look of panic crossed his face, soon followed by relief and finally amusement. His brother was lying on the floor right in front of the sofa, fast asleep, holding a folder tightly against him. Charlie cocked his head to assess the situation: obviously, Don had originally been sitting on the floor against the couch as he worked before falling asleep and listing to his side to end up on the floor.
The mathematician watched him for a moment, half smiling. Suddenly, Don's hand slid slightly, letting a piece of paper and a pen fall on the floor. Without waking up, he wrapped his hand around the folder and pulled it more closely against him.
Noticing a sort of diagram on the paper that Don had let go, Amita crouched and carefully reached out to pick it up, making sure not to awake the agent.
"Charlie, look," she called out softly.
The professor craned his head to look over the young woman's shoulder. His eyebrows shot up as he saw the paper. "Wow. Let me see," he replied, eagerly taking it from her.
In the middle of the page, a box with a question mark was connected by arrows to a dozen other boxes. Each box contained the names of what seemed to be cases his brother was working on. Along each arrow, Don had written comments like "Days", "Vics", "MO", "Weapons". Some case names were written in several boxes and highlighted in yellow. Charlie turned to the files and compared their positions with the schema - it reflected exactly the way Don had placed them on the floor: it was anything but random.
His tiredness forgotten, Charlie knelt on the floor to pick up a couple of files to have a quick read-through. They related to robberies that had happened over the last past few weeks in LA. He knew Don had been working on them without much luck. In fact, the team wasn't even sure that they had been perpetrated by the same gang. The team except for Don, that was. From the very beginning, the agent had been certain there was a connection although they couldn't find any.
"What's going on in here?"
The couple jumped and whipped their heads around. They were so engrossed in Don's schema that they hadn't heard Alan come in. Quickly, Charlie gestured him to lower his voice and thumbed at the sofa with a smirk. Intrigued, Alan moved silently toward the couch and stopped short when he saw his eldest sprawled on the floor. His eyes widened in surprise then his expression turned into a frown. He was obviously not amused at all.
"What is wrong with your brother?" he asked, clearly upset. "Can't he sleep in a bed like any normal being? He doesn't even go for the couch now!"
"I don't think he planned on falling asleep, Dad," Charlie tried to explain.
"Yeah well, that's what happens when you work 24/7." The look Alan gave Charlie made it clear that the professor was also included in that remark. The older man walked over to Don to wake him up but Charlie pulled him back.
"Wait!" he whispered hurriedly. "Let me take a little photo-souvenir, just to see his face tomorrow morning," he explained as he took a couple of photos of his brother with his cell phone.
"I doubt if it affects him a lot," groaned the older man. He gestured to the files. "And what's all that mess about?"
"It's amazing Dad! Don did it!" Charlie's eyes were shining with excitement.
"Yeah, your brother can be quite good at messing things up but it's usually his love life, not his work. What's going on exactly?" he asked warily.
Charlie and Amita tugged Alan away from Don, who was starting to fidget in his sleep, obviously disturbed by the low voices around him. The younger Eppes showed his father the schema.
"Look Dad," Charlie started, excitedly. "Don made-"
"A mapping," Alan finished matter-of-factly. "I've seen him do that quite often. It's not new."
"Yes... okay... maybe." Charlie shook his head as to dismiss what his father had just said and put his hands together to give more weight to his words. "What is important here is the way he mapped the information, in this case, the files. He probably didn't realise it but he used an Exploratory Data Analysis."
Alan rubbed his ear and pursed his lips before glancing at his eldest. "Hmm... I think it's safe to assume that Don hasn't realised that."
They all turned around and stood still when Don started to stir, mumbled something then turned onto his side, face against the base of the couch, still holding his folder. Then suddenly, with a speed that surprised them all, he sat up letting the folder fall on the floor while his right hand went reaching for the gun hanging at his hip, startling the little group in the process. Don stopped short, his hand resting on his holster as he recognised the figures in front of him. Amita made a mental note to never take him by surprise – that would be way too dangerous. Don blinked, surprised and a little nervous to see the small group watching him warily, then ran his right hand in his hair before kneading his brow.
"What's going on?" he asked sleepily.
Alan was the first one to recover. "Apparently, Donnie, you created an Exploratory Data Analysis or ... something."
Don stared blankly for a couple of seconds then with one hand on the couch, pushed himself up and walked over to the group. It was only when he saw the piece of paper Charlie was still holding that he understood what they were talking about. "It's a mapping," he explained in a tired voice.
Charlie shook his head with force. "Not just any mapping, Don... Right, can you explain how you came to that analysis?" he asked expectantly.
Don frowned. He couldn't understand why his brother seemed so thrilled. "No analysis, Charlie. I was just trying to find a correlation between the robberies."
"And you found one?" Amita asked in anticipation.
Don squinted, trying to wake up but mainly trying to make sense of the situation. "Hmm, yeah... I found something interesting. I... " He stopped to yawn and rub his eyes.
"Don, focus!" Charlie pressed him. "How did you come to this result?"
Taken aback by the intensity in his brother's voice, the agent stared at him and Amita before looking questioningly at his father who shrugged with sympathy.
"Okay," he started to explain, a little self consciously. "I was sure that the same gang was behind most of these robberies so I decided to classify them according to the type of victims, locations, MOs, the kind of goods stolen, time of the robberies, number and description of the suspects, weapons used and so on. As the mapping shows: ten robberies targeted elderly people, eleven were on families with young children- meaning that the victims couldn't or wouldn't dare fight back, fifteen attacks happened mid-morning , twenty-two were committed by 3 or 4 armed robbers, eighteen were located in the valley, etc... Some robberies share several similarities of course. This one for example," He said, pointing at a file, "fits the location, the MO and the stolen goods, whereas that one matches the MO, the weapons, the stolen goods and the time of the attack, proving that there are connections between these robberies. There's definitely a pattern emerging and we should have enough information now to profile those guys and find out who they are. I'm planning to call... What?" he asked suddenly when he realised that Charlie and Amita were staring at him with wide eyes.
"You did all this during the night?" Amita finally asked, amazed.
Uncertain whether it was a good thing or not, Don nodded warily.
Charlie was getting more and more enthusiastic. "That's amazing! You even identified some anomalies," he commented, pointing at several files left aside.
"These cases don't match the others in any way so I'm confident to say that they have nothing to do with my investigation, that's all," Don explained calmly.
"That's all? Don!" Charlie was now pacing the room. Don still couldn't figure out if his brother was happy, excited or angry at him. And if he was angry, why? The professor turned around and asked suddenly.
"Why didn't you ask me to do it? I could've created an algorithm for this."
"I can't see when? You've just spent the last two days in a seminar and before that, you were requisitioned by the NSA to work on some secret project. We haven't seen you for almost two weeks."
"Hey! They didn't give me much choice. I would've preferred to work for you, believe, me," Charlie replied defensively.
Don closed his eyes briefly. He was tired and was starting to run out of patience. He sighed deeply to calm down before saying quietly, "Charlie, it wasn't a reproach. I'm not accusing you of anything here." He shook his head. "I don't get it. What's your problem? I just did a mapping. No big deal".
"You're right, I'm sorry... Actually no, it's not... I mean it is... a big deal."
Don blinked at him several times, trying to follow what his brother was talking about. He looked desperately at this father for support but the elderly man raised his hands to indicate his own puzzlement.
Before his brother could say something, Charlie added quickly, "You see, mapping information to find and categorise something is a well-known technique. What is far more unusual is your approach to the problem, the type of data you looked for and the way you processed it and mixed it. To do so, you used an Exploratory Data Analysis".
"Or EDA. It's an approach to analyzing data for the purpose of formulating a hypothesis worth testing," Amita started to explain calmly but Charlie was too excited to let her finish. After all, it was his brother they were talking about!
"In your case, the data you analysed is the specific pieces of information you took from the files, like the MOs or the type of victims, and the hypothesis you're testing is: have these robberies been perpetrated by the same gang?" Charlie shook his head admiringly. "And you did all that without the help of a computer! Of course, with one, it would've taken a couple of hours to sort this data..."
"Whereas it took me..." He glanced at his watch and groaned. "Way too long! Man, I started before diner." No wonder he was so tired.
The professor walked over to his brother to stand just in front of him. "Don, you're missing the point here. What I'm trying to say is that you processed the information in a mathematical way."
"Oh Charlie, don't get so worked up. It's pure coincidence."
"Maybe but after spending all these years watching your brother, I don't think it is, Don," Amita observed. "I mean, you are definitely a multi-level thinker and you have reacted several times now like a mathematician."
"True! Remember the shooting at the high school four years ago? The, uh, DMG case," the professor pointed at his brother. "And you're the one who saw the music notes that allowed us to decipher the Janus list."
"We didn't have to explain to you the dynamic adaptive system we applied to predict Colby's next move when he was on the run. You understood it as soon as you saw it," Amita added forcefully.
"You even found a flaw in our analysis when we only considered the stations and not the trains themselves!" Charlie finished even more excited, before stating as if talking to himself, "My big brother is becoming a mathematician."
Don held his hand up and shook his head in alarm. "Easy, Charlie, I wouldn't go that far."
Alan smiled at his two sons as he crossed his arms and leaned against the table. Evidently he was finding the whole situation highly entertaining. However, he felt he needed to put his thoughts in. "You two have always had very analytical minds but you use them in different ways. Charlie, you see everything in numbers, patterns and sequences. For you, everything has an explanation that can be turned into a mathematical formula. Your brother bases his analysis on facts, logic, his knowledge of human behavior and his instinct. You're both very rational, logical, quick thinkers and open minded, which allow you to think outside the box and to be adaptable to any situation. That's why you're both so good at what you do. And in a way, I believe that's why you get on so well today and are so successful in working together. As David once put it: "You might be very different but you're also very alike." Alan yawned widely and stood up. "Alright, now that we have established that I have two very smart sons who can use their heads in an intelligent way – although that's no newsflash, except for them maybe," he added, winking at Amita who smiled in response. "I suggest that we all go get some rest. Oh and Donny, I would appreciate if you could use your bed once in a while. The couch was already not a good idea but frankly sleeping on the floor is pushing things a bit too far. What are you trying to do? Train for bootcamp?"
"I didn't mean to fall asleep, Dad."
"Exactly what I said," Charlie intervened.
"Okay Genius, but I maintain that it wouldn't happen if you didn't overwork," Alan insisted, his eyes darting from one son to the other.
Charlie decided to ignore his father's remark and gently patted his brother's shoulder. "Impressive EDA, bro."
Don smiled back. "Thanks but I still call that mapping. It doesn't sound as impressive but it's as effective".
"Fair enough... By the way, there's something I'd like to show you." Charlie pulled his cell phone out of his pocket to display the pictures of Don sleeping on the floor. "Feeling a bit lonely so you had to hold on to a file to keep you company?" Charlie teased him.
Don shrugged dismissively. "What can I say? I've never been the Teddy Bear type."
Amita laughed and, sliding an arm tenderly around Charlie's waist, pushed him toward the stairs.
When Don started to move as if to head back to the living room, Alan frowned and grabbed his son's arm.
"Where are you going?" he asked suspiciously. He was not going back to work on his case, was he?
Don gestured toward the files on the floor. "Putting them away."
Alan tightened his hold on his son's arm. "Don, it's 3.30 in the morning. You're tired. Leave it. They'll still be there tomorrow. Come on," he ordered, pulling him away from the living room.
Don hesitated then, glancing at his father, realised he wouldn't win. He half-smiled and nodded before moving towards the stairs. Alan turned the lights off and followed his son.
Half an hour later, everybody was asleep - in a proper bed - to Alan's greatest satisfaction.
Feed-back always welcome!